Markovian Monte Carlo program EvolFMC v.2 for solving QCD evolution equations
NASA Astrophysics Data System (ADS)
Jadach, S.; Płaczek, W.; Skrzypek, M.; Stokłosa, P.
2010-02-01
We present the program EvolFMC v.2 that solves the evolution equations in QCD for the parton momentum distributions by means of the Monte Carlo technique based on the Markovian process. The program solves the DGLAP-type evolution as well as modified-DGLAP ones. In both cases the evolution can be performed in the LO or NLO approximation. The quarks are treated as massless. The overall technical precision of the code has been established at 5×10. This way, for the first time ever, we demonstrate that with the Monte Carlo method one can solve the evolution equations with precision comparable to the other numerical methods. New version program summaryProgram title: EvolFMC v.2 Catalogue identifier: AEFN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including binary test data, etc.: 66 456 (7407 lines of C++ code) No. of bytes in distributed program, including test data, etc.: 412 752 Distribution format: tar.gz Programming language: C++ Computer: PC, Mac Operating system: Linux, Mac OS X RAM: Less than 256 MB Classification: 11.5 External routines: ROOT ( http://root.cern.ch/drupal/) Nature of problem: Solution of the QCD evolution equations for the parton momentum distributions of the DGLAP- and modified-DGLAP-type in the LO and NLO approximations. Solution method: Monte Carlo simulation of the Markovian process of a multiple emission of partons. Restrictions:Limited to the case of massless partons. Implemented in the LO and NLO approximations only. Weighted events only. Unusual features: Modified-DGLAP evolutions included up to the NLO level. Additional comments: Technical precision established at 5×10. Running time: For the 10 6 events at 100 GeV: DGLAP NLO: 27s; C-type modified DGLAP NLO: 150s (MacBook Pro with Mac OS X v.10
NASA Astrophysics Data System (ADS)
These are the proceedings of the QCD Evolution 2015 Workshop which was held 26-30 May, 2015 at Jefferson Lab, Newport News, Virginia, USA. The workshop is a continuation of a series of workshops held during four consecutive years 2011, 2012, 2013 at Jefferson Lab, and in 2014 in Santa Fe, NM. With the rapid developments in our understanding of the evolution of parton distributions including low-x, TMDs, GPDs, higher-twist correlation functions, and the associated progress in perturbative QCD, lattice QCD and effective field theory techniques we look forward with great enthusiasm to the 2015 meeting. A special attention was also paid to participation of experimentalists as the topics discussed are of immediate importance for the JLab 12 experimental program and a future Electron Ion Collider.
Archeology and evolution of QCD
NASA Astrophysics Data System (ADS)
De Rújula, A.
2017-03-01
These are excerpts from the closing talk at the "XIIth Conference on Quark Confinement and the Hadron Spectrum", which took place last Summer in Thessaloniki -an excellent place to enjoy an interest in archeology. A more complete personal view of the early days of QCD and the rest of the Standard Model is given in [1]. Here I discuss a few of the points which -to my judgement- illustrate well the QCD evolution (in time), both from a scientific and a sociological point of view.
NASA Astrophysics Data System (ADS)
Gay Ducati, M. B.
The dynamics of the partonic distribution is a main concern in high energy physics, once it provides the initial condition for the Heavy Ion colliders. The determination of the evolution equation which drives the partonic behavior is subject of great interest since is connected to the observables. This lecture aims to present a brief review of the evolution equations that describe the partonic dynamics at high energies. First the linear evolution equations (DGLAP and BFKL) are presented. Then, the formulations developed to deal with the high density effects, which originate the non-linear evolution equations (GLR, AGL, BK, JIMWLK) are discussed, as well as an example of related phenomenology.
Equation of State from Lattice QCD Calculations
Gupta, Rajan
2011-01-01
We provide a status report on the calculation of the Equation of State (EoS) of QCD at finite temperature using lattice QCD. Most of the discussion will focus on comparison of recent results obtained by the HotQCD and Wuppertal-Budapest collaborations. We will show that very significant progress has been made towards obtaining high precision results over the temperature range of T = 150-700 MeV. The various sources of systematic uncertainties will be discussed and the differences between the two calculations highlighted. Our final conclusion is that these lattice results of EoS are precise enough to be used in the phenomenological analysis of heavy ion experiments at RHIC and LHC.
Dyson-Schwinger equations : density, temperature and continuum strong QCD.
Roberts, C. D.; Schmidt, S. M.; Physics
2000-01-01
Continuum strong QCD is the application of models and continuum quantum field theory to the study of phenomena in hadronic physics, which includes; e.g., the spectrum of QCD bound states and their interactions; and the transition to, and properties of, a quark gluon plasma. We provide a contemporary perspective, couched primarily in terms of the Dyson-Schwinger equations but also making comparisons with other approaches and models. Our discourse provides a practitioners' guide to features of the Dyson-Schwinger equations [such as confinement and dynamical chiral symmetry breaking] and canvasses phenomenological applications to light meson and baryon properties in cold, sparse QCD. These provide the foundation for an extension to hot, dense QCD, which is probed via the introduction of the intensive thermodynamic variables: chemical potential and temperature. We describe order parameters whose evolution signals deconfinement and chiral symmetry restoration, and chronicle their use in demarcating the quark gluon plasma phase boundary and characterizing the plasma's properties. Hadron traits change in an equilibrated plasma. We exemplify this and discuss putative signals of the effects. Finally, since plasma formation is not an equilibrium process, we discuss recent developments in kinetic theory and its application to describing the evolution from a relativistic heavy ion collision to an equilibrated quark gluon plasma.
QCDNUM: Fast QCD evolution and convolution
NASA Astrophysics Data System (ADS)
Botje, M.
2011-02-01
The QCDNUM program numerically solves the evolution equations for parton densities and fragmentation functions in perturbative QCD. Un-polarised parton densities can be evolved up to next-to-next-to-leading order in powers of the strong coupling constant, while polarised densities or fragmentation functions can be evolved up to next-to-leading order. Other types of evolution can be accessed by feeding alternative sets of evolution kernels into the program. A versatile convolution engine provides tools to compute parton luminosities, cross-sections in hadron-hadron scattering, and deep inelastic structure functions in the zero-mass scheme or in generalised mass schemes. Input to these calculations are either the QCDNUM evolved densities, or those read in from an external parton density repository. Included in the software distribution are packages to calculate zero-mass structure functions in un-polarised deep inelastic scattering, and heavy flavour contributions to these structure functions in the fixed flavour number scheme. Program summaryProgram title: QCDNUM version: 17.00 Catalogue identifier: AEHV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHV_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU Public Licence No. of lines in distributed program, including test data, etc.: 45 736 No. of bytes in distributed program, including test data, etc.: 911 569 Distribution format: tar.gz Programming language: Fortran-77 Computer: All Operating system: All RAM: Typically 3 Mbytes Classification: 11.5 Nature of problem: Evolution of the strong coupling constant and parton densities, up to next-to-next-to-leading order in perturbative QCD. Computation of observable quantities by Mellin convolution of the evolved densities with partonic cross-sections. Solution method: Parametrisation of the parton densities as linear or quadratic splines on a discrete grid, and evolution of the spline
R evolution: Improving perturbative QCD
Hoang, Andre H.; Jain, Ambar; Stewart, Iain W.; Scimemi, Ignazio
2010-07-01
Perturbative QCD results in the MS scheme can be dramatically improved by switching to a scheme that accounts for the dominant power law dependence on the factorization scale in the operator product expansion. We introduce the ''MSR scheme'' which achieves this in a Lorentz and gauge invariant way and has a very simple relation to MS. Results in MSR depend on a cutoff parameter R, in addition to the {mu} of MS. R variations can be used to independently estimate (i.) the size of power corrections, and (ii.) higher-order perturbative corrections (much like {mu} in MS). We give two examples at three-loop order, the ratio of mass splittings in the B*-B and D*-D systems, and the Ellis-Jaffe sum rule as a function of momentum transfer Q in deep inelastic scattering. Comparing to data, the perturbative MSR results work well even for Q{approx}1 GeV, and power corrections are reduced compared to MS.
Phenomenological QCD equations of state for neutron stars
NASA Astrophysics Data System (ADS)
Kojo, Toru; Powell, Philip D.; Song, Yifan; Baym, Gordon
2016-12-01
We delineate the properties of QCD matter at baryon density nB = 1 - 10n0 (n0: nuclear saturation density), through the construction of neutron star equations of state that satisfy the neutron star mass-radius constraints as well as physical conditions on the speed of sound. The QCD matter is described in the 3-window modeling: at nB ≲ 2n0 purely nuclear matter; at nB ≳ 5n0 percolated quark matter; and at 2n0 ≲nB ≲ 5n0 matter intermediate between these two which are constructed by interpolation. Using a schematic quark model with effective interactions inspired from hadron and nuclear physics, we analyze the strength of interactions necessary to describe observed neutron star properties. Our finding is that the interactions should remain as strong as in the QCD vacuum, indicating that gluons at nB = 1 - 10n0 remain non-perturbative even after quark matter formation.
Vertex Sensitivity in the Schwinger-Dyson Equations of QCD
David J. Wilson, Michael R. Pennington
2012-01-01
The nonperturbative gluon and ghost propagators in Landau gauge QCD are obtained using the Schwinger-Dyson equation approach. The propagator equations are solved in Euclidean space using Landau gauge with a range of vertex inputs. Initially we solve for the ghost alone, using a model gluon input, which leads us to favour a finite ghost dressing in the nonperturbative region. In order to then solve the gluon and ghost equations simultaneously, we find that non-trivial vertices are required, particularly for the gluon propagator in the small momentum limit. We focus on the properties of a number vertices and how these differences influence the final solutions. The self-consistent solutions we obtain are all qualitatively similar and contain a mass-like term in the gluon propagator dressing in agreement with related studies, supporting the long-held proposal of Cornwall.
Hot QCD equations of state and relativistic heavy ion collisions
NASA Astrophysics Data System (ADS)
Chandra, Vinod; Kumar, Ravindra; Ravishankar, V.
2007-11-01
We study two recently proposed equations of state obtained from high-temperature QCD and show how they can be adapted to use them for making predictions for relativistic heavy ion collisions. The method involves extracting equilibrium distribution functions for quarks and gluons from the equation of state (EOS), which in turn will allow a determination of the transport and other bulk properties of the quark gluon-plasma. Simultaneously, the method also yields a quasiparticle description of interacting quarks and gluons. The first EOS is perturbative in the QCD coupling constant and has contributions of O(g5). The second EOS is an improvement over the first, with contributions up to O[g6ln(1/g)]; it incorporates the nonperturbative hard thermal contributions. The interaction effects are shown to be captured entirely by the effective chemical potentials for the gluons and the quarks, in both cases. The chemical potential is seen to be highly sensitive to the EOS. As an application, we determine the screening lengths, which are, indeed, the most important diagnostics for QGP. The screening lengths are seen to behave drastically differently depending on the EOS considered and therefore yield a way to distinguish the two equations of state in heavy ion collisions.
Equation of state for cold and dense heavy QCD
NASA Astrophysics Data System (ADS)
Glesaaen, Jonas; Neuman, Mathias; Philipsen, Owe
2016-03-01
A previously derived three-dimensional effective lattice theory describing the thermodynamics of QCD with heavy quarks in the cold and dense region is extended through order ˜ u 5 κ 8 in the combined character and hopping expansion of the original four-dimensional Wilson action. The systematics of the effective theory is investigated to determine its range of validity in parameter space. We demonstrate the severe cut-off effects due to lattice saturation, which afflict any lattice results at finite baryon density independent of the sign problem or the quality of effective theories, and which have to be removed by continuum extrapolation. We then show how the effective theory can be solved analytically by means of a linked cluster expansion, which is completely unaffected by the sign problem, in quantitative agreement with numerical simulations. As an application, we compute the cold nuclear equation of state of heavy QCD. Our continuum extrapolated result is consistent with a polytropic equation of state for non-relativistic fermions.
Hydrodynamical Evolution near the QCD Critical End Point
NASA Astrophysics Data System (ADS)
Nonaka, Chiho; Asakawa, Masayuki
2003-10-01
Recently, the possibility of the existence of a critical end point (CEP) in the QCD phase diagram has attracted a lot of attention and several experimental signatures have been proposed for it^1. Berdnikov and Rajagopal discussed the growth of the correlation length near the critical end point in heavy-ion collision from the schematic argument^2. However, there has seen, so far, no quantitative study on the hydrodynamic evolution near CEP. Here we quantitatively evaluate the effect of the critical end point on the observables using the hydrodynamical model. First, we construct an equation of state (EOS) that includes critical behavior of CEP. Here we assume that the singular part of EOS near CEP belongs to the same universality class as the 3-d Ising model. Then we match the singular part of EOS with known QGP and hadronic EOS. We found the strong focusing effect near the critical end point in n_B/s trajectories in T-μ plane. This behavior is very different from an EOS of Bag model which is used in usual hydrodynamical models. This suggests that the effect of CEP appears strongly in the time evolution of system and the experimental observables. Next we investigate the time evolution and the behavior of correlation length near CEP along n_B/s trajectories. In addition, we also discuss the consequences of CEP in experimental results such as fluctuations and the kinetic freeze-out temperature. ^1M. Stephanov, K. Rajagopal, and E. Shuryak, Phys. Rev. Lett. 81 (1998) 4816. ^2B. Berdnikov and K. Rajagopal, Phys. Rev. D61 (2000) 105017.
The QCD equation of state with charm quarks from lattice QCD
NASA Astrophysics Data System (ADS)
Cheng, Michael
Recently, there have been several calculations of the QCD equation of state (EoS) on the lattice. These calculations take into account the two light quarks and the strange quark, but have ignored the effects of the charm quark, assuming that the charm mass (mc ≈ 1300 MeV) is exponentially suppressed at the temperatures which are explored. However, future heavy ion collisions, such as those planned at the LHC, may well probe temperature regimes where the charm quarks play an important role in the dynamics of the QGP. We present a calculation of the charm quark contribution to the QCD EoS using p4-improved staggered fermions at Nt = 4, 6, 8. This calculation is done with a quenched charm quark, i.e. the relevant operators are measured using a valence charm quark mass on a 2+1 flavor gauge field background. The charm quark masses are determined by calculating charmonium masses (metac and mJ/Psi) and fixing these mesons to their physical masses. The interaction measure, pressure, energy density, and entropy density are calculated. We find that the charm contribution makes a significant contribution, even down to temperatures as low as the pseudo-critical temperature, Tc. However, there are significant scaling corrections at the lattice spacings that we use, preventing a reliable continuum extrapolation.
Mode decomposition evolution equations
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2011-01-01
Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be
QCD equation of state to O (μB6) from lattice QCD
NASA Astrophysics Data System (ADS)
Bazavov, A.; Ding, H.-T.; Hegde, P.; Kaczmarek, O.; Karsch, F.; Laermann, E.; Maezawa, Y.; Mukherjee, Swagato; Ohno, H.; Petreczky, P.; Sandmeyer, H.; Steinbrecher, P.; Schmidt, C.; Sharma, S.; Soeldner, W.; Wagner, M.
2017-03-01
We calculated the QCD equation of state using Taylor expansions that include contributions from up to sixth order in the baryon, strangeness and electric charge chemical potentials. Calculations have been performed with the Highly Improved Staggered Quark action in the temperature range T ∈[135 MeV ,330 MeV ] using up to four different sets of lattice cutoffs corresponding to lattices of size Nσ3×Nτ with aspect ratio Nσ/Nτ=4 and Nτ=6 - 16 . The strange quark mass is tuned to its physical value, and we use two strange to light quark mass ratios ms/ml=20 and 27, which in the continuum limit correspond to a pion mass of about 160 and 140 MeV, respectively. Sixth-order results for Taylor expansion coefficients are used to estimate truncation errors of the fourth-order expansion. We show that truncation errors are small for baryon chemical potentials less then twice the temperature (μB≤2 T ). The fourth-order equation of state thus is suitable for the modeling of dense matter created in heavy ion collisions with center-of-mass energies down to √{sN N}˜12 GeV . We provide a parametrization of basic thermodynamic quantities that can be readily used in hydrodynamic simulation codes. The results on up to sixth-order expansion coefficients of bulk thermodynamics are used for the calculation of lines of constant pressure, energy and entropy densities in the T -μB plane and are compared with the crossover line for the QCD chiral transition as well as with experimental results on freeze-out parameters in heavy ion collisions. These coefficients also provide estimates for the location of a possible critical point. We argue that results on sixth-order expansion coefficients disfavor the existence of a critical point in the QCD phase diagram for μB/T ≤2 and T /Tc(μB=0 )>0.9 .
NASA Astrophysics Data System (ADS)
Brodsky, Stanley J.; de Téramond, Guy F.; Deur, Alexandre; Dosch, Hans Günter
2015-09-01
The valence Fock-state wavefunctions of the light-front (LF) QCD Hamiltonian satisfy a relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to LF Hamiltonian theory, the potential U has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic LF quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. The corresponding LF Dirac equation provides a dynamical and spectroscopic model of nucleons. The same LF equations arise from the holographic mapping of the soft-wall model modification of AdS5 space with a unique dilaton profile to QCD (3+1) at fixed LF time. LF holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of Anti-de Sitter (AdS) space and the boost-invariant LFWFs describing the internal structure of hadrons in physical space-time. We also show how the mass scale underlying confinement and the masses of light-quark hadrons determines the scale controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the LF and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The data for the effective coupling defined from the Bjorken sum rule are remarkably consistent with the
BFKL equation with running QCD coupling and HERA data
NASA Astrophysics Data System (ADS)
Levin, Eugene; Potashnikova, Irina
2014-02-01
In this paper we developed approach based on the BFKL evolution in ln( Q 2). We show that the simplest diffusion approximation with running QCD coupling is able to describe the HERA experimental data on the deep inelastic structure function with good χ2 /d .o .f . ≈ 1 .3. From our description of the experimental data we learned several lessons; (i) the non-perturbative physics at long distances started to show up at Q 2 = 0 .25 GeV2; (ii) the scattering amplitude at Q 2 = 0 .25 GeV2 cannot be written as sum of soft Pomeron and the secondary Reggeon but the Pomeron interactions should be taken into account; (iii) the Pomeron interactions can be reduced to the enhanced diagrams and, therefore, we do not see any needs for the shadowing corrections at HERA energies; and (iv) we demonstrated that the shadowing correction could be sizable at higher than HERA energies without any contradiction with our initial conditions.
Effects of QCD equation of state on the stochastic gravitational wave background
NASA Astrophysics Data System (ADS)
Anand, Sampurn; Dey, Ujjal Kumar; Mohanty, Subhendra
2017-03-01
Cosmological phase transitions can be a source of Stochastic Gravitational Wave (SGW) background. Apart from the dynamics of the phase transition, the characteristic frequency and the fractional energy density Ωgw of the SGW depends upon the temperature of the transition. In this article, we compute the SGW spectrum in the light of QCD equation of state provided by the lattice results. We find that the inclusion of trace anomaly from lattice QCD, enhances the SGW signal generated during QCD phase transition by ~ 50% and the peak frequency of the QCD era SGW are shifted higher by ~ 25% as compared to the earlier estimates without trace anomaly. This result is extremely significant for testing the phase transition dynamics near QCD epoch.
Real time evolution of non-Gaussian cumulants in the QCD critical regime
Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi
2015-09-23
In this study, we derive a coupled set of equations that describe the nonequilibrium evolution of cumulants of critical fluctuations for spacetime trajectories on the crossover side of the QCD phase diagram. In particular, novel expressions are obtained for the nonequilibrium evolution of non-Gaussian skewness and kurtosis cumulants. UBy utilizing a simple model of the spacetime evolution of a heavy-ion collision, we demonstrate that, depending on the relaxation rate of critical fluctuations, skewness and kurtosis can differ significantly in magnitude as well as in sign from equilibrium expectations. Memory effects are important and shown to persist even for trajectories thatmore » skirt the edge of the critical regime. We use phenomenologically motivated parametrizations of freeze-out curves and of the beam-energy dependence of the net baryon chemical potential to explore the implications of our model study for the critical-point search in heavy-ion collisions.« less
Real time evolution of non-Gaussian cumulants in the QCD critical regime
Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi
2015-09-23
In this study, we derive a coupled set of equations that describe the nonequilibrium evolution of cumulants of critical fluctuations for spacetime trajectories on the crossover side of the QCD phase diagram. In particular, novel expressions are obtained for the nonequilibrium evolution of non-Gaussian skewness and kurtosis cumulants. UBy utilizing a simple model of the spacetime evolution of a heavy-ion collision, we demonstrate that, depending on the relaxation rate of critical fluctuations, skewness and kurtosis can differ significantly in magnitude as well as in sign from equilibrium expectations. Memory effects are important and shown to persist even for trajectories that skirt the edge of the critical regime. We use phenomenologically motivated parametrizations of freeze-out curves and of the beam-energy dependence of the net baryon chemical potential to explore the implications of our model study for the critical-point search in heavy-ion collisions.
Conformal symmetry of the Lange-Neubert evolution equation
NASA Astrophysics Data System (ADS)
Braun, V. M.; Manashov, A. N.
2014-04-01
The Lange-Neubert evolution equation describes the scale dependence of the wave function of a meson built of an infinitely heavy quark and light antiquark at light-like separations, which is the hydrogen atom problem of QCD. It has numerous applications to the studies of B-meson decays. We show that the kernel of this equation can be written in a remarkably compact form, as a logarithm of the generator of special conformal transformation in the light-ray direction. This representation allows one to study solutions of this equation in a very simple and mathematically consistent manner. Generalizing this result, we show that all heavy-light evolution kernels that appear in the renormalization of higher-twist B-meson distribution amplitudes can be written in the same form.
Evolution equation for quantum coherence
Hu, Ming-Liang; Fan, Heng
2016-01-01
The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures. PMID:27382933
Brodsky, Stanley J.; de Teramond, Guy F.; Deur, Alexandre P.; Dosch, Hans G.
2015-09-01
The valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a relativistic equation of motion with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. If one requires that the effective action which underlies the QCD Lagrangian remains conformally invariant and extends the formalism of de Alfaro, Fubini and Furlan to light front Hamiltonian theory, the potential U has a unique form of a harmonic oscillator potential, and a mass gap arises. The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter κ appears. Light-front holography thus provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. We also show how the mass scale κ underlying confinement and hadron masses determines the scale Λ_{{ovr MS}} controlling the evolution of the perturbative QCD coupling. The relation between scales is obtained by matching the nonperturbative dynamics, as described by an effective conformal theory mapped to the light-front and its embedding in AdS space, to the perturbative QCD regime computed to four-loop order. The result is an effective coupling defined at all momenta. The predicted value Λ_{{ovr MS}}=0.328±0.034 GeV is in agreement with the world average 0.339±0.010 GeV. The analysis applies to any renormalization scheme.
Euler-Lagrange Equations for the Gribov Reggeon Calculus in QCD and in Gravity
NASA Astrophysics Data System (ADS)
Lipatov, L. N.
The theory of the high energy scattering in QCD and gravity is based on the reggeization of gluons and gravitons, respectively. We discuss the corresponding effective actions for reggeized particle interactions. The Euler-Lagrange equations in these theories are constructed with a variational approach for the effective actions and by using their invariance under the gauge and general coordinate transformations.
Euler-Lagrange equations for the Gribov reggeon calculus in QCD and in gravity
NASA Astrophysics Data System (ADS)
Lipatov, L. N.
2016-10-01
The theory of the high energy scattering in QCD and gravity is based on the reggeization of gluons and gravitons, respectively. We discuss the corresponding effective actions for reggeized particle interactions. The Euler-Lagrange equations in these theories are constructed with a variational approach for the effective actions and by using their invariance under the gauge and general coordinate transformations.
The IR sector of QCD: lattice versus Schwinger-Dyson equations
NASA Astrophysics Data System (ADS)
Binosi, Daniele
2010-12-01
Important information about the infrared dynamics of QCD is encoded in the behavior of its (of-shell) Green's functions, most notably the gluon and the ghost propagators. Due to recent improvements in the quality of lattice data and the truncation schemes employed for the Schwinger-Dyson equations we have now reached a point where the interplay between these two non-perturbative tools can be most fruitful. In this talk several of the above points will be reviewed, with particular emphasis on the implications for the ghost sector, the non-perturbative effective charge of QCD, and the Kugo-Ojima function.
QCD constraints on the equation of state for compact stars
Fraga, E. S.; Kurkela, A.; Schaffner-Bielich, J.; Vuorinen, A.
2016-01-22
In recent years, there have been several successful attempts to constrain the equation of state of neutron star matter using input from low-energy nuclear physics and observational data. We demonstrate that significant further restrictions can be placed by additionally requiring the pressure to approach that of deconfined quark matter at high densities. Remarkably, the new constraints turn out to be highly insensitive to the amount - or even presence - of quark matter inside the stars. In this framework, we also present a simple effective equation of state for cold quark matter that consistently incorporates the effects of interactions and furthermore includes a built-in estimate of the inherent systematic uncertainties. This goes beyond the MIT bag model description in a crucial way, yet leads to an equation of state that is equally straightforward to use.
QCD constraints on the equation of state for compact stars
NASA Astrophysics Data System (ADS)
Fraga, E. S.; Kurkela, A.; Schaffner-Bielich, J.; Vuorinen, A.
2016-01-01
In recent years, there have been several successful attempts to constrain the equation of state of neutron star matter using input from low-energy nuclear physics and observational data. We demonstrate that significant further restrictions can be placed by additionally requiring the pressure to approach that of deconfined quark matter at high densities. Remarkably, the new constraints turn out to be highly insensitive to the amount - or even presence - of quark matter inside the stars. In this framework, we also present a simple effective equation of state for cold quark matter that consistently incorporates the effects of interactions and furthermore includes a built-in estimate of the inherent systematic uncertainties. This goes beyond the MIT bag model description in a crucial way, yet leads to an equation of state that is equally straightforward to use.
QCD constraints on the equation of state for compact stars
NASA Astrophysics Data System (ADS)
Fraga, E. S.; Kurkela, A.; Schaffner-Bielich, J.; Vuorinen, A.
2016-12-01
In recent years, there have been several successful attempts to constrain the equation of state of neutron star matter using input from low-energy nuclear physics and observational data. We demonstrate that significant further restrictions can be placed by additionally requiring the pressure to approach that of deconfined quark matter at high densities. Remarkably, the new constraints turn out to be highly insensitive to the amount - or even presence - of quark matter inside the stars. In this framework, we also present a simple effective equation of state for cold quark matter that consistently incorporates the effects of interactions and furthermore includes a built-in estimate of the inherent systematic uncertainties. This goes beyond the MIT bag model description in a crucial way, yet leads to an equation of state that is equally straightforward to use.
Master integrals for splitting functions from differential equations in QCD
NASA Astrophysics Data System (ADS)
Gituliar, Oleksandr
2016-02-01
A method for calculating phase-space master integrals for the decay process 1 → n masslesspartonsinQCDusingintegration-by-partsanddifferentialequationstechniques is discussed. The method is based on the appropriate choice of the basis for master integrals which leads to significant simplification of differential equations. We describe an algorithm how to construct the desirable basis, so that the resulting system of differential equations can be recursively solved in terms of (G) HPLs as a series in the dimensional regulator ɛ to any order. We demonstrate its power by calculating master integrals for the NLO time-like splitting functions and discuss future applications of the proposed method at the NNLO precision.
QCD chiral transition temperature in a Dyson-Schwinger-equation context
Blank, M.; Krassnigg, A.
2010-08-01
We analyze the chiral phase transition with the help of the QCD gap equation. Various models for the effective interaction in rainbow truncation are contrasted with regard to the resulting chiral transition temperatures. In particular, we investigate possible systematic relations of the details of the effective interaction and the value of T{sub c}. In addition, we quantify changes to the transition temperature beyond the rainbow truncation.
Quark Matter Equation of State from Perturbative QCD
NASA Astrophysics Data System (ADS)
Vuorinen, Aleksi
2017-03-01
In this proceedings contribution, we discuss recent developments in the perturbative determination of the Equation of State of dense quark matter, relevant for the microscopic description of neutron star cores. First, we introduce the current state of the art in the problem, both at zero and small temperatures, and then present results from two recent perturbative studies that pave the way towards extending the EoS to higher orders in perturbation theory.
Global Properties of Rotating Neutron Stars with QCD Equations of State
NASA Astrophysics Data System (ADS)
Gorda, Tyler
2016-11-01
We numerically investigate global properties of rotating neutron stars (NSs) using the allowed band of QCD equations of state derived by Kurkela et al. This band is constrained by chiral effective theory at low densities and perturbative QCD at high densities, and is thus, in essence, a controlled constraint from first-principles physics. Previously, this band of equations of state was used to investigate non-rotating NSs only; in this work, we extend these results to any rotation frequency below the mass-shedding limit. We investigate mass–radius curves, allowed mass–frequency regions, radius–frequency curves for a typical 1.4{M}ȯ star, and the values of the moment of inertia of the double pulsar PSR J0737-3039A, a pulsar for which the moment of inertia may be constrained observationally in a few years. We present limits on observational data coming from these constraints, and identify values of observationally relevant parameters that would further constrain the allowed region for the QCD equation of state. We also discuss how much this region would be constrained by a measurement of the moment of inertia of the double pulsar PSR J0737-3039A.
The equation of state of QCD under hard-dense-loop approximation
NASA Astrophysics Data System (ADS)
Sun, Weimin; Jiang, Yu; Zong, Hongshi
2009-10-01
Based on the method proposed by Zong et al., we calculate the equation of state (EOS) of QCD at zero temperature and finite quark chemical potential under the hard-dense-loop (HDL) approximation. A comparison between the EOS under HDL approximation and the cold, perturbative EOS of QCD proposed by Fraga, Pisarski and Schaffner-Bielich is made. It is found that when µ is less than 4.7 GeV, the pressure density calculated using HDL approximation is much larger than that calculated using perturbation theory. This enhancement of the obtained pressure density with respect to that of perturbation theory can be regarded as a possible explanation for the strong coupled QGP. It is also expected that the obtained EOS can be applied in the study of neutron stars.
The QCD equation of state at finite density from analytical continuation
NASA Astrophysics Data System (ADS)
Günther, Jana; Bellwied, Rene; Borsanyi, Szabolcs; Fodor, Zoltan; Katz, Sandor D.; Pasztor, Attila; Ratti, Claudia
2017-03-01
An effcient way to study the QCD phase diagram at small finite density is to extrapolate thermodynamical observables from imaginary chemical potential. In this talk we present results on several observables for the equation of state to order (μB/T)6. The observables are calculated along the isentropic trajectories in the (T, μB) plane corresponding to the RHIC Beam Energy Scan collision energies. The simulations are performed at the physical mass for the light and strange quarks. μs was tuned in a way to enforce strangeness neutrality to match the experimental conditions; the results are continuum extrapolated using lattices of up to Nt = 16 temporal resolution.
Euler-Lagrange equations for effective actions in QCD and gravity at high energies
NASA Astrophysics Data System (ADS)
Lipatov, L. N.
2017-03-01
Gluons in QCD and gravitons in quantum gravity lie on the Regge trajectories, which allows to formulate the high-energy scattering in these models in the framework of the reggeon field theory. In particular, the BFKL Pomeron is a composite state of reggeized gluons. In N = 4 SUSY the Pomeron is dual to the reggeized graviton living in the 10-dimensional anti-de-Sitter space. The effective actions for reggeized gluon and graviton interactions are formulated locally in the particle rapidities. The corresponding Euler-Lagrange equations are derived and their simple solutions are constructed.
COLLINEAR SPLITTING, PARTON EVOLUTION AND THE STRANGE-QUARK ASYMMETRY OF THE NUCLEON IN NNLO QCD.
RODRIGO,G.CATANI,S.DE FLORIAN, D.VOGELSANG,W.
2004-04-25
We consider the collinear limit of QCD amplitudes at one-loop order, and their factorization properties directly in color space. These results apply to the multiple collinear limit of an arbitrary number of QCD partons, and are a basic ingredient in many higher-order computations. In particular, we discuss the triple collinear limit and its relation to flavor asymmetries in the QCD evolution of parton densities at three loops. As a phenomenological consequence of this new effect, and of the fact that the nucleon has non-vanishing quark valence densities, we study the perturbative generation of a strange-antistrange asymmetry s(x)-{bar s}(x) in the nucleon's sea.
Modeling the QCD Equation of State in Relativistic Heavy Ion Collisions on BlueGene/L
Soltz, R; Grady, J; Hartouni, E P; Gupta, R; Vitev, I; Mottola, E; Petreczky, P; Karsch, F; Christ, N; Mawhinney, R; Bass, S; Mueller, B; Vranas, P; Levkova, L; Molnar, D; Teaney, D; De Tar, C; Toussaint, D; Sugar, R
2006-04-10
On 9,10 Feb 2006 a workshop was held at LLNL to discuss how a 10% allocation of the ASC BG/L supercomputer performing a finite temperature Lattice QCD (LQCD) calculation of the equation of state and non-equilibrium properties of the quark-gluon state of matter could lead to a breakthrough in our understanding of recent data from the Relativistic Heavy Ion Collider at Brookhaven National Lab. From this meeting and subsequent discussions we present a detailed plan for this calculation, including mechanisms for working in a secure computing environment and inserting the resulting equation of state into hydrodynamic transport models that will be compared directly to the RHIC data. We discuss expected benefits for DOE Office of Science research programs within the context of the NNSA mission.
Exact Pressure Evolution Equation for Incompressible Fluids
NASA Astrophysics Data System (ADS)
Tessarotto, M.; Ellero, M.; Aslan, N.; Mond, M.; Nicolini, P.
2008-12-01
An important aspect of computational fluid dynamics is related to the determination of the fluid pressure in isothermal incompressible fluids. In particular this concerns the construction of an exact evolution equation for the fluid pressure which replaces the Poisson equation and yields an algorithm which is a Poisson solver, i.e., it permits to time-advance exactly the same fluid pressure without solving the Poisson equation. In fact, the incompressible Navier-Stokes equations represent a mixture of hyperbolic and elliptic pde's, which are extremely hard to study both analytically and numerically. This amounts to transform an elliptic type fluid equation into a suitable hyperbolic equation, a result which usually is reached only by means of an asymptotic formulation. Besides being a still unsolved mathematical problem, the issue is relevant for at least two reasons: a) the proliferation of numerical algorithms in computational fluid dynamics which reproduce the behavior of incompressible fluids only in an asymptotic sense (see below); b) the possible verification of conjectures involving the validity of appropriate equations of state for the fluid pressure. Another possible motivation is, of course, the ongoing quest for efficient numerical solution methods to be applied for the construction of the fluid fields {ρ,V,p}, solutions of the initial and boundary-value problem associated to the incompressible N-S equations (INSE). In this paper we intend to show that an exact solution to this problem can be achieved adopting the approach based on inverse kinetic theory (IKT) recently developed for incompressible fluids by Tessarotto et al. [7, 6, 7, 8, 9]. In particular we intend to prove that the evolution of the fluid fields can be achieved by means of a suitable dynamical system, to be identified with the so-called Navier-Stokes (N-S) dynamical system. As a consequence it is found that the fluid pressure obeys a well-defined evolution equation. The result appears
NASA Astrophysics Data System (ADS)
Mukherjee, Swagato; Venugopalan, Raju; Yin, Yi
2016-12-01
We report on recent progress in the study of the evolution of non-Gaussian cumulants of critical fluctuations. We explore the implications of non-equilibrium effects on the search for the QCD critical point.
Interface effect in QCD phase transitions via Dyson-Schwinger equation approach
NASA Astrophysics Data System (ADS)
Gao, Fei; Liu, Yu-xin
2016-11-01
With the chiral susceptibility criterion, we obtain the phase diagram of strong-interaction matter in terms of temperature and chemical potential in the framework of Dyson-Schwinger equations of QCD. After calculating the pressure and some other thermodynamic properties of the matter in the Dyson-Schwinger method, we get the phase diagram in terms of temperature and baryon number density. We also obtain the interface tension and the interface entropy density to describe the inhomogeneity of the two phases in the coexistence region of the first-order phase transition. After including the interface effect, we find that the total entropy density of the system increases in both the deconfinement (dynamical chiral symmetry restoration) and the hadronization (dynamical chiral symmetry breaking) processes of the first-order phase transitions and thus solve the entropy puzzle in the hadronization process.
Inoue, Takashi; Aoki, Sinya; Doi, Takumi; Hatsuda, Tetsuo; Ikeda, Yoichi; Ishii, Noriyoshi; Murano, Keiko; Nemura, Hidekatsu; Sasaki, Kenji
2013-09-13
Quark mass dependence of the equation of state (EOS) for nucleonic matter is investigated, on the basis of the Brueckner-Hartree-Fock method with the nucleon-nucleon interaction extracted from lattice QCD simulations. We observe saturation of nuclear matter at the lightest available quark mass corresponding to the pseudoscalar meson mass ≃469 MeV. Mass-radius relation of the neutron stars is also studied with the EOS for neutron-star matter from the same nuclear force in lattice QCD. We observe that the EOS becomes stiffer and thus the maximum mass of neutron star increases as the quark mass decreases toward the physical point.
Kinematical and dynamical aspects of higher-spin bound-state equations in holographic QCD
de Téramond, Guy F.; Dosch, Hans Günter; Brodsky, Stanley J.
2013-04-01
In this paper we derive holographic wave equations for hadrons with arbitrary spin starting from an effective action in a higher-dimensional space asymptotic to anti–de Sitter (AdS) space. Our procedure takes advantage of the local tangent frame, and it applies to all spins, including half-integer spins. An essential element is the mapping of the higher-dimensional equations of motion to the light-front Hamiltonian, thus allowing a clear distinction between the kinematical and dynamical aspects of the holographic approach to hadron physics. Accordingly, the nontrivial geometry of pure AdS space encodes the kinematics, and the additional deformations of AdS space encode the dynamics, including confinement. It thus becomes possible to identify the features of holographic QCD, which are independent of the specific mechanisms of conformal symmetry breaking. In particular, we account for some aspects of the striking similarities and differences observed in the systematics of the meson and baryon spectra.
Implicit Degenerate Evolution Equations and Applications.
1980-07-01
implicit evolution equations divides historically into three cases. The first and certainly the easiest is where 9 0 A - is Lipschitz or monotone in...on all V, and its Yoshida pproximation A - )’I(I - J,), a monotone Lipschitz function defined on all V. For u e V we have AA(u) e A(JA(u)). We denote...a) (u (t) + (v (t)) + BAlu t)) - f(t) dt (3.2.b) vXlt) e AluAlt) t e (0,T] Since (I + A) - 1 and BX are both Lipschitz continuous from V to V, (3.2
QCD phase transitions via a refined truncation of Dyson-Schwinger equations
NASA Astrophysics Data System (ADS)
Gao, Fei; Liu, Yu-xin
2016-10-01
We investigate both the chiral and deconfinement phase transitions of QCD matter in a refined scheme of Dyson-Schwinger equations, which have been shown to be successful in giving the meson mass spectrum and matching the interaction with the results from ab initio computation. We verify the equivalence of the chiral susceptibility criterion with different definitions for the susceptibility and confirm that the chiral susceptibility criterion is efficient to fix not only the chiral phase boundary but also the critical end point (CEP), especially when one could not have the effective thermodynamical potential. We propose a generalized Schwinger function criterion for the confinement. We give the phase diagram of both phase transitions and show that in the refined scheme the position of the CEP shifts to lower chemical potential and higher temperature. Based on our calculation and previous results of the chemical freeze-out conditions, we propose that the CEP is located in the states of the matter generated by the Au-Au collisions with √{sN N }=9 - 15 GeV .
Some new solutions of nonlinear evolution equations with variable coefficients
NASA Astrophysics Data System (ADS)
Virdi, Jasvinder Singh
2016-05-01
We construct the traveling wave solutions of nonlinear evolution equations (NLEEs) with variable coefficients arising in physics. Some interesting nonlinear evolution equations are investigated by traveling wave solutions which are expressed by the hyperbolic functions, the trigonometric functions and rational functions. The applied method will be used in further works to establish more entirely new solutions for other kinds of such nonlinear evolution equations with variable coefficients arising in physics.
An Evolution Operator Solution for a Nonlinear Beam Equation
1990-12-01
uniqueness for the parabolic problem Ug + (-A) m u+ I I- u = f (14) on RN X (0, 1). Again, certain restrictions apply. The Schr ~ dinger equation , [68:pg 823...evolution equation because of the time dependence in the definition of the operator A. He identifies conditions for the existence of a unique solution. In...The arguments for the adjoint and dissipativity are not repeated. Because of the explicit time dependence , (71) is called an evolution equation . For
Karsch,F.; Kharzeev, D.; Molnar, K.; Petreczky, P.; Teaney, D.
2008-04-21
The interpretation of relativistic heavy-ion collisions at RHIC energies with thermal concepts is largely based on the relative success of ideal (nondissipative) hydrodynamics. This approach can describe basic observables at RHIC, such as particle spectra and momentum anisotropies, fairly well. On the other hand, recent theoretical efforts indicate that dissipation can play a significant role. Ideally viscous hydrodynamic simulations would extract, if not only the equation of state, but also transport coefficients from RHIC data. There has been a lot of progress with solving relativistic viscous hydrodynamics. There are already large uncertainties in ideal hydrodynamics calculations, e.g., uncertainties associated with initial conditions, freezeout, and the simplified equations of state typically utilized. One of the most sensitive observables to the equation of state is the baryon momentum anisotropy, which is also affected by freezeout assumptions. Up-to-date results from lattice quantum chromodynamics on the transition temperature and equation of state with realistic quark masses are currently available. However, these have not yet been incorporated into the hydrodynamic calculations. Therefore, the RBRC workshop 'Hydrodynamics in Heavy Ion Collisions and QCD Equation of State' aimed at getting a better understanding of the theoretical frameworks for dissipation and near-equilibrium dynamics in heavy-ion collisions. The topics discussed during the workshop included techniques to solve the dynamical equations and examine the role of initial conditions and decoupling, as well as the role of the equation of state and transport coefficients in current simulations.
NASA Astrophysics Data System (ADS)
Ma, Bailing; Ji, Chueng-Ryong
2017-01-01
Due to the simplicity and the inherent characteristics of confinement, the 1+1 dimensional QCD known as 't Hooft model has attracted a lot of interest for many yers. In the large Nc limit, the contribution from non-planar diagrams are negligible, hence an iterative equation can be simplified and solved numerically for the quark propagator dressed by gluons. While 't Hooft model was originally solved using the Light Front Dynamics (LFD), people have also done similar work afterwards in the Instant Form Dynamics (IFD). We attempt to interpolate the 1+1 dimensional QCD between IFD and LFD by introducing an angle called the interpolation angle. Using this interpolation method, we analyze the formulation of the single quark mass gap equation in dynamical forms between IFD and LFD. Examining that our interpolating results reproduce the IFD and LFD results previously obtained by others, we discuss the fate of the vacuum condensation, the chiral angle, and the effective mass in the limit to the IFD and the LFD. This work was supported by the U.S. Department of Energy (Grant No. DE-FG02-03ER41260).
Fast wavelet based algorithms for linear evolution equations
NASA Technical Reports Server (NTRS)
Engquist, Bjorn; Osher, Stanley; Zhong, Sifen
1992-01-01
A class was devised of fast wavelet based algorithms for linear evolution equations whose coefficients are time independent. The method draws on the work of Beylkin, Coifman, and Rokhlin which they applied to general Calderon-Zygmund type integral operators. A modification of their idea is applied to linear hyperbolic and parabolic equations, with spatially varying coefficients. A significant speedup over standard methods is obtained when applied to hyperbolic equations in one space dimension and parabolic equations in multidimensions.
Exact traveling wave solutions for system of nonlinear evolution equations.
Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H
2016-01-01
In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.
Prolongation structures of nonlinear evolution equations
NASA Technical Reports Server (NTRS)
Wahlquist, H. D.; Estabrook, F. B.
1975-01-01
A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.
Invariant tori for a class of nonlinear evolution equations
Kolesov, A Yu; Rozov, N Kh
2013-06-30
The paper looks at quite a wide class of nonlinear evolution equations in a Banach space, including the typical boundary value problems for the main wave equations in mathematical physics (the telegraph equation, the equation of a vibrating beam, various equations from the elastic stability and so on). For this class of equations a unified approach to the bifurcation of invariant tori of arbitrary finite dimension is put forward. Namely, the problem of the birth of such tori from the zero equilibrium is investigated under the assumption that in the stability problem for this equilibrium the situation arises close to an infinite-dimensional degeneracy. Bibliography: 28 titles.
NLO Hierarchy of Wilson Lines Evolution
Balitsky, Ian
2015-03-01
The high-energy behavior of QCD amplitudes can be described in terms of the rapidity evolution of Wilson lines. I present the hierarchy of evolution equations for Wilson lines in the next-to-leading order.
None
2016-07-12
Modern QCD - Lecture 3 We will introduce processes with initial-state hadrons and discuss parton distributions, sum rules, as well as the need for a factorization scale once radiative corrections are taken into account. We will then discuss the DGLAP equation, the evolution of parton densities, as well as ways in which parton densities are extracted from data.
Variable-coefficient extended mapping method for nonlinear evolution equations
NASA Astrophysics Data System (ADS)
Zhang, Sheng; Xia, Tiecheng
2008-03-01
In this Letter, a variable-coefficient extended mapping method is proposed to seek new and more general exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients and ( 2+1)-dimensional Nizhnik-Novikov-Veselov equations. As a result, many new and more general exact solutions are obtained including Jacobi elliptic function solutions, hyperbolic function solutions and trigonometric function solutions. It is shown that the proposed method provides a very effective and powerful mathematical tool for solving a great many nonlinear evolution equations in mathematical physics.
The relativistic equations of stellar structure and evolution
NASA Technical Reports Server (NTRS)
Thorne, K. S.
1977-01-01
The general-relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general-relativistic version of the mixing-length formalism for convection is presented.
Cusp Formation for a Nonlocal Evolution Equation
NASA Astrophysics Data System (ADS)
Hoang, Vu; Radosz, Maria
2017-02-01
Córdoba et al. (Ann Math 162(3):1377-1389, 2005) introduced a nonlocal active scalar equation as a one-dimensional analogue of the surface-quasigeostrophic equation. It has been conjectured, based on numerical evidence, that the solution forms a cusp-like singularity in finite time. Up until now, no active scalar with nonlocal flux is known for which cusp formation has been rigorously shown. In this paper, we introduce and study a nonlocal active scalar, inspired by the Córdoba-Córdoba-Fontelos equation, and prove that either a cusp- or needle-like singularity forms in finite time.
Exact null controllability of degenerate evolution equations with scalar control
Fedorov, Vladimir E; Shklyar, Benzion
2012-12-31
Necessary and sufficient conditions for the exact null controllability of a degenerate linear evolution equation with scalar control are obtained. These general results are used to examine the exact null controllability of the Dzektser equation in the theory of seepage. Bibliography: 13 titles.
The effects of QCD equation of state on the relic density of WIMP dark matter
Drees, Manuel; Hajkarim, Fazlollah; Schmitz, Ernany Rossi
2015-06-12
Weakly Interactive Massive Particles (WIMPs) are the most widely studied candidate particles forming the cold dark matter (CDM) whose existence can be inferred from a wealth of astrophysical and cosmological observations. In the framework of the minimal cosmological model detailed measurements on the cosmic microwave background by the PLANCK collaboration fix the scaled CDM relic density to Ω{sub c}h{sup 2}=0.1193±0.0014, with an error of less than 1.5%. In order to fully exploit this observational precision, theoretical calculations should have a comparable or smaller error. In this paper we use recent lattice QCD calculations to improve the description of the thermal plasma. This affects the predicted relic density of “thermal WIMPs”, which once were in chemical equilibrium with Standard Model particles. For WIMP masses between 3 and 15 GeV, where QCD effects are most important, our predictions differ from earlier results by up to 9% (12%) for pure S-wave (P-wave) annihilation. We use these results to compute the thermally averaged WIMP annihilation cross section that reproduces the correct CDM relic density, for WIMP masses between 0.1 GeV and 10 TeV.
Mimicking the QCD equation of state with a dual black hole
Gubser, Steven S.; Nellore, Abhinav
2008-10-15
We present numerical and analytical studies of the equation of state of translationally invariant black hole solutions to five-dimensional gravity coupled to a single scalar. As an application, we construct a family of black holes that closely mimics the equation of state of quantum chromodynamics at zero chemical potential.
QCD equations of state and the quark-gluon plasma liquid model
NASA Astrophysics Data System (ADS)
Letessier, Jean; Rafelski, Johann
2003-03-01
Recent advances in the study of equations of state of thermal lattice quantum chromodynamics obtained at nonzero baryon density allow validation of the quark-gluon plasma (QGP) liquid model equations of state (EOS). We study here the properties of the QGP-EOS near to the phase transformation boundary at finite baryon density and show a close agreement with the lattice results.
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1988-01-01
An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.
The relativistic equations of stellar structure and evolution
NASA Technical Reports Server (NTRS)
Thorne, K. S.
1975-01-01
The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. A general relativistic version of the mixing-length formalism for convection is presented. It is argued that in work on spherical systems, general relativity theorists have identified the wrong quantity as total mass-energy inside radius r.
On pathwise uniqueness of stochastic evolution equations in Hilbert spaces
NASA Astrophysics Data System (ADS)
Xie, Bin
2008-08-01
The pathwise uniqueness of stochastic evolution equations driven by Q-Wiener processes is mainly investigated in this article. We focus on the case that the modulus of the continuity of the coefficients is not controlled by a linear function. Additionally, we show that the corresponding diffusion process is Feller.
On the solutions of fractional order of evolution equations
NASA Astrophysics Data System (ADS)
Morales-Delgado, V. F.; Taneco-Hernández, M. A.; Gómez-Aguilar, J. F.
2017-01-01
In this paper we present a discussion of generalized Cauchy problems in a diffusion wave process, we consider bi-fractional-order evolution equations in the Riemann-Liouville, Liouville-Caputo, and Caputo-Fabrizio sense. Through Fourier transforms and Laplace transform we derive closed-form solutions to the Cauchy problems mentioned above. Similarly, we establish fundamental solutions. Finally, we give an application of the above results to the determination of decompositions of Dirac type for bi-fractional-order equations and write a formula for the moments for the fractional vibration of a beam equation. This type of decomposition allows us to speak of internal degrees of freedom in the vibration of a beam equation.
An evolution equation modeling inversion of tulip flames
Dold, J.W.; Joulin, G.
1995-02-01
The authors attempt to reduce the number of physical ingredients needed to model the phenomenon of tulip-flame inversion to a bare minimum. This is achieved by synthesizing the nonlinear, first-order Michelson-Sivashinsky (MS) equation with the second order linear dispersion relation of Landau and Darrieus, which adds only one extra term to the MS equation without changing any of its stationary behavior and without changing its dynamics in the limit of small density change when the MS equation is asymptotically valid. However, as demonstrated by spectral numerical solutions, the resulting second-order nonlinear evolution equation is found to describe the inversion of tulip flames in good qualitative agreement with classical experiments on the phenomenon. This shows that the combined influences of front curvature, geometric nonlinearity and hydrodynamic instability (including its second-order, or inertial effects, which are an essential result of vorticity production at the flame front) are sufficient to reproduce the inversion process.
Langevin Equation for the Morphological Evolution of Strained Epitaxial Films
NASA Astrophysics Data System (ADS)
Vvedensky, Dimitri; Haselwandter, Christoph
2006-03-01
A stochastic partial differential equation for the morphological evolution of strained epitaxial films is derived from an atomistic master equation. The transition rules in this master equation are based on previous kinetic Monte Carlo (KMC) simulations of a model that incorporates the effects of strain through local environment-dependent energy barriers to adatom detachment from step edges. The morphological consequences of these rules are seen in the transition from layer-by-layer growth to the appearance of three-dimensional islands with increasing strain. The regularization of the exact Langevin description of these rules yields a continuum equation whose lowest-order terms provide a coarse-grained theory of this model. The coefficients in this equation are expressed in terms of the parameters of the original lattice model, so a direct comparison between the morphologies produced by KMC simulations and this Langevin equation are meaningful. Comparisons with previous approaches are made to provide an atomistic interpretation of a similar equation derived by Golovin et al. based on classical elasticity.
Inverse Problem of Variational Calculus for Nonlinear Evolution Equations
NASA Astrophysics Data System (ADS)
Ali, Sk. Golam; Talukdar, B.; Das, U.
2007-06-01
We couple a nonlinear evolution equation with an associated one and derive the action principle. This allows us to write the Lagrangian density of the system in terms of the original field variables rather than Casimir potentials. We find that the corresponding Hamiltonian density provides a natural basis to recast the pair of equations in the canonical form. Amongst the case studies presented the KdV and modified KdV pairs exhibit bi-Hamiltonian structure and allow one to realize the associated fields in physical terms.
Second-order neutral impulsive stochastic evolution equations with delay
NASA Astrophysics Data System (ADS)
Ren, Yong; Sun, Dandan
2009-10-01
In this paper, we study the second-order neutral stochastic evolution equations with impulsive effect and delay (SNSEEIDs). We establish the existence and uniqueness of mild solutions to SNSEEIDs under non-Lipschitz condition with Lipschitz condition being considered as a special case by the successive approximation. Furthermore, we give the continuous dependence of solutions on the initial data by means of corollary of the Bihari inequality. An application to the stochastic nonlinear wave equation with impulsive effect and delay is given to illustrate the theory.
Non-perturbative scale evolution of four-fermion operators in two-flavour QCD
NASA Astrophysics Data System (ADS)
Herdoiza, Gregorio
2006-12-01
We apply finite-size recursion techniques based on the Schrödinger functional formalism to de- termine the renormalization group running of four-fermion operators which appear in the S = 2 effective weak Hamiltonian of the Standard Model. Our calculations are done using O(a) im- proved Wilson fermions with Nf = 2 dynamical flavours. Preliminary results are presented for the four-fermion operator which determines the BK -parameter in tmQCD.
Solutions of evolution equations associated to infinite-dimensional Laplacian
NASA Astrophysics Data System (ADS)
Ouerdiane, Habib
2016-05-01
We study an evolution equation associated with the integer power of the Gross Laplacian ΔGp and a potential function V on an infinite-dimensional space. The initial condition is a generalized function. The main technique we use is the representation of the Gross Laplacian as a convolution operator. This representation enables us to apply the convolution calculus on a suitable distribution space to obtain the explicit solution of the perturbed evolution equation. Our results generalize those previously obtained by Hochberg [K. J. Hochberg, Ann. Probab. 6 (1978) 433.] in the one-dimensional case with V=0, as well as by Barhoumi-Kuo-Ouerdiane for the case p=1 (See Ref. [A. Barhoumi, H. H. Kuo and H. Ouerdiane, Soochow J. Math. 32 (2006) 113.]).
On an evolution equation in a cell motility model
NASA Astrophysics Data System (ADS)
Mizuhara, Matthew S.; Berlyand, Leonid; Rybalko, Volodymyr; Zhang, Lei
2016-04-01
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells on a substrate. The key issue is the evolution of the cell membrane (interface curve) which involves shape change and net motion. This issue can be addressed both qualitatively and quantitatively by studying the evolution equation of the sharp interface limit for this system. However, this equation is non-linear and non-local and existence of solutions presents a significant analytical challenge. We establish existence of solutions for a wide class of initial data in the so-called subcritical regime. Existence is proved in a two step procedure. First, for smooth (H2) initial data we use a regularization technique. Second, we consider non-smooth initial data that are more relevant from the application point of view. Here, uniform estimates on the time when solutions exist rely on a maximum principle type argument. We also explore the long time behavior of the model using both analytical and numerical tools. We prove the nonexistence of traveling wave solutions with nonzero velocity. Numerical experiments show that presence of non-linearity and asymmetry of the initial curve results in a net motion which distinguishes it from classical volume preserving curvature motion. This is done by developing an algorithm for efficient numerical resolution of the non-local term in the evolution equation.
The quark propagator in QCD and G2 QCD
NASA Astrophysics Data System (ADS)
Contant, Romain; Huber, Markus Q.
2017-03-01
QCD-like theories provide testing grounds for truncations of functional equations at non-zero density, since comparisons with lattice results are possible due to the absence of the sign problem. As a first step towards such a comparison, we determine for QCD and G2 QCD the chiral and confinement/deconfinement transitions from the quark propagator Dyson-Schwinger equation at zero chemical potential by calculating the chiral and dual chiral condensates, respectively.
Evolution equation for non-linear cosmological perturbations
Brustein, Ram; Riotto, Antonio E-mail: Antonio.Riotto@cern.ch
2011-11-01
We present a novel approach, based entirely on the gravitational potential, for studying the evolution of non-linear cosmological matter perturbations. Starting from the perturbed Einstein equations, we integrate out the non-relativistic degrees of freedom of the cosmic fluid and obtain a single closed equation for the gravitational potential. We then verify the validity of the new equation by comparing its approximate solutions to known results in the theory of non-linear cosmological perturbations. First, we show explicitly that the perturbative solution of our equation matches the standard perturbative solutions. Next, using the mean field approximation to the equation, we show that its solution reproduces in a simple way the exponential suppression of the non-linear propagator on small scales due to the velocity dispersion. Our approach can therefore reproduce the main features of the renormalized perturbation theory and (time)-renormalization group approaches to the study of non-linear cosmological perturbations, with some possibly important differences. We conclude by a preliminary discussion of the nature of the full solutions of the equation and their significance.
Equation of state for hot quark-gluon plasma transitions to hadrons with full QCD potential
NASA Astrophysics Data System (ADS)
Sheikholeslami-Sabzevari, Bijan
2002-05-01
A practical method based on Mayer's cluster expansion to calculate critical values for a quark-gluon plasma (QGP) phase transition to hadrons is represented. It can be applied to a high-temperature QGP for clustering of quarks to mesons and baryons. The potential used is the Cornell potential, i.e., a potential containing both confining and gluon exchange terms. Debye screening effects are included. An equation of state (EOS) for hadron production is found by analytical methods, which is valid near the critical point. The example of the formation of J/ψ and Υ is recalculated. It is shown that in the range of temperatures available by today's accelerators, the latter particles are suppressed. This is further confirmation for heavy quarkonia suppression and, hence, for a signature of a QGP. The EOS presented here also shows that in future colliders there will be no heavy quarkonia production by the mechanism of phase transition. Hence, if there will be heavy quarkonia production, it must be based on some other mechanisms, perhaps on the basis of some recently suggested possibilities.
Wei-Norman equations for a unitary evolution
NASA Astrophysics Data System (ADS)
Charzyński, Szymon; Kuś, Marek
2013-07-01
The Wei-Norman technique allows one to express the solution of a system of linear non-autonomous differential equations in terms of product of exponentials with time-dependent exponents being solutions of a system of nonlinear differential equations. We show that in the unitary case, i.e. when the solution of the linear system is given by a unitary evolution operator, the nonlinear system, by an appropriate choice of ordering, can be reduced to a hierarchy of matrix Riccati equations. To this end, we consider a general linear non-autonomous dynamical system on the special linear group SL(N, {C}). The unitary case, of particular significance for quantum optimal control problems, is then obtained by restriction to anti-Hermitian generators. We also point to the connections of the obtained results with the theory of the so-called Lie systems.
Parameterization and Monte Carlo solutions to PDF evolution equations
NASA Astrophysics Data System (ADS)
Suciu, Nicolae; Schüler, Lennart; Attinger, Sabine; Knabner, Peter
2015-04-01
The probability density function (PDF) of the chemical species concentrations transported in random environments is governed by unclosed evolution equations. The PDF is transported in the physical space by drift and diffusion processes described by coefficients derived by standard upscaling procedures. Its transport in the concentration space is described by a drift determined by reaction rates, in a closed form, as well as a term accounting for the sub-grid mixing process due to molecular diffusion and local scale hydrodynamic dispersion. Sub-grid mixing processes are usually described by models of the conditionally averaged diffusion flux or models of the conditional dissipation rate. We show that in certain situations mixing terms can also be derived, in the form of an Itô process, from simulated or measured concentration time series. Monte Carlo solutions to PDF evolution equations are usually constructed with systems of computational particles, which are well suited for highly dimensional advection-dominated problems. Such solutions require the fulfillment of specific consistency conditions relating the statistics of the random concentration field, function of both space and time, to that of the time random function describing an Itô process in physical and concentration spaces which governs the evolution of the system of particles. We show that the solution of the Fokker-Planck equation for the concentration-position PDF of the Itô process coincides with the solution of the PDF equation only for constant density flows in spatially statistically homogeneous systems. We also find that the solution of the Fokker-Planck equation is still equivalent to the solution of the PDF equation weighted by the variable density or by other conserved scalars. We illustrate the parameterization of the sub-grid mixing by time series and the Monte Carlo solution for a problem of contaminant transport in groundwater. The evolution of the system of computational particles whose
NASA Astrophysics Data System (ADS)
Korennoy, Ya. A.; Man'ko, V. I.
2017-04-01
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time). The general formalism of quantizers and dequantizers determining the star product quantization scheme in these representations is given. Taking the Gaussian functions as the distributions of the tomographic parameters the correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators in the form of singular and regular generalized functions are derived. Evolution equations and stationary states equations for symplectic and optical joint probability distributions are obtained.
NASA Astrophysics Data System (ADS)
Korennoy, Ya. A.; Man'ko, V. I.
2016-12-01
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time). The general formalism of quantizers and dequantizers determining the star product quantization scheme in these representations is given. Taking the Gaussian functions as the distributions of the tomographic parameters the correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators in the form of singular and regular generalized functions are derived. Evolution equations and stationary states equations for symplectic and optical joint probability distributions are obtained.
Molnar, Denes
2016-05-25
The Section below summarizes research activities and achievements during the fifth (last) year of the PI’s Early Career Research Project (ECRP). Unlike the first four years of the project, the last year was not funded under the American Recovery and Reinvestment Act (ARRA). The ECRP advanced two main areas: i) radiative 3 ↔ 2 radiative transport, via development of a new computer code MPC/Grid that solves the Boltzmann transport equation in full 6+1D (3X+3V+time); and ii) application of relativistic hydrodynamics, via development of a self-consistent framework to convert viscous fluids to particles. In Year 5 we finalized thermalization studies with radiative gg ↔ ggg transport (Sec. 1.1.1) and used nonlinear covariant transport to assess the accuracy of fluid-to-particle conversion models (Sec. 1.1.2), calculated observables with self-consistent fluid-to-particle conversion from realistic viscous hydrodynamic evolution (Secs. 1.2.1 and 1.2.2), extended the covariant energy loss formulation to heavy quarks (Sec. 1.4.1) and studied energy loss in small systems (Sec. 1.4.2), and also investigated how much of the elliptic flow could have non-hydrodynamic origin (Sec 1.3). Years 1-4 of the ECRP were ARRA-funded and, therefore, they have their own report document ’Final Technical Report for Years 1-4 of the Early Career Research Project “Viscosity and equation of state of hot and dense QCD matter”’ (same award number DE-SC0004035). The PI’s group was also part of the DOE JET Topical Collaboration, a multi-institution project that overlapped in time significantly with the ECRP. Purdue achievements as part of the JET Top- ical Collaboration are in a separate report “Final Technical Report summarizing Purdue research activities as part of the DOE JET Topical Collaboration” (award DE-SC0004077).
Structure scalars and evolution equations in f( G) cosmology
NASA Astrophysics Data System (ADS)
Sharif, M.; Fatima, H. Ismat
2017-01-01
In this paper, we study the dynamics of self-gravitating fluid using structure scalars for spherical geometry in the context of f( G) cosmology. We construct structure scalars through orthogonal splitting of the Riemann tensor and deduce a complete set of equations governing the evolution of dissipative anisotropic fluid in terms of these scalars. We explore different causes of density inhomogeneity which turns out to be a necessary condition for viable models. It is explicitly shown that anisotropic inhomogeneous static spherically symmetric solutions can be expressed in terms of these scalar functions.
Kawamura, Hiroyuki; Tanaka, Kazuhiro
2010-06-01
The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory, corresponding to a long-distance component in the factorization formula for exclusive B-meson decays. The evolution equation for the B-meson DA is governed by the cusp anomalous dimension as well as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these anomalous dimensions give the ''quasilocal'' kernel in the coordinate-space representation. We show that this evolution equation can be solved analytically in the coordinate space, accomplishing the relevant Sudakov resummation at the next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite simple form of our solution which determines the B-meson DA with a quark-antiquark light-cone separation t in terms of the DA at a lower renormalization scale {mu} with smaller interquark separations zt (z{<=}1). This formula allows us to present rigorous calculation of the B-meson DA at the factorization scale {approx}{radical}(m{sub b{Lambda}QCD}) for t less than {approx}1 GeV{sup -1}, using the recently obtained operator product expansion of the DA as the input at {mu}{approx}1 GeV. We also derive the master formula, which reexpresses the integrals of the DA at {mu}{approx}{radical}(m{sub b{Lambda}QCD}) for the factorization formula by the compact integrals of the DA at {mu}{approx}1 GeV.
Multivalued perturbations of subdifferential type evolution equations in Hilbert spaces
NASA Astrophysics Data System (ADS)
Kravvaritis, Dimitrios; Papageorgiou, Nikolaos S.
In this paper we study the multivalued evolution equation - ẋ(t) ɛ∂ϑ(x(t)) + F(t, x(t)), x(0) = x 0, where ϑ: X → R¯ is a proper, convex, lower semicontinuous (l.s.c.) function, F(·, ·) is a multivalued perturbation, and X is an infinite dimensional, separable Hilbert space. We have an existence result for F(·, ·) being nonconvex valued, and another for F(·, ·) being convex valued but not closed valued. When ϑ = δK = indicator function of a compact, convex set K, we obtain some extensions of earlier results by Moreau and Henry. Then using the Kuratowski-Mosco convergence of sets and the τ-convergence of functions, we prove a well posedness result for the evolution inclusion we are studying. Also we consider a random version of it and prove the existence of a random solution. Finally we present applications to problems in partial differential equations.
Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics
NASA Astrophysics Data System (ADS)
Mirzazadeh, Mohammad; Ekici, Mehmet; Sonmezoglu, Abdullah; Ortakaya, Sami; Eslami, Mostafa; Biswas, Anjan
2016-05-01
This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.
High energy asymptotics of scattering processes in QCD
NASA Astrophysics Data System (ADS)
Enberg, R.; Golec-Biernat, K.; Munier, S.
2005-10-01
High energy scattering in the QCD parton model was recently shown to be a reaction-diffusion process and, thus, to lie in the universality class of the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation. We recall that the latter appears naturally in the context of the parton model. We provide a thorough numerical analysis of the mean-field approximation, given in QCD by the Balitsky-Kovchegov equation. In the framework of a simple stochastic toy model that captures the relevant features of QCD, we discuss and illustrate the universal properties of such stochastic models. We investigate, in particular, the validity of the mean-field approximation and how it is broken by fluctuations. We find that the mean-field approximation is a good approximation in the initial stages of the evolution in rapidity.
Multiple scales analysis and travelling wave solutions for KdV type nonlinear evolution equations
NASA Astrophysics Data System (ADS)
Ayhan, Burcu; Ozer, M. Naci; Bekir, Ahmet
2017-01-01
Nonlinear evolution equations are the mathematical models of problems that arise in many field of science. These equations has become an important field of study in applied mathematics in recent years. We apply exact solution methods and multiple scale method which is known as a perturbation method to nonlinear evolution equations. Using exact solution methods we get travelling wave solutions expressed by hyperbolic functions, trigonometric functions and rational functions. Also we derive Nonlinear Schrödinger (NLS) type equations from Korteweg-de Vries (KdV) type nonlinear evolution equations and we get approximate solutions for KdV type equations using multiple scale method. The proposed methods are direct and effective and can be used for many nonlinear evolution equations. It is shown that these methods provide a powerful mathematical tool to solve nonlinear evolution equations in mathematical physics.
Central equation of state in spherical characteristic evolutions
Barreto, W.; Castillo, L.; Barrios, E.
2009-10-15
We study the evolution of a perfect-fluid sphere coupled to a scalar radiation field. By ensuring a Ricci invariant regularity as a conformally flat spacetime at the central world line we find that the fluid coupled to the scalar field satisfies the equation of state {rho}{sub c}+3p{sub c}=const at the center of the sphere, where the energy {rho}{sub c} density and the pressure p{sub c} do not necessarily contain the scalar field contribution. The fluid can be interpreted as anisotropic and radiant because of the scalar field, but it becomes perfect and nonradiative at the center of the sphere. These results are currently being considered to build up a numerical relativistic hydrodynamic solver.
Rogue waves of a (3 + 1) -dimensional nonlinear evolution equation
NASA Astrophysics Data System (ADS)
Shi, Yu-bin; Zhang, Yi
2017-03-01
General high-order rogue waves of a (3 + 1) -dimensional Nonlinear Evolution Equation ((3+1)-d NEE) are obtained by the Hirota bilinear method, which are given in terms of determinants, whose matrix elements possess plain algebraic expressions. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background with a line profile and then disappear into the constant background again. Two subclass of nonfundamental rogue waves are analyzed in details. By proper means of the regulations of free parameters, the dynamics of multi-rogue waves and high-order rogue waves have been illustrated in (x,t) plane and (y,z) plane by three dimensional figures.
Entropy production and the geometry of dissipative evolution equations
NASA Astrophysics Data System (ADS)
Reina, Celia; Zimmer, Johannes
2015-11-01
Purely dissipative evolution equations are often cast as gradient flow structures, z ˙=K (z ) D S (z ) , where the variable z of interest evolves towards the maximum of a functional S according to a metric defined by an operator K . While the functional often follows immediately from physical considerations (e.g., the thermodynamic entropy), the operator K and the associated geometry does not necessarily do so (e.g., Wasserstein geometry for diffusion). In this paper, we present a variational statement in the sense of maximum entropy production that directly delivers a relationship between the operator K and the constraints of the system. In particular, the Wasserstein metric naturally arises here from the conservation of mass or energy, and depends on the Onsager resistivity tensor, which, itself, may be understood as another metric, as in the steepest entropy ascent formalism. This variational principle is exemplified here for the simultaneous evolution of conserved and nonconserved quantities in open systems. It thus extends the classical Onsager flux-force relationships and the associated variational statement to variables that do not have a flux associated to them. We further show that the metric structure K is intimately linked to the celebrated Freidlin-Wentzell theory of stochastically perturbed gradient flows, and that the proposed variational principle encloses an infinite-dimensional fluctuation-dissipation statement.
Brodsky, Stanley J.; de Teramond, Guy F.; /Costa Rica U.
2012-02-16
-front QCD Hamiltonian 'Light-Front Holography'. Light-Front Holography is in fact one of the most remarkable features of the AdS/CFT correspondence. The Hamiltonian equation of motion in the light-front (LF) is frame independent and has a structure similar to eigenmode equations in AdS space. This makes a direct connection of QCD with AdS/CFT methods possible. Remarkably, the AdS equations correspond to the kinetic energy terms of the partons inside a hadron, whereas the interaction terms build confinement and correspond to the truncation of AdS space in an effective dual gravity approximation. One can also study the gauge/gravity duality starting from the bound-state structure of hadrons in QCD quantized in the light-front. The LF Lorentz-invariant Hamiltonian equation for the relativistic bound-state system is P{sub {mu}}P{sup {mu}}|{psi}(P)> = (P{sup +}P{sup -} - P{sub {perpendicular}}{sup 2})|{psi}(P)> = M{sup 2}|{psi}(P)>, P{sup {+-}} = P{sup 0} {+-} P{sup 3}, where the LF time evolution operator P{sup -} is determined canonically from the QCD Lagrangian. To a first semiclassical approximation, where quantum loops and quark masses are not included, this leads to a LF Hamiltonian equation which describes the bound-state dynamics of light hadrons in terms of an invariant impact variable {zeta} which measures the separation of the partons within the hadron at equal light-front time {tau} = x{sup 0} + x{sup 3}. This allows us to identify the holographic variable z in AdS space with an impact variable {zeta}. The resulting Lorentz-invariant Schroedinger equation for general spin incorporates color confinement and is systematically improvable. Light-front holographic methods were originally introduced by matching the electromagnetic current matrix elements in AdS space with the corresponding expression using LF theory in physical space time. It was also shown that one obtains identical holographic mapping using the matrix elements of the energy-momentum tensor by perturbing
LATTICE QCD THERMODYNAMICS WITH WILSON QUARKS.
EJIRI,S.
2007-11-20
We review studies of QCD thermodynamics by lattice QCD simulations with dynamical Wilson quarks. After explaining the basic properties of QCD with Wilson quarks at finite temperature including the phase structure and the scaling properties around the chiral phase transition, we discuss the critical temperature, the equation of state and heavy-quark free energies.
Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio
2014-01-01
The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530
Extraction of quark transversity distribution and Collins fragmentation functions with QCD evolution
NASA Astrophysics Data System (ADS)
Kang, Zhong-Bo; Prokudin, Alexei; Sun, Peng; Yuan, Feng
2016-01-01
We study the transverse-momentum-dependent (TMD) evolution of the Collins azimuthal asymmetries in e+e- annihilations and semi-inclusive hadron production in deep inelastic scattering processes. All the relevant coefficients are calculated up to the next-to-leading-logarithmic-order accuracy. By applying the TMD evolution at the approximate next-to-leading-logarithmic order in the Collins-Soper-Sterman formalism, we extract transversity distributions for u and d quarks and Collins fragmentation functions from current experimental data by a global analysis of the Collins asymmetries in back-to-back dihadron productions in e+e- annihilations measured by BELLE and BABAR collaborations and semi-inclusive hadron production in deep inelastic scattering data from HERMES, COMPASS, and JLab HALL A experiments. The impact of the evolution effects and the relevant theoretical uncertainties are discussed. We further discuss the TMD interpretation for our results and illustrate the unpolarized quark distribution, transversity distribution, unpolarized quark fragmentation, and Collins fragmentation functions depending on the transverse momentum and the hard momentum scale. We make detailed predictions for future experiments and discuss their impact.
Extraction of quark transversity distribution and Collins fragmentation functions with QCD evolution
Kang, Zhong-Bo; Prokudin, Alexei; Sun, Peng; Yuan, Feng
2016-01-13
In this paper, we study the transverse momentum dependent (TMD) evolution of the Collins azimuthal asymmetries in e^{+}e^{-} annihilations and semi-inclusive hadron production in deep inelastic scattering (SIDIS) processes. All the relevant coefficients are calculated up to the next-to-leading logarithmic (NLL) order accuracy. By applying the TMD evolution at the approximate NLL order in the Collins- Soper-Sterman (CSS) formalism, we extract transversity distributions for u and d quarks and Collins fragmentation functions from current experimental data by a global analysis of the Collins asymmetries in back-to-back di-hadron productions in e^{+}e^{-} annihilations measured by BELLE and BABAR Collaborations and SIDIS data from HERMES, COMPASS, and JLab HALL A experiments. The impact of the evolution effects and the relevant theoretical uncertainties are discussed. We further discuss the TMD interpretation for our results, and illustrate the unpolarized quark distribution, transversity distribution, unpolarized quark fragmentation and Collins fragmentation functions depending on the transverse momentum and the hard momentum scale. Finally, we give predictions and discuss impact of future experiments.
Extraction of quark transversity distribution and Collins fragmentation functions with QCD evolution
Kang, Zhong-Bo; Prokudin, Alexei; Sun, Peng; ...
2016-01-13
In this paper, we study the transverse momentum dependent (TMD) evolution of the Collins azimuthal asymmetries in e+e- annihilations and semi-inclusive hadron production in deep inelastic scattering (SIDIS) processes. All the relevant coefficients are calculated up to the next-to-leading logarithmic (NLL) order accuracy. By applying the TMD evolution at the approximate NLL order in the Collins- Soper-Sterman (CSS) formalism, we extract transversity distributions for u and d quarks and Collins fragmentation functions from current experimental data by a global analysis of the Collins asymmetries in back-to-back di-hadron productions in e+e- annihilations measured by BELLE and BABAR Collaborations and SIDIS datamore » from HERMES, COMPASS, and JLab HALL A experiments. The impact of the evolution effects and the relevant theoretical uncertainties are discussed. We further discuss the TMD interpretation for our results, and illustrate the unpolarized quark distribution, transversity distribution, unpolarized quark fragmentation and Collins fragmentation functions depending on the transverse momentum and the hard momentum scale. Finally, we give predictions and discuss impact of future experiments.« less
Renormalization of the unitary evolution equation for coined quantum walks
NASA Astrophysics Data System (ADS)
Boettcher, Stefan; Li, Shanshan; Portugal, Renato
2017-03-01
We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attention as a framework for coined quantum walks that are essential for attaining the Grover limit for quantum search algorithms in physically realizable, low-dimensional geometries. In particular, we analyze the exact real-space renormalization group (RG) procedure recently introduced to study the scaling of quantum walks on fractal networks. While this procedure, when implemented numerically, was able to provide some deep insights into the relation between classical and quantum walks, its analytic basis has remained obscure. Our discussion here is laying the groundwork for a rigorous implementation of the RG for this important class of transport and algorithmic problems, although some instances remain unresolved. Specifically, we find that the RG fixed-point analysis of the classical walk, which typically focuses on the dominant Jacobian eigenvalue {λ1} , with walk dimension dw\\text{RW}={{log}2}{λ1} , needs to be extended to include the subdominant eigenvalue {λ2} , such that the dimension of the quantum walk obtains dw\\text{QW}={{log}2}\\sqrt{{λ1}{λ2}} . With that extension, we obtain analytically previously conjectured results for dw\\text{QW} of Grover walks on all but one of the fractal networks that have been considered.
NASA Astrophysics Data System (ADS)
Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.
2016-09-01
dynamics, and it gives a remarkable connection between the perturbative QCD scale Λ and hadron masses. One can also identify a specific scale Q0 which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including lattice QCD, the Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating their conflicting predictions, we discuss the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances in this difficult area, but also to suggest what could be an optimal definition of αs(Q2) in order to bring better unity to the subject.
On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations
Christov, Ivan C.
2015-08-20
We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.
Equations of State: Gateway to Planetary Origin and Evolution (Invited)
NASA Astrophysics Data System (ADS)
Melosh, J.
2013-12-01
Research over the past decades has shown that collisions between solid bodies govern many crucial phases of planetary origin and evolution. The accretion of the terrestrial planets was punctuated by planetary-scale impacts that generated deep magma oceans, ejected primary atmospheres and probably created the moons of Earth and Pluto. Several extrasolar planetary systems are filled with silicate vapor and condensed 'tektites', probably attesting to recent giant collisions. Even now, long after the solar system settled down from its violent birth, a large asteroid impact wiped out the dinosaurs, while other impacts may have played a role in the origin of life on Earth and perhaps Mars, while maintaining a steady exchange of small meteorites between the terrestrial planets and our moon. Most of these events are beyond the scale at which experiments are possible, so that our main research tool is computer simulation, constrained by the laws of physics and the behavior of materials during high-speed impact. Typical solar system impact velocities range from a few km/s in the outer solar system to 10s of km/s in the inner system. Extrasolar planetary systems expand that range to 100s of km/sec typical of the tightly clustered planetary systems now observed. Although computer codes themselves are currently reaching a high degree of sophistication, we still rely on experimental studies to determine the Equations of State (EoS) of materials critical for the correct simulation of impact processes. The recent expansion of the range of pressures available for study, from a few 100 GPa accessible with light gas guns up to a few TPa from current high energy accelerators now opens experimental access to the full velocity range of interest in our solar system. The results are a surprise: several groups in both the USA and Japan have found that silicates and even iron melt and vaporize much more easily in an impact than previously anticipated. The importance of these findings is
Efficient Numerical Methods for Evolution Partial Differential Equations
1989-09-30
public lease; distribution mlim ed.-.... 13. ABSTRACT (Maxmum 200 woard Generalized Korteweg - de Vries equation (GKdV). This equation is written as...McKinney. On Optimal high-order in time approxiniations.for the Korteweg -de Vries equation ..To appear in Math. Comp.. 3. J.L. Bona, V.A. Dougalis...O.Karakashian and W. Mckinney, Conservative high-order schemes for the Generalized Korteweg -de Vries equation . In preparation. 4. G. D. Akrivis, V.A
Constraining supermassive black hole evolution through the continuity equation
NASA Astrophysics Data System (ADS)
Tucci, Marco; Volonteri, Marta
2017-03-01
The population of supermassive black holes (SMBHs) is split between those that are quiescent, such as those seen in local galaxies including the Milky Way, and those that are active, resulting in quasars and active galactic nuclei (AGN). Outside our neighborhood, all the information we have on SMBHs is derived from quasars and AGN, giving us a partial view. We study the evolution of the SMBH population, total and active, by the continuity equation, backwards in time from z = 0 to z = 4. Type-1 and type-2 AGN are differentiated in our model on the basis of their respective Eddington ratio distributions, chosen on the basis of observational estimates. The duty cycle is obtained by matching the luminosity function of quasars, and the average radiative efficiency is the only free parameter in the model. For higher radiative efficiencies (≳ 0.07), a large fraction of the SMBH population, most of them quiescent, must already be in place by z = 4. For lower radiative efficiencies ( 0.05), the duty cycle increases with the redshift and the SMBH population evolves dramatically from z = 4 onwards. The mass function of active SMBHs does not depend on the choice of the radiative efficiency or of the local SMBH mass function, but it is mainly determined by the quasar luminosity function once the Eddington ratio distribution is fixed. Only direct measurement of the total black-hole mass function at redshifts z ≳ 2 could break these degeneracies, offering important constraints on the average radiative efficiency. Focusing on type-1 AGN, for which observational estimates of the mass function and Eddington ratio distribution exist at various redshifts, models with lower radiative efficiencies better reproduce the high-mass end of the mass function at high z, but tend to over-predict it at low z, and vice-versa for models with higher radiative efficiencies.
Evolution of basic equations for nearshore wave field
ISOBE, Masahiko
2013-01-01
In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680
On numerical solutions to the QCD ’t Hooft equation in the limit of large quark mass
Zubov, Roman; Prokhvatilov, Evgeni
2016-01-22
First we give a short informal introduction to the theory behind the ’t Hooft equation. Then we consider numerical solutions to this equation in the limit of large fermion masses. It turns out that the spectrum of eigenvalues coincides with that of the Airy differential equation. Moreover when we take the Fourier transform of eigenfunctions, they look like the corresponding Airy functions with appropriate symmetry. It is known that these functions correspond to solutions of a one dimensional Schrodinger equation for a particle in a triangular potential well. So we find the analogy between this problem and the ’t Hooft equation. We also present a simple intuition behind these results.
NASA Astrophysics Data System (ADS)
Cahill, R. T.
1992-06-01
A review is given of progress in deriving the effective action for hadronic physics, S[π, ϱ, ω,.., overlineN, N,..] , from the fundamental defining action of QCD, S[ overlineq, q, A μa] . This is a problem in quantum field theory and the most success so far has been achieved using functional integral calculus (FIC) techniques. This formulates the problem as an exercise in changing the variables of integration in the functional integrals, from those of the quark and gluon fields to those of the (bare) meson and baryon fields. The appropriate variables are determined by the dynamics of QCD, and the final hadronic variables (essentially the 'normal modes' of QCD) are local fields describing the 'centre-of-mass' motion of extended bound states of quarks. The quarks are extensively dressed by the gluons, and the detailed aspects of the hidden chiral symmetry emerge naturally from the formalism. Particular attention is given to covariant integral equations which determine bare nucleon structure (i.e. in the quenched approximation). These equations, which arise from the closed double-helix diagrams of the FIC analysis, describe the baryons in terms of quark-diquark structure, in the form of Faddeev equations. This hadronisation of QCD also generates the dressing of these baryons by the pions, and the non-local πNN coupling.
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Motsa, S. S.; Magagula, V. M.; Sibanda, P.
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature. PMID:25254252
Exact Travelling Wave Solutions of the Nonlinear Evolution Equations by Auxiliary Equation Method
NASA Astrophysics Data System (ADS)
Kaplan, Melike; Akbulut, Arzu; Bekir, Ahmet
2015-10-01
The auxiliary equation method presents wide applicability to handling nonlinear wave equations. In this article, we establish new exact travelling wave solutions of the nonlinear Zoomeron equation, coupled Higgs equation, and equal width wave equation. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions, and rational functions. It is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. Throughout the article, all calculations are made with the aid of the Maple packet program.
NASA Astrophysics Data System (ADS)
Nishihara, Hiroki; Harada, Masayasu
2014-12-01
We study the asymmetric nuclear matter using a holographic QCD model by introducing a baryonic charge in the infrared boundary. We first show that, in the normal hadron phase, the predicted values of the symmetry energy and its slope parameter are comparable with the empirical values. We find that the phase transition from the normal phase to the pion condensation phase is delayed compared with the pure mesonic matter: the critical chemical potential is larger than the pion mass which is obtained for the pure mesonic matter. We also show that, in the pion condensation phase, the pion contribution to the isospin number density increases with the chemical potential, while the baryonic contribution is almost constant. Furthermore, the value of chiral condensation implies that the enhancement of the chiral symmetry breaking occurs in the asymmetric nuclear matter as in the pure mesonic matter. We also give a discussion on how to understand the delay in terms of the four-dimensional chiral Lagrangian including the rho and omega mesons based on the hidden local symmetry.
Phenomenological consequences of enhanced bulk viscosity near the QCD critical point
NASA Astrophysics Data System (ADS)
Monnai, Akihiko; Mukherjee, Swagato; Yin, Yi
2017-03-01
In the proximity of the QCD critical point the bulk viscosity of quark-gluon matter is expected to be proportional to nearly the third power of the critical correlation length, and become significantly enhanced. This work is the first attempt to study the phenomenological consequences of enhanced bulk viscosity near the QCD critical point. For this purpose, we implement the expected critical behavior of the bulk viscosity within a non-boost-invariant, longitudinally expanding 1 +1 dimensional causal relativistic hydrodynamical evolution at nonzero baryon density. We demonstrate that the critically enhanced bulk viscosity induces a substantial nonequilibrium pressure, effectively softening the equation of state, and leads to sizable effects in the flow velocity and single-particle distributions at the freeze-out. The observable effects that may arise due to the enhanced bulk viscosity in the vicinity of the QCD critical point can be used as complementary information to facilitate searches for the QCD critical point.
Moments of solutions of evolution equations and suboptimal programmed controls
NASA Astrophysics Data System (ADS)
Khrychev, D. A.
2007-08-01
Moments of solutions of non-linear differential equations subjected to random perturbations satisfy infinite systems of equations that do not contain finite closed subsystems. One of the methods for approximate solution of such infinite systems consists in replacing them by finite systems obtained from the original one as a result of equating to zero all the moments of sufficiently high order. It is shown that the moments of solutions of a wide class of ordinary differential equations, as well as of certain classes of partial differential equations, are approximated by solutions of those finite systems. The results obtained are used for constructing suboptimal programmed controls of dynamical systems with random parameters. Bibliography: 10 titles.
Bounded solutions of a second order evolution equation and applications
NASA Astrophysics Data System (ADS)
Leiva, Hugo
2001-02-01
In this paper we study the following abstract second order differential equation with dissipation in a Hilbert space H: u″+cu'+dA u+kG(u)=P(t), u∈H, t∈R, where c, d and k are positive constants, G:H→H is a Lipschitzian function and P:R→H is a continuous and bounded function. A:D(A)⊂H→H is an unbounded linear operator which is self-adjoint, positive definite and has compact resolvent. Under these conditions we prove that for some values of d, c and k this system has a bounded solution which is exponentially asymptotically stable. Moreover; if P(t) is almost periodic, then this bounded solution is also almost periodic. These results are applied to a very well known second order system partial differential equations; such as the sine-Gordon equation, The suspension bridge equation proposed by Lazer and McKenna, etc.
Integrable nonlinear evolution partial differential equations in 4 + 2 and 3 + 1 dimensions.
Fokas, A S
2006-05-19
The derivation and solution of integrable nonlinear evolution partial differential equations in three spatial dimensions has been the holy grail in the field of integrability since the late 1970s. The celebrated Korteweg-de Vries and nonlinear Schrödinger equations, as well as the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations, are prototypical examples of integrable evolution equations in one and two spatial dimensions, respectively. Do there exist integrable analogs of these equations in three spatial dimensions? In what follows, I present a positive answer to this question. In particular, I first present integrable generalizations of the KP and DS equations, which are formulated in four spatial dimensions and which have the novelty that they involve complex time. I then impose the requirement of real time, which implies a reduction to three spatial dimensions. I also present a method of solution.
New Traveling Wave Solutions for a Class of Nonlinear Evolution Equations
NASA Astrophysics Data System (ADS)
Bai, Cheng-Jie; Zhao, Hong; Xu, Heng-Ying; Zhang, Xia
The deformation mapping method is extended to solve a class of nonlinear evolution equations (NLEEs). Many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, and Jacobian elliptic function solutions, are obtained by a simple algebraic transformation relation between the solutions of the NLEEs and those of the cubic nonlinear Klein-Gordon (NKG) equation.
Angular Structure of the In-Medium QCD Cascade.
Blaizot, J-P; Mehtar-Tani, Y; Torres, M A C
2015-06-05
We study the angular broadening of a medium-induced QCD cascade. We derive the equation that governs the evolution of the average transverse momentum squared of the gluons in the cascade as a function of the medium length, and we solve this equation analytically. Two regimes are identified. For a medium of a not too large size, and for not too soft gluons, the transverse momentum grows with the size of the medium according to standard momentum broadening. The other regime, visible for a medium of a sufficiently large size and very soft gluons, is a regime dominated by multiple branchings: there, the average transverse momentum saturates to a value that is independent of the size of the medium. This structure of the in-medium QCD cascade is, at least qualitatively, compatible with the recent LHC data on dijet asymmetry.
Solving nonlinear evolution equation system using two different methods
NASA Astrophysics Data System (ADS)
Kaplan, Melike; Bekir, Ahmet; Ozer, Mehmet N.
2015-12-01
This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G0/G, 1/G)-expansion and (1/G0)-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial differential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.
Approximation and Numerical Analysis of Nonlinear Equations of Evolution.
1980-01-31
les Espaces d’ Interpolation; Dualitg", Math. Scand., 9, 1961, pp. 147-177. 9. __ "Equations Diff~rentielles Op ~ rationnelles dan les Espaces de Hilbert...relaxation," Revue Francaise d’automatique, informatique, recherche operationnelle, R3, 1973, p. 5-32. Ill DOUGLAS, J. and GALLIE, T.MI. "On the Numerical
Group theoretical approach to nonlinear evolution equations of lax type III. The Boussinesq equation
NASA Astrophysics Data System (ADS)
Levi, D.; Olshanetsky, M. A.; Perelomov, A. M.; Ragnisco, O.
1980-06-01
Within the group theoretical framework recently proposed by Berezin and Perelomov, we are able to derive an abstract (operator) generalization of the classical Boussinesq equation, which possesses an infinite sequence of conserved quantities.
Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.
2016-05-09
regime and its prediction for the analytic form of $$\\alpha_s(Q^2)$$. The AdS/QCD light-front holographic analysis predicts the color confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale $$\\Lambda$$ and hadron masses. One can also identify a specific scale $$Q_0$$ which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including Lattice QCD, Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating conflicting results, we provide a partial discussion on the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances on this difficult subject, but also to suggest what could be the best definition of $$\\alpha_s(Q^2)$$ in order to bring better unity to the subject.« less
Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.
2016-05-09
for the analytic form of $\\alpha_s(Q^2)$. The AdS/QCD light-front holographic analysis predicts the color confinement potential underlying hadron spectroscopy and dynamics, and it gives a remarkable connection between the perturbative QCD scale $\\Lambda$ and hadron masses. One can also identify a specific scale $Q_0$ which demarcates the division between perturbative and nonperturbative QCD. We also review other important methods for computing the QCD coupling, including Lattice QCD, Schwinger-Dyson equations and the Gribov-Zwanziger analysis. After describing these approaches and enumerating conflicting results, we provide a partial discussion on the origin of these discrepancies and how to remedy them. Our aim is not only to review the advances on this difficult subject, but also to suggest what could be the best definition of $\\alpha_s(Q^2)$ in order to bring better unity to the subject.
Particle swarms in gases: the velocity-average evolution equations from Newton's law.
Ferrari, Leonardo
2003-08-01
The evolution equation for a generic average quantity relevant to a swarm of particles homogeneously dispersed in a uniform gas, is obtained directly from the Newton's law, without having recourse to the (intermediary) Boltzmann equation. The procedure makes use of appropriate averages of the term resulting from the impulsive force (due to collisions) in the Newton's law. When the background gas is assumed to be in thermal equilibrium, the obtained evolution equation is shown to agree with the corresponding one following from the Boltzmann equation. But the new procedure also allows to treat physical situations in which the Boltzmann equation is not valid, as it happens when some correlation exists (or is assumed) between the velocities of swarm and gas particles.
An almost symmetric Strang splitting scheme for nonlinear evolution equations.
Einkemmer, Lukas; Ostermann, Alexander
2014-07-01
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.
NASA Astrophysics Data System (ADS)
Luo, Lin
2017-02-01
In this paper, based on a discrete spectral problem and the corresponding zero curvature representation, the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curvature equations is then established for such integrable systems. the commutation relations of Lax operators corresponding to the isospectral and non-isospectral lattice flows are worked out, the master symmetries of each lattice equation in the isospectral hierarchyand are generated, thus a τ-symmetry algebra for the lattice integrable systems is engendered from this theory. Supported by the National Science Foundation of China under Grant No. 11371244 and the Applied Mathematical Subject of SSPU under Grant No. XXKPY1604
Evolution of transverse momentum dependent distribution and fragmentation functions
NASA Astrophysics Data System (ADS)
Henneman, A. A.; Boer, Daniël; Mulders, P. J.
2002-01-01
We use Lorentz invariance and the QCD equations of motion to study the evolution of functions that appear at leading order in a 1/ Q expansion in azimuthal asymmetries. This includes the evolution equation of the Collins fragmentation function. The moments of these functions are matrix elements of known twist two and twist three operators. We present the evolution in the large Nc limit, restricting to non-singlet for the chiral-even functions.
NASA Astrophysics Data System (ADS)
Nawa, Kanabu; Suganuma, Hideo; Kojo, Toru
2007-04-01
We study baryons in holographic QCD with D4/D8/D8¯ multi-D-brane system. In holographic QCD, the baryon appears as a topologically nontrivial chiral soliton in a four-dimensional effective theory of mesons. We call this topological soliton brane-induced Skyrmion. Some review of D4/D8/D8¯ holographic QCD is presented from the viewpoints of recent hadron physics and QCD phenomenologies. A four-dimensional effective theory with pions and ρ mesons is uniquely derived from the non-Abelian Dirac-Born-Infeld (DBI) action of D8 brane with D4 supergravity background at the leading order of large Nc, without small amplitude expansion of meson fields to discuss chiral solitons. For the hedgehog configuration of pion and ρ-meson fields, we derive the energy functional and the Euler-Lagrange equation of brane-induced Skyrmion from the meson effective action induced by holographic QCD. Performing the numerical calculation, we obtain the soliton solution and figure out the pion profile F(r) and the ρ-meson profile G˜(r) of the brane-induced Skyrmion with its total energy, energy density distribution, and root-mean-square radius. These results are compared with the experimental quantities of baryons and also with the profiles of standard Skyrmion without ρ mesons. We analyze interaction terms of pions and ρ mesons in brane-induced Skyrmion, and find a significant ρ-meson component appearing in the core region of a baryon.
Nawa, Kanabu; Suganuma, Hideo; Kojo, Toru
2007-04-15
We study baryons in holographic QCD with D4/D8/D8 multi-D-brane system. In holographic QCD, the baryon appears as a topologically nontrivial chiral soliton in a four-dimensional effective theory of mesons. We call this topological soliton brane-induced Skyrmion. Some review of D4/D8/D8 holographic QCD is presented from the viewpoints of recent hadron physics and QCD phenomenologies. A four-dimensional effective theory with pions and {rho} mesons is uniquely derived from the non-Abelian Dirac-Born-Infeld (DBI) action of D8 brane with D4 supergravity background at the leading order of large N{sub c}, without small amplitude expansion of meson fields to discuss chiral solitons. For the hedgehog configuration of pion and {rho}-meson fields, we derive the energy functional and the Euler-Lagrange equation of brane-induced Skyrmion from the meson effective action induced by holographic QCD. Performing the numerical calculation, we obtain the soliton solution and figure out the pion profile F(r) and the {rho}-meson profile G-tilde(r) of the brane-induced Skyrmion with its total energy, energy density distribution, and root-mean-square radius. These results are compared with the experimental quantities of baryons and also with the profiles of standard Skyrmion without {rho} mesons. We analyze interaction terms of pions and {rho} mesons in brane-induced Skyrmion, and find a significant {rho}-meson component appearing in the core region of a baryon.
Finitely approximable random sets and their evolution via differential equations
NASA Astrophysics Data System (ADS)
Ananyev, B. I.
2016-12-01
In this paper, random closed sets (RCS) in Euclidean space are considered along with their distributions and approximation. Distributions of RCS may be used for the calculation of expectation and other characteristics. Reachable sets on initial data and some ways of their approximate evolutionary description are investigated for stochastic differential equations (SDE) with initial state in some RCS. Markov property of random reachable sets is proved in the space of closed sets. For approximate calculus, the initial RCS is replaced by a finite set on the integer multidimensional grid and the multistage Markov chain is substituted for SDE. The Markov chain is constructed by methods of SDE numerical integration. Some examples are also given.
NASA Astrophysics Data System (ADS)
Gibbon, John
2007-06-01
More than 160 years after their invention by Hamilton, quaternions are now widely used in the aerospace and computer animation industries to track the orientation and paths of moving objects undergoing three-axis rotations. Here it is shown that they provide a natural way of selecting an appropriate orthonormal frame—designated the quaternion-frame—for a particle in a Lagrangian flow, and of obtaining the equations for its dynamics. How these ideas can be applied to the three-dimensional Euler fluid equations is then considered. This work has some bearing on the issue of whether the Euler equations develop a singularity in a finite time. Some of the literature on this topic is reviewed, which includes both the Beale-Kato-Majda theorem and associated work on the direction of vorticity by Constantin, Fefferman, and Majda and by Deng, Hou, and Yu. It is then shown how the quaternion formalism provides an alternative formulation in terms of the Hessian of the pressure.
QCD at nonzero chemical potential: Recent progress on the lattice
Aarts, Gert; Jäger, Benjamin; Attanasio, Felipe; Seiler, Erhard; Sexty, Dénes; Stamatescu, Ion-Olimpiu
2016-01-22
We summarise recent progress in simulating QCD at nonzero baryon density using complex Langevin dynamics. After a brief outline of the main idea, we discuss gauge cooling as a means to control the evolution. Subsequently we present a status report for heavy dense QCD and its phase structure, full QCD with staggered quarks, and full QCD with Wilson quarks, both directly and using the hopping parameter expansion to all orders.
Toward a gauge theory for evolution equations on vector-valued spaces
Cardanobile, Stefano; Mugnolo, Delio
2009-10-15
We investigate symmetry properties of vector-valued diffusion and Schroedinger equations. For a separable Hilbert space H we characterize the subspaces of L{sup 2}(R{sup 3};H) that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge symmetries in mathematical physics is explored.
Frenkel, A L; Indireshkumar, K
1999-10-01
Wavy film flow of incompressible Newtonian fluid down an inclined plane is considered. The question is posed as to the parametric conditions under which the description of evolution can be approximately reduced for all time to a single evolution equation for the film thickness. An unconventional perturbation approach yields the most general evolution equation and least restrictive conditions on its validity. The advantages of this equation for analytical and numerical studies of three-dimensional waves in inclined films are pointed out.
The evolution of galaxies in the mirror of the coagulation equation
NASA Astrophysics Data System (ADS)
Kontorovich, V. M.
2017-01-01
Smoluchowski equation and its generalizations, describing the merger of the particles, allow us to understand the main stages of the formation of galaxy mass functions, established as a result of mergers, and their evolution and thus provides an explanation for the results of long-term observations with the Hubble Space Telescope and large ground-based telescopes.
Evolution Equation for a Joint Tomographic Probability Distribution of Spin-1 Particles
NASA Astrophysics Data System (ADS)
Korennoy, Ya. A.; Man'ko, V. I.
2016-11-01
The nine-component positive vector optical tomographic probability portrait of quantum state of spin-1 particles containing full spatial and spin information about the state without redundancy is constructed. Also the suggested approach is expanded to symplectic tomography representation and to representations with quasidistributions like Wigner function, Husimi Q-function, and Glauber-Sudarshan P-function. The evolution equations for constructed vector optical and symplectic tomograms and vector quasidistributions for arbitrary Hamiltonian are found. The evolution equations are also obtained in special case of the quantum system of charged spin-1 particle in arbitrary electro-magnetic field, which are analogs of non-relativistic Proca equation in appropriate representations. The generalization of proposed approach to the cases of arbitrary spin is discussed. The possibility of formulation of quantum mechanics of the systems with spins in terms of joint probability distributions without the use of wave functions or density matrices is explicitly demonstrated.
Neutron star structure from QCD
NASA Astrophysics Data System (ADS)
Fraga, Eduardo S.; Kurkela, Aleksi; Vuorinen, Aleksi
2016-03-01
In this review article, we argue that our current understanding of the thermodynamic properties of cold QCD matter, originating from first principles calculations at high and low densities, can be used to efficiently constrain the macroscopic properties of neutron stars. In particular, we demonstrate that combining state-of-the-art results from Chiral Effective Theory and perturbative QCD with the current bounds on neutron star masses, the Equation of State of neutron star matter can be obtained to an accuracy better than 30% at all densities.
Analysis of transcription-factor binding-site evolution by using the Hamilton-Jacobi equations
NASA Astrophysics Data System (ADS)
Ancliff, Mark; Park, Jeong-Man
2016-12-01
We investigate a quasi-species mutation-selection model of transcription-factor binding-site evolution. By considering the mesa and the crater fitness landscapes designed to describe these binding sites and point mutations, we derive an evolution equation for the population distribution of binding sequences. In the long-length limit, the evolution equation is replaced by a Hamilton-Jacobi equation which we solve for the stationary state solution. From the stationary solution, we derive the population distributions and find that an error threshold, separating populations in which the binding site does or does not evolve, only exists for certain values of the fitness parameters. A phase diagram in this parameter space is derived and shows a critical line below which no error threshold exists. We also investigate the evolution of multiple binding sites for the same transcription factor. For two binding sites, we perform an analysis similar to that for a single site and determine a phase diagram showing different phases with both, one, or no binding sites selected. In the phase diagram, the phase boundary between the one-or-two selected site phases is qualitatively different for the mesa and the crater fitness landscapes. As fitness benefits for a second bound transcription factor tend to zero, the minimum mutation rate at which the two-site phase occurs diverges in the mesa landscape whereas the mutation rate at the phase boundary tends to a finite value for the crater landscape.
Threefold Complementary Approach to Holographic QCD
Brodsky, Stanley J.; de Teramond, Guy F.; Dosch, Hans Gunter
2013-12-27
A complementary approach, derived from (a) higher-dimensional anti-de Sitter (AdS) space, (b) light-front quantization and (c) the invariance properties of the full conformal group in one dimension leads to a nonperturbative relativistic light-front wave equation which incorporates essential spectroscopic and dynamical features of hadron physics. The fundamental conformal symmetry of the classical QCD Lagrangian in the limit of massless quarks is encoded in the resulting effective theory. The mass scale for confinement emerges from the isomorphism between the conformal group andSO(2,1). This scale appears in the light-front Hamiltonian by mapping to the evolution operator in the formalism of de Alfaro, Fubini and Furlan, which retains the conformal invariance of the action. Remarkably, the specific form of the confinement interaction and the corresponding modification of AdS space are uniquely determined in this procedure.
A well-posed Cauchy problem for an evolution equation with coefficients of low regularity
NASA Astrophysics Data System (ADS)
Cicognani, Massimo; Colombini, Ferruccio
In the hyperbolic Cauchy problem, the well-posedness in Sobolev spaces is strictly related to the modulus of continuity of the coefficients. This holds true for p-evolution equations with real characteristics (p=1 hyperbolic equations, p=2 vibrating plate and Schrödinger type models, …). We show that, for p⩾2, a lack of regularity in t can be balanced by a damping of the too fast oscillations as the space variable x→∞. This cannot happen in the hyperbolic case p=1 because of the finite speed of propagation.
Approximated Lax pairs for the reduced order integration of nonlinear evolution equations
NASA Astrophysics Data System (ADS)
Gerbeau, Jean-Frédéric; Lombardi, Damiano
2014-05-01
A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations. It is based on approximations of generalized Lax pairs. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the basis on which the solution is searched for evolves in time according to a dynamics specific to the problem. It is therefore well-suited to solving problems with progressive front or wave propagation. Another difference with other reduced-order methods is that it is not based on an off-line/on-line strategy. Numerical examples are shown for the linear advection, KdV and FKPP equations, in one and two dimensions.
Implicit Euler approximation of stochastic evolution equations with fractional Brownian motion
NASA Astrophysics Data System (ADS)
Kamrani, Minoo; Jamshidi, Nahid
2017-03-01
This work was intended as an attempt to motivate the approximation of quasi linear evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter H >1/2 . The spatial approximation method is based on Galerkin and the temporal approximation is based on implicit Euler scheme. An error bound and the convergence of the numerical method are given. The numerical results show usefulness and accuracy of the method.
Schüler, D; Alonso, S; Torcini, A; Bär, M
2014-12-01
Pattern formation often occurs in spatially extended physical, biological, and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and their characteristic length scales. However, patterns resulting from the simultaneous occurrence of instabilities cannot be expected to be simple superposition of the patterns associated with the considered instabilities. To address this issue, we design two simple models composed by two asymmetrically coupled equations of non-conserved (Swift-Hohenberg equations) or conserved (Cahn-Hilliard equations) order parameters with different characteristic wave lengths. The patterns arising in these systems range from coexisting static patterns of different wavelengths to traveling waves. A linear stability analysis allows to derive a two parameter phase diagram for the studied models, in particular, revealing for the Swift-Hohenberg equations, a co-dimension two bifurcation point of Turing and wave instability and a region of coexistence of stationary and traveling patterns. The nonlinear dynamics of the coupled evolution equations is investigated by performing accurate numerical simulations. These reveal more complex patterns, ranging from traveling waves with embedded Turing patterns domains to spatio-temporal chaos, and a wide hysteretic region, where waves or Turing patterns coexist. For the coupled Cahn-Hilliard equations the presence of a weak coupling is sufficient to arrest the coarsening process and to lead to the emergence of purely periodic patterns. The final states are characterized by domains with a characteristic length, which diverges logarithmically with the coupling amplitude.
Recent progress on the understanding of the medium-induced jet evolution and energy loss in pQCD
NASA Astrophysics Data System (ADS)
Apolinário, Liliana
2017-03-01
Motivated by the striking modifications of jets observed both at RHIC and the LHC, significant progress towards the understanding of jet dynamics within QGP has occurred over the last few years. In this talk, I review the recent theoretical developments in the study of medium-induced jet evolution and energy loss within a perturbative framework. The main mechanisms of energy loss and broadening will be firstly addressed with focus on leading particle calculations beyond the eikonal approximation. Then, I will provide an overview of the modifications of the interference pattern between the different parton emitters that build up the parton shower when propagating through an extended coloured medium. I will show that the interplay between color coherence/decoherence that arises from such effects is the main mechanism for the modification of the jet core angular structure. Finally, I discuss the possibility of a probabilistic picture of the parton shower evolution in the limit of a very dense or infinite medium.
An equation for the evolution of solar and stellar flare loops
NASA Technical Reports Server (NTRS)
Fisher, George H.; Hawley, Suzanne L.
1990-01-01
An ordinary differential equation describing the evolution of a coronal loop subjected to a spatially uniform but time-varying heating rate is discussed. It is assumed that the duration of heating is long compared to the sound transit time through the loop, which is assumed to have uniform cross section area. The form of the equation changes as the loop evolves through three states: 'strong evaporation', 'scaling law behavior', and 'strong condensation'. Solutions to the equation may be used to compute the time dependence of the average coronal temperature and emission measure for an assumed temporal variation of the flare heating rate. The results computed from the model agree reasonably well with recent published numerical simulations and may be obtained with far less computational effort. The model is then used to study the May 21, 1980, solar flare observed by SMM and the giant April 12, 1985, flare observed on the star AD Leo.
Birth and death master equation for the evolution of complex networks
NASA Astrophysics Data System (ADS)
Alvarez-Martínez, R.; Cocho, G.; Rodríguez, R. F.; Martínez-Mekler, G.
2014-05-01
Master equations for the evolution of complex networks with positive (birth) and negative (death) transition probabilities per unit time are analyzed. Explicit equations for the time evolution of the total number of nodes and for the relative node frequencies are given. It is shown that, in the continuous limit, the master equation reduces to a Fokker-Planck equation (FPE). The basic dynamical function for its stationary solution is the ratio between its drift and diffusion coefficients. When this ratio is approximated by partial fractions (Padé's approximants), a hierarchy of stationary solutions of the FPE is obtained analytically, which are expressed as an exponential times the product of powers of monomials and binomials. It is also shown that if the difference between birth and death transition probabilities goes asymptotically to zero, the exponential factor in the solution is absent. Fits to real complex network probability distribution functions are shown. Comparison with rank-ordered data shows that, in general, the value of this exponential factor is close to unity, evidencing crossovers among power-law scale invariant regimes which might be associated to an underlying criticality and are related to a generalization of the beta distribution. The time dependent solution is also obtained analytically in terms of hyper-geometric functions. It is also shown that the FPE has similarity solutions. The limitations of the approach here presented are also discussed.
On the interface between perturbative and nonperturbative QCD
NASA Astrophysics Data System (ADS)
Deur, Alexandre; Brodsky, Stanley J.; de Téramond, Guy F.
2016-06-01
The QCD running coupling αs (Q2) sets the strength of the interactions of quarks and gluons as a function of the momentum transfer Q. The Q2 dependence of the coupling is required to describe hadronic interactions at both large and short distances. In this article we adopt the light-front holographic approach to strongly-coupled QCD, a formalism which incorporates confinement, predicts the spectroscopy of hadrons composed of light quarks, and describes the low-Q2 analytic behavior of the strong coupling αs (Q2). The high-Q2 dependence of the coupling αs (Q2) is specified by perturbative QCD and its renormalization group equation. The matching of the high and low Q2 regimes of αs (Q2) then determines the scale Q0 which sets the interface between perturbative and nonperturbative hadron dynamics. The value of Q0 can be used to set the factorization scale for DGLAP evolution of hadronic structure functions and the ERBL evolution of distribution amplitudes. We discuss the scheme-dependence of the value of Q0 and the infrared fixed-point of the QCD coupling. Our analysis is carried out for the MS ‾, g1, MOM and V renormalization schemes. Our results show that the discrepancies on the value of αs at large distance seen in the literature can be explained by different choices of renormalization schemes. We also provide the formulae to compute αs (Q2) over the entire range of space-like momentum transfer for the different renormalization schemes discussed in this article.
QCD thermodynamics and missing hadron states
NASA Astrophysics Data System (ADS)
Petreczky, Peter
2016-03-01
Equation of State and fluctuations of conserved charges in hot strongly interacting matter are being calculated with increasing accuracy in lattice QCD, and continuum results at physical quark masses become available. At sufficiently low temperature the thermodynamic quantities can be understood in terms of hadron resonance gas model that includes known hadrons and hadronic resonances from Particle Data Book. However, for some quantities it is necessary to include undiscovered hadronic resonances (missing states) that are, however, predicted by quark model and lattice QCD study of hadron spectrum. Thus, QCD thermodynamics can provide indications for the existence of yet undiscovered hadron states.
Random walk through recent CDF QCD results
C. Mesropian
2003-04-09
We present recent results on jet fragmentation, jet evolution in jet and minimum bias events, and underlying event studies. The results presented in this talk address significant questions relevant to QCD and, in particular, to jet studies. One topic discussed is jet fragmentation and the possibility of describing it down to very small momentum scales in terms of pQCD. Another topic is the studies of underlying event energy originating from fragmentation of partons not associated with the hard scattering.
NASA Astrophysics Data System (ADS)
Barnes, T.
2005-12-01
In this contribution we briefly summarize aspects of the physics of QCD which are relevant to the supernova problem. The topic of greatest importance is the equation of state (EOS) of nuclear and strongly-interacting matter, which is required to describe the physics of the proto-neutron star (PNS) and the neutron star remnant (NSR) formed during a supernova event. Evaluation of the EOS in the regime of relevance for these systems, especially the NSR, requires detailed knowledge of the spectrum and strong interactions of hadrons of the accessible hadronic species, as well as other possible phases of strongly interacting matter, such as the quark-gluon plasma (QGP). The forces between pairs of baryons (both nonstrange and strange) are especially important in determining the EOS at NSR densities. Predictions for these forces are unfortunately rather model dependent where not constrained by data, and there are several suggestions for the QCD mechanism underlying these short-range hadronic interactions. The models most often employed for determining these strong interactions are broadly of two types, 1) meson exchange models (usually assumed in the existing neutron star and supernova literature), and 2) quark-gluon models (mainly encountered in the hadron, nuclear and heavy-ion literature). Here we will discuss the assumptions made in these models, and discuss how they are applied to the determination of hadronic forces that are relevant to the supernova problem.
An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations.
Mirzaev, Inom; Byrne, Erin C; Bortz, David M
2016-01-01
We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach.
An inverse problem for a class of conditional probability measure-dependent evolution equations
NASA Astrophysics Data System (ADS)
Mirzaev, Inom; Byrne, Erin C.; Bortz, David M.
2016-09-01
We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by partial differential equation models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach.
NASA Astrophysics Data System (ADS)
Annamalai, Subramanian; Balachandar, S.; Sridharan, P.; Jackson, T. L.
2017-02-01
An analytical expression describing the unsteady pressure evolution of the dispersed phase driven by variations in the carrier phase is presented. In this article, the term "dispersed phase" represents rigid particles, droplets, or bubbles. Letting both the dispersed and continuous phases be inhomogeneous, unsteady, and compressible, the developed pressure equation describes the particle response and its eventual equilibration with that of the carrier fluid. The study involves impingement of a plane traveling wave of a given frequency and subsequent volume-averaged particle pressure calculation due to a single wave. The ambient or continuous fluid's pressure and density-weighted normal velocity are identified as the source terms governing the particle pressure. Analogous to the generalized Faxén theorem, which is applicable to the particle equation of motion, the pressure expression is also written in terms of the surface average of time-varying incoming flow properties. The surface average allows the current formulation to be generalized for any complex incident flow, including situations where the particle size is comparable to that of the incoming flow. Further, the particle pressure is also found to depend on the dispersed-to-continuous fluid density ratio and speed of sound ratio in addition to dynamic viscosities of both fluids. The model is applied to predict the unsteady pressure variation inside an aluminum particle subjected to normal shock waves. The results are compared against numerical simulations and found to be in good agreement. Furthermore, it is shown that, although the analysis is conducted in the limit of negligible flow Reynolds and Mach numbers, it can be used to compute the density and volume of the dispersed phase to reasonable accuracy. Finally, analogous to the pressure evolution expression, an equation describing the time-dependent particle radius is deduced and is shown to reduce to the Rayleigh-Plesset equation in the linear limit.
Nuclear reactions from lattice QCD
Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C.
2015-01-13
In this study, one of the overarching goals of nuclear physics is to rigorously compute properties of hadronic systems directly from the fundamental theory of strong interactions, Quantum Chromodynamics (QCD). In particular, the hope is to perform reliable calculations of nuclear reactions which will impact our understanding of environments that occur during big bang nucleosynthesis, the evolution of stars and supernovae, and within nuclear reactors and high energy/density facilities. Such calculations, being truly ab initio, would include all two-nucleon and three- nucleon (and higher) interactions in a consistent manner. Currently, lattice QCD provides the only reliable option for performing calculationsmore » of some of the low-energy hadronic observables. With the aim of bridging the gap between lattice QCD and nuclear many-body physics, the Institute for Nuclear Theory held a workshop on Nuclear Reactions from Lattice QCD on March 2013. In this review article, we report on the topics discussed in this workshop and the path planned to move forward in the upcoming years.« less
Nuclear reactions from lattice QCD
Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C.
2015-01-13
In this study, one of the overarching goals of nuclear physics is to rigorously compute properties of hadronic systems directly from the fundamental theory of strong interactions, Quantum Chromodynamics (QCD). In particular, the hope is to perform reliable calculations of nuclear reactions which will impact our understanding of environments that occur during big bang nucleosynthesis, the evolution of stars and supernovae, and within nuclear reactors and high energy/density facilities. Such calculations, being truly ab initio, would include all two-nucleon and three- nucleon (and higher) interactions in a consistent manner. Currently, lattice QCD provides the only reliable option for performing calculations of some of the low-energy hadronic observables. With the aim of bridging the gap between lattice QCD and nuclear many-body physics, the Institute for Nuclear Theory held a workshop on Nuclear Reactions from Lattice QCD on March 2013. In this review article, we report on the topics discussed in this workshop and the path planned to move forward in the upcoming years.
Lattice QCD input for axion cosmology
NASA Astrophysics Data System (ADS)
Berkowitz, Evan; Buchoff, Michael I.; Rinaldi, Enrico
2015-08-01
One intriguing beyond-the-Standard-Model particle is the QCD axion, which could simultaneously provide a solution to the Strong C P Problem and account for some, if not all, of the dark matter density in the Universe. This particle is a pseudo-Nambu-Goldstone boson of the conjectured Peccei-Quinn symmetry of the Standard Model. Its mass and interactions are suppressed by a heavy symmetry-breaking scale, fa, the value of which is roughly greater than 109 GeV (or, conversely, the axion mass, ma, is roughly less than 104 μ eV ). The density of axions in the Universe, which cannot exceed the relic dark matter density and is a quantity of great interest in axion experiments like ADMX, is a result of the early Universe interplay between cosmological evolution and the axion mass as a function of temperature. The latter quantity is proportional to the second derivative of the temperature-dependent QCD free energy with respect to the C P -violating phase, θ . However, this quantity is generically nonperturbative, and previous calculations have only employed instanton models at the high temperatures of interest (roughly 1 GeV). In this and future works, we aim to calculate the temperature-dependent axion mass at small θ from first-principle lattice calculations, with controlled statistical and systematic errors. Once calculated, this temperature-dependent axion mass is input for the classical evolution equations of the axion density of the Universe, which is required to be less than or equal to the dark matter density. Due to a variety of lattice systematic effects at the very high temperatures required, we perform a calculation of the leading small-θ cumulant of the theta vacua on large volume lattices for SU(3) Yang-Mills with high statistics as a first proof of concept, before attempting a full QCD calculation in the future. From these pure glue results, the misalignment mechanism yields the axion mass bound ma≥(14.6 ±0.1 ) μ eV when Peccei-Quinn breaking occurs
Heavy Quarks, QCD, and Effective Field Theory
Thomas Mehen
2012-10-09
The research supported by this OJI award is in the area of heavy quark and quarkonium production, especially the application Soft-Collinear E ective Theory (SCET) to the hadronic production of quarkonia. SCET is an e ffective theory which allows one to derive factorization theorems and perform all order resummations for QCD processes. Factorization theorems allow one to separate the various scales entering a QCD process, and in particular, separate perturbative scales from nonperturbative scales. The perturbative physics can then be calculated using QCD perturbation theory. Universal functions with precise fi eld theoretic de nitions describe the nonperturbative physics. In addition, higher order perturbative QCD corrections that are enhanced by large logarithms can be resummed using the renormalization group equations of SCET. The applies SCET to the physics of heavy quarks, heavy quarkonium, and similar particles.
Towards a theoretical description of dense QCD
NASA Astrophysics Data System (ADS)
Philipsen, Owe
2017-03-01
The properties of matter at finite baryon densities play an important role for the astrophysics of compact stars as well as for heavy ion collisions or the description of nuclear matter. Because of the sign problem of the quark determinant, lattice QCD cannot be simulated by standard Monte Carlo at finite baryon densities. I review alternative attempts to treat dense QCD with an effective lattice theory derived by analytic strong coupling and hopping expansions, which close to the continuum is valid for heavy quarks only, but shows all qualitative features of nuclear physics emerging from QCD. In particular, the nuclear liquid gas transition and an equation of state for baryons can be calculated directly from QCD. A second effective theory based on strong coupling methods permits studies of the phase diagram in the chiral limit on coarse lattices.
Mechanisms of chiral symmetry breaking in QCD: A lattice perspective
NASA Astrophysics Data System (ADS)
Giusti, Leonardo
2016-01-01
I briefly review two recent studies on chiral symmetry breaking in QCD: (a) a computation of the spectral density of the Dirac operator in QCD Lite, (b) a precise determination of the topological charge distribution in the SU(3) Yang-Mills theory as defined by evolving the fundamental gauge field with the Yang-Mills gradient flow equation.
On the classification of scalar evolution equations with non-constant separant
NASA Astrophysics Data System (ADS)
Hümeyra Bilge, Ayşe; Mizrahi, Eti
2017-01-01
The ‘separant’ of the evolution equation u t = F, where F is some differentiable function of the derivatives of u up to order m, is the partial derivative \\partial F/\\partial {{u}m}, where {{u}m}={{\\partial}m}u/\\partial {{x}m} . As an integrability test, we use the formal symmetry method of Mikhailov-Shabat-Sokolov, which is based on the existence of a recursion operator as a formal series. The solvability of its coefficients in the class of local functions gives a sequence of conservation laws, called the ‘conserved densities’ {ρ(i)}, i=-1,1,2,3,\\ldots . We apply this method to the classification of scalar evolution equations of orders 3≤slant m≤slant 15 , for which {ρ(-1)}={≤ft[\\partial F/\\partial {{u}m}\\right]}-1/m} and {{ρ(1)} are non-trivial, i.e. they are not total derivatives and {ρ(-1)} is not linear in its highest order derivative. We obtain the ‘top level’ parts of these equations and their ‘top dependencies’ with respect to the ‘level grading’, that we defined in a previous paper, as a grading on the algebra of polynomials generated by the derivatives u b+i , over the ring of {{C}∞} functions of u,{{u}1},\\ldots,{{u}b} . In this setting b and i are called ‘base’ and ‘level’, respectively. We solve the conserved density conditions to show that if {ρ(-1)} depends on u,{{u}1},\\ldots,{{u}b}, then, these equations are level homogeneous polynomials in {{u}b+i},\\ldots,{{u}m} , i≥slant 1 . Furthermore, we prove that if {ρ(3)} is non-trivial, then {ρ(-1)}={≤ft(α ub2+β {{u}b}+γ \\right)}1/2} , with b≤slant 3 while if {{ρ(3)} is trivial, then {ρ(-1)}={≤ft(λ {{u}b}+μ \\right)}1/3} , where b≤slant 5 and α, β, γ, λ and μ are functions of u,\\ldots,{{u}b-1} . We show that the equations that we obtain form commuting flows and we construct their recursion operators that are respectively of orders 2 and 6 for non-trivial and trivial {{ρ(3)} respectively. Omitting lower order
A 0-D flame wrinkling equation to describe the turbulent flame surface evolution in SI engines
NASA Astrophysics Data System (ADS)
Richard, Stéphane; Veynante, Denis
2015-03-01
The current development of reciprocating engines relies increasingly on system simulation for both design activities and conception of algorithms for engine control. These numerical simulation tools require high computational efficiencies, as calculations have to be performed in times close to real-time. Then, they are today mainly based on simple empirical laws to describe the combustion processes in the cylinders. However, with the rapid evolution of emission regulations and fuel formulation, more and more physics is expected in combustion models. A solution consists in reducing 3-D combustion models to build 0-dimensional models that are both CPU-efficient and based on physical quantities. This approach has been used in a previous work to reduce the 3-D ECFM (Extended Coherent Flame Model), leading to the so-called CFM1D. A key feature of the latter is to be based on a 0-D equation for the flame wrinkling derived from the 3-D equation for the flame surface density. The objective of this paper is to present in details the theoretical derivation of the wrinkling equation and the underlying modeling assumptions as well. Academic validations are performed against experimental data for several turbulence intensities and fuels. Finally, the proposed model is applied to engine simulations for a wide range of operating conditions. Comparisons are successfully conducted between in-cylinder measurements and the model predictions, highlighting the interest of reducing 3-D CFD models for calculations performed in the context of system simulation.
Cauchy Problem for Evolution Equations of Schrödinger Type
NASA Astrophysics Data System (ADS)
Agliardi, Rossella
2002-03-01
In (R. Agliardi, 1995, Internat. J. Math.6, 791-804) we proved the well-posedness of the Cauchy problem in H∞ for some p-evolution equations (p⩾1) with real characteristic roots. For this purpose some assumptions on the lower order terms are needed, which, in the special case p=1, recapture well-known results for hyperbolic operators. In (R. Agliardi, 1995, Internat. J. Math.6, 791-804) the leading coefficients are assumed to be constant. In this paper we allow them to be variable. Our result is applicable to 2-evolution differential operators with real characteristics, i.e., to Schrödinger type operators. This class of operators comprehends, for example, Schrödinger operator Dt-Δx or the plate operator D2t-Δ2x. The Cauchy problem in H∞ for such evolution operators has been studied extensively by Takeuchi when the coefficients in the principal part are constant and the characteristic roots are distinct.
Non-perturbative QCD and hadron physics
NASA Astrophysics Data System (ADS)
Cobos-Martínez, J. J.
2016-10-01
A brief exposition of contemporary non-perturbative methods based on the Schwinger-Dyson (SDE) and Bethe-Salpeter equations (BSE) of Quantum Chromodynamics (QCD) and their application to hadron physics is given. These equations provide a non-perturbative continuum formulation of QCD and are a powerful and promising tool for the study of hadron physics. Results on some properties of hadrons based on this approach, with particular attention to the pion distribution amplitude, elastic, and transition electromagnetic form factors, and their comparison to experimental data are presented.
NASA Astrophysics Data System (ADS)
Mukherjee, Abhik; Janaki, M. S.; Kundu, Anjan
2015-07-01
A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.
Mukherjee, Abhik Janaki, M. S. Kundu, Anjan
2015-07-15
A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the corresponding growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.
Nucleon QCD sum rules in the instanton medium
Ryskin, M. G.; Drukarev, E. G. Sadovnikova, V. A.
2015-09-15
We try to find grounds for the standard nucleon QCD sum rules, based on a more detailed description of the QCD vacuum. We calculate the polarization operator of the nucleon current in the instanton medium. The medium (QCD vacuum) is assumed to be a composition of the small-size instantons and some long-wave gluon fluctuations. We solve the corresponding QCD sum rule equations and demonstrate that there is a solution with the value of the nucleon mass close to the physical one if the fraction of the small-size instantons contribution is w{sub s} ≈ 2/3.
NASA Astrophysics Data System (ADS)
Freire, Igor Leite; Santos Sampaio, Júlio Cesar
2014-02-01
In this paper we consider a class of evolution equations up to fifth-order containing many arbitrary smooth functions from the point of view of nonlinear self-adjointness. The studied class includes many important equations modeling different phenomena. In particular, some of the considered equations were studied previously by other researchers from the point of view of quasi self-adjointness or strictly self-adjointness. Therefore we find new local conservation laws for these equations invoking the obtained results on nonlinearly self-adjointness and the conservation theorem proposed by Nail Ibragimov.
Evolution equations for the joint probability of several compositions in turbulent combustion
Bakosi, Jozsef
2010-01-01
One-point statistical simulations of turbulent combustion require models to represent the molecular mixing of species mass fractions, which then determine the reaction rates. For multi-species mixing the Dirichlet distribution has been used to characterize the assumed joint probability density function (PDF) of several scalars, parametrized by solving modeled evolution equations for their means and the sum of their variances. The PDF is then used to represent the mixing state and to obtain the chemical reactions source terms in moment closures or large eddy simulation. We extend the Dirichlet PDF approach to transported PDF methods by developing its governing stochastic differential equation (SDE). The transport equation, as opposed to parametrizing the assumed PDF, enables (1) the direct numerical computation of the joint PDF (and therefore the mixing model to directly account for the flow dynamics (e.g. reaction) on the shape of the evolving PDF), and (2) the individual specification of the mixing timescales of each species. From the SDE, systems of equations are derived that govern the first two moments, based on which constraints are established that provide consistency conditions for material mixing. A SDE whose solution is the generalized Dirichlet PDF is also developed and some of its properties from the viewpoint of material mixing are investigated. The generalized Dirichlet distribution has the following advantages over the standard Dirichlet distribution due to its more general covariance structure: (1) its ability to represent differential diffusion (i.e. skewness) without affecting the scalar means, and (2) it can represent both negatively and positively correlated scalars. The resulting development is a useful representation of the joint PDF of inert or reactive scalars in turbulent flows: (1) In moment closures, the mixing physics can be consistently represented by one underlying modeling principle, the Dirichlet or the generalized Dirichlet PDF, and
Nuclear forces from lattice QCD
Ishii, Noriyoshi
2011-05-06
Lattice QCD construction of nuclear forces is reviewed. In this method, the nuclear potentials are constructed by solving the Schroedinger equation, where equal-time Nambu-Bethe-Salpeter (NBS) wave functions are regarded as quantum mechanical wave functions. Since the long distance behavior of equal-time NBS wave functions is controlled by the scattering phase, which is in exactly the same way as scattering wave functions in quantum mechanics, the resulting potentials are faithful to the NN scattering data. The derivative expansion of this potential leads to the central and the tensor potentials at the leading order. Some of numerical results of these two potentials are shown based on the quenched QCD.
Chiral magnetic wave in an expanding QCD fluid
NASA Astrophysics Data System (ADS)
Taghavi, Seyed Farid; Wiedemann, Urs Achim
2015-02-01
As a consequence of the chiral anomaly, the hydrodynamics of hot quantum chromodynamics (QCD) matter coupled to quantum electrodynamics allows for a long-wavelength mode of chiral charge density, the chiral magnetic wave (CMW), that provides for a mechanism of electric charge separation along the direction of an external magnetic field. Here, we investigate the efficiency of this mechanism for values of the time-dependent magnetic field and of the energy density attained in the hot QCD matter of ultrarelativistic heavy-ion collisions. To this end, we derive the CMW equations of motion for expanding systems by treating the CMW as a charge perturbation on top of an expanding Bjorken-type background field in the limit μ /T ≪1 . Both, approximate analytical and full numerical solutions to these equations of motion, indicate that for the lifetime and thermodynamic conditions of ultrarelativistic heavy-ion collisions, the efficiency of CMW-induced electric charge separation decreases with increasing center-of-mass energy and that the effect is numerically very small. We note, however, that if sizable oriented asymmetries in the axial charge distribution (that are not induced by the CMW) are present in the early fluid dynamic evolution, then the mechanism of CMW-induced electric charge separation can be much more efficient.
Diffusion-equation representations of landform evolution in the simplest circumstances: Appendix C
Hanks, Thomas C.
2009-01-01
Most of us here know that the diffusion equation has also been used to describe the evolution through time of scarp-like landforms, including fault scarps, shoreline scarps, or a set of marine terraces. The methods, models, and data employed in such studies have been described in the literature many times over the past 25 years. For most situations, everything you will ever need (or want) to know can be found in Hanks et al. (1984) and Hanks (2000), the latter being a review of numerous studies of the 1980s and 1990s and a summary of available estimates of the mass diffusivity κ. The geometric parameterization of scarp-like landforms is shown in Figure 1.
Holographic models and the QCD trace anomaly
Jose L. Goity, Roberto C. Trinchero
2012-08-01
Five dimensional dilaton models are considered as possible holographic duals of the pure gauge QCD vacuum. In the framework of these models, the QCD trace anomaly equation is considered. Each quantity appearing in that equation is computed by holographic means. Two exact solutions for different dilaton potentials corresponding to perturbative and non-perturbative {beta}-functions are studied. It is shown that in the perturbative case, where the {beta}-function is the QCD one at leading order, the resulting space is not asymptotically AdS. In the non-perturbative case, the model considered presents confinement of static quarks and leads to a non-vanishing gluon condensate, although it does not correspond to an asymptotically free theory. In both cases analyses based on the trace anomaly and on Wilson loops are carried out.
El Mouden, C; André, J-B; Morin, O; Nettle, D
2014-02-01
Transmitted culture can be viewed as an inheritance system somewhat independent of genes that is subject to processes of descent with modification in its own right. Although many authors have conceptualized cultural change as a Darwinian process, there is no generally agreed formal framework for defining key concepts such as natural selection, fitness, relatedness and altruism for the cultural case. Here, we present and explore such a framework using the Price equation. Assuming an isolated, independently measurable culturally transmitted trait, we show that cultural natural selection maximizes cultural fitness, a distinct quantity from genetic fitness, and also that cultural relatedness and cultural altruism are not reducible to or necessarily related to their genetic counterparts. We show that antagonistic coevolution will occur between genes and culture whenever cultural fitness is not perfectly aligned with genetic fitness, as genetic selection will shape psychological mechanisms to avoid susceptibility to cultural traits that bear a genetic fitness cost. We discuss the difficulties with conceptualizing cultural change using the framework of evolutionary theory, the degree to which cultural evolution is autonomous from genetic evolution, and the extent to which cultural change should be seen as a Darwinian process. We argue that the nonselection components of evolutionary change are much more important for culture than for genes, and that this and other important differences from the genetic case mean that different approaches and emphases are needed for cultural than genetic processes.
NASA Astrophysics Data System (ADS)
Hill, Richard J.; Solon, Mikhail P.
2015-02-01
Models of weakly interacting massive particles (WIMPs) specified at the electroweak scale are systematically matched to effective theories at hadronic scales where WIMP-nucleus scattering observables are evaluated. Anomalous dimensions and heavy-quark threshold matching conditions are computed for the complete basis of lowest-dimension effective operators involving quarks and gluons. The resulting QCD renormalization group evolution equations are solved. The status of relevant hadronic matrix elements is reviewed and phenomenological illustrations are given, including details for the computation of the universal limit of nucleon scattering with heavy S U (2 )W×U (1 )Y charged WIMPs. Several cases of previously underestimated hadronic uncertainties are isolated. The results connect arbitrary models specified at the electroweak scale to a basis of nf=3 -flavor QCD operators. The complete basis of operators and Lorentz invariance constraints through order v2/c2 in the nonrelativistic nucleon effective theory are derived.
Bäcklund Transformations and Non-Abelian Nonlinear Evolution Equations: a Novel Bäcklund Chart
NASA Astrophysics Data System (ADS)
Carillo, Sandra; Lo Schiavo, Mauro; Schiebold, Cornelia
2016-08-01
Classes of third order non-Abelian evolution equations linked to that of Korteweg-de Vries-type are investigated and their connections represented in a non-commutative Bäcklund chart, generalizing results in [Fuchssteiner B., Carillo S., Phys. A 154 (1989), 467-510]. The recursion operators are shown to be hereditary, thereby allowing the results to be extended to hierarchies. The present study is devoted to operator nonlinear evolution equations: general results are presented. The implied applications referring to finite-dimensional cases will be considered separately.
Nonlinear Evolution Equation of a Step with Anisotropy in a Diffusion Field for the Two-Sided Model
NASA Astrophysics Data System (ADS)
Mori, H.; Soma, T.; Okuda, K.; Wada, K.
2004-05-01
The nonlinear evolution equation for the fluctuation of a terrace edge with anisotropy in step stiffness during step flow growth is derived in the two-sided model where adatoms can be incorporated into the step from the upper terrace as well as from the lower terrace. It is shown by reductive perturbation method based on the linear stability analysis that (1) up to ɛ3 order in the smallness parameter of instability the nonlinear evolution equation reduces to the closed Kuramoto-Sivashinsky (KS) equation with extra coefficients compared with the one-sided model and (2) the nonlinear evolution equation up to ɛ5 order is also derived in order to take into account the anisotropy in step stiffness in the lowest order. The nonlinear evolution equation is numerically calculated for various parameters included. It is also shown that the asymmetry of attachment into a step and the Gibbs-Thomson effect with anisotropy in step stiffness bring about various growth patterns of the step from chaotic growth to periodic growth and further to an inclined straight step mode with a single peak.
NASA Astrophysics Data System (ADS)
Parkes, E. J.; Duffy, B. R.
1996-11-01
The tanh-function method for finding explicit travelling solitary wave solutions to non-linear evolution equations is described. The method is usually extremely tedious to use by hand. We present a Mathematica package ATFM that deals with the tedious algebra and outputs directly the required solutions. The use of the package is illustrated by applying it to a variety of equations; not only are previously known solutions recovered but in some cases more general forms of solution are obtained.
NASA Astrophysics Data System (ADS)
Kogoj, Alessia E.
2017-02-01
We show how to apply harmonic spaces potential theory in the study of the Dirichlet problem for a general class of evolution hypoelliptic partial differential equations of second order. We construct Perron-Wiener solution and we provide a sufficient condition for the regularity of the boundary points. Our criterion extends and generalizes the classical parabolic-cone criterion for the Heat equation due to Effros and Kazdan.
NASA Astrophysics Data System (ADS)
Bai, Yang; Schwaller, Pedro
2014-03-01
Most of the mass of ordinary matter has its origin from quantum chromodynamics (QCD). A similar strong dynamics, dark QCD, could exist to explain the mass origin of dark matter. Using infrared fixed points of the two gauge couplings, we provide a dynamical mechanism that relates the dark QCD confinement scale to our QCD scale, and hence provides an explanation for comparable dark baryon and proton masses. Together with a mechanism that generates equal amounts of dark baryon and ordinary baryon asymmetries in the early Universe, the similarity of dark matter and ordinary matter energy densities can be naturally explained. For a large class of gauge group representations, the particles charged under both QCD and dark QCD, necessary ingredients for generating the infrared fixed points, are found to have masses at 1-2 TeV, which sets the scale for dark matter direct detection and novel collider signatures involving visible and dark jets.
NASA Astrophysics Data System (ADS)
Wilczek, Frank
Introduction Symmetry and the Phenomena of QCD Apparent and Actual Symmetries Asymptotic Freedom Confinement Chiral Symmetry Breaking Chiral Anomalies and Instantons High Temperature QCD: Asymptotic Properties Significance of High Temperature QCD Numerical Indications for Quasi-Free Behavior Ideas About Quark-Gluon Plasma Screening Versus Confinement Models of Chiral Symmetry Breaking More Refined Numerical Experiments High-Temperature QCD: Phase Transitions Yoga of Phase Transitions and Order Parameters Application to Glue Theories Application to Chiral Transitions Close Up on Two Flavors A Genuine Critical Point! (?) High-Density QCD: Methods Hopes, Doubts, and Fruition Another Renormalization Group Pairing Theory Taming the Magnetic Singularity High-Density QCD: Color-Flavor Locking and Quark-Hadron Continuity Gauge Symmetry (Non)Breaking Symmetry Accounting Elementary Excitations A Modified Photon Quark-Hadron Continuity Remembrance of Things Past More Quarks Fewer Quarks and Reality
APFEL: A PDF evolution library with QED corrections
NASA Astrophysics Data System (ADS)
Bertone, Valerio; Carrazza, Stefano; Rojo, Juan
2014-06-01
Quantum electrodynamics and electroweak corrections are important ingredients for many theoretical predictions at the LHC. This paper documents APFEL, a new PDF evolution package that allows for the first time to perform DGLAP evolution up to NNLO in QCD and to LO in QED, in the variable-flavor-number scheme and with either pole or MS bar heavy quark masses. APFEL consistently accounts for the QED corrections to the evolution of quark and gluon PDFs and for the contribution from the photon PDF in the proton. The coupled QCD ⊗ QED equations are solved in x-space by means of higher order interpolation, followed by Runge-Kutta solution of the resulting discretized evolution equations. APFEL is based on an innovative and flexible methodology for the sequential solution of the QCD and QED evolution equations and their combination. In addition to PDF evolution, APFEL provides a module that computes Deep-Inelastic Scattering structure functions in the FONLL general-mass variable-flavor-number scheme up to O(αs2) . All the functionalities of APFEL can be accessed via a Graphical User Interface, supplemented with a variety of plotting tools for PDFs, parton luminosities and structure functions. Written in FORTRAN 77, APFEL can also be used via the C/C++ and Python interfaces, and is publicly available from the HepForge repository.
Frontiers of finite temperature lattice QCD
NASA Astrophysics Data System (ADS)
Borsányi, Szabolcs
2017-03-01
I review a selection of recent finite temperature lattice results of the past years. First I discuss the extension of the equation of state towards high temperatures and finite densities, then I show recent results on the QCD topological susceptibility at high temperatures and highlight its relevance for dark matter search.
NASA Astrophysics Data System (ADS)
Liu, Yin-Ping; Li, Zhi-Bin
2003-03-01
Based on a type of elliptic equation, a new algebraic method to construct a series of exact solutions for nonlinear evolution equations is proposed, meanwhile, its complete implementation TRWS in Maple is presented. The TRWS can output a series of travelling wave solutions entirely automatically, which include polynomial solutions, exponential function solutions, triangular function solutions, hyperbolic function solutions, rational function solutions, Jacobi elliptic function solutions, and Weierstrass elliptic function solutions. The effectiveness of the package is illustrated by applying it to a variety of equations. Not only are previously known solutions recovered but also new solutions and more general form of solutions are obtained.
QCD thermodynamics on a lattice
NASA Astrophysics Data System (ADS)
Levkova, Ludmila A.
Numerical simulations of full QCD on anisotropic lattices provide a convenient way to study QCD thermodynamics with fixed physics scales and reduced lattice spacing errors. We report results from calculations with two flavors of dynamical staggered fermions, where all bare parameters and the renormalized anisotropy are kept constant and the temperature is changed in small steps by varying only the number of time slices. Including results from zero-temperature scale setting simulations, which determine the Karsch coefficients, allows for the calculation of the Equation of State at finite temperatures. We also report on studies of the chiral properties of dynamical domain-wall fermions combined with the DBW2 gauge action for different gauge couplings and fermion masses. For quenched theories, the DBW2 action gives a residual chiral symmetry breaking much smaller than what was found with more traditional choices for the gauge action. Our goal is to investigate the possibilities which this and further improvements provide for the study of QCD thermodynamics and other simulations at stronger couplings.
Continuous Advances in QCD 2008
NASA Astrophysics Data System (ADS)
Peloso, Marco M.
2008-12-01
1. High-order calculations in QCD and in general gauge theories. NLO evolution of color dipoles / I. Balitsky. Recent perturbative results on heavy quark decays / J. H. Piclum, M. Dowling, A. Pak. Leading and non-leading singularities in gauge theory hard scattering / G. Sterman. The space-cone gauge, Lorentz invariance and on-shell recursion for one-loop Yang-Mills amplitudes / D. Vaman, Y.-P. Yao -- 2. Heavy flavor physics. Exotic cc¯ mesons / E. Braaten. Search for new physics in B[symbol]-mixing / A. J. Lenz. Implications of D[symbol]-D[symbol] mixing for new physics / A. A. Petrov. Precise determinations of the charm quark mass / M. Steinhauser -- 3. Quark-gluon dynamics at high density and/or high temperature. Crystalline condensate in the chiral Gross-Neveu model / G. V. Dunne, G. Basar. The strong coupling constant at low and high energies / J. H. Kühn. Quarkyonic matter and the phase diagram of QCD / L. McLerran. Statistical QCD with non-positive measure / J. C. Osborn, K. Splittorff, J. J. M. Verbaarschot. From equilibrium to transport properties of strongly correlated fermi liquids / T. Schäfer. Lessons from random matrix theory for QCD at finite density / K. Splittorff, J. J. M. Verbaarschot -- 4. Methods and models of holographic correspondence. Soft-wall dynamics in AdS/QCD / B. Batell. Holographic QCD / N. Evans, E. Threlfall. QCD glueball sum rules and vacuum topology / H. Forkel. The pion form factor in AdS/QCD / H. J. Kwee, R. F. Lebed. The fast life of holographic mesons / R. C. Myers, A. Sinha. Properties of Baryons from D-branes and instantons / S. Sugimoto. The master space of N = 1 quiver gauge theories: counting BPS operators / A. Zaffaroni. Topological field congurations. Skyrmions in theories with massless adjoint quarks / R. Auzzi. Domain walls, localization and confinement: what binds strings inside walls / S. Bolognesi. Static interactions of non-abelian vortices / M. Eto. Vortices which do not abelianize dynamically: semi
NLO evolution of color dipoles in N=4 SYM
Chirilli, Giovanni A.; Balitsky, Ian
2009-07-04
Here, high-energy behavior of amplitudes in a gauge theory can be reformulated in terms of the evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the conformally invariant BK equation for the evolution of color dipoles. In QCD, the next-to-leading order BK equation has both conformal and non-conformal parts, the latter providing the running of the coupling constant. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformal ${\\cal N}$=4 SYM theory. We define the "composite dipole operator" with the rapidity cutoff preserving conformal invariance.
Cruz, Hans; Schuch, Dieter; Castaños, Octavio; Rosas-Ortiz, Oscar
2015-09-15
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.
Hansson, T; Lisak, M; Anderson, D
2012-02-10
It is shown that the evolution equations describing partially coherent wave propagation in noninstantaneous Kerr media are integrable and have an infinite number of invariants. A recursion relation for generating these invariants is presented, and it is demonstrated how to express them in the coherent density, self-consistent multimode, mutual coherence, and Wigner formalisms.
NASA Technical Reports Server (NTRS)
Thorne, K. S.; Zytkow, A. N.
1976-01-01
The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general relativistic version of the mixing-length formalism for convection is presented. Finally, it is argued that in previous work on spherical systems general relativity theorists have identified the wrong quantity as "total mass-energy inside radius r."
Anomalous mass dimension in multiflavor QCD
NASA Astrophysics Data System (ADS)
Doff, A.; Natale, A. A.
2016-10-01
Models of strongly interacting theories with a large mass anomalous dimension (γm) provide an interesting possibility for the dynamical origin of the electroweak symmetry breaking. A laboratory for these models is QCD with many flavors, which may present a nontrivial fixed point associated to a conformal region. Studies based on conformal field theories and on Schwinger-Dyson equations have suggested the existence of bounds on the mass anomalous dimension at the fixed points of these models. In this note we discuss γm values of multiflavor QCD exhibiting a nontrivial fixed point and affected by relevant four-fermion interactions.
Norniella, Olga; /Barcelona, IFAE
2005-01-01
Recent QCD measurements from the CDF collaboration at the Tevatron are presented, together with future prospects as the luminosity increases. The measured inclusive jet cross section is compared to pQCD NLO predictions. Precise measurements on jet shapes and hadronic energy flows are compared to different phenomenological models that describe gluon emissions and the underlying event in hadron-hadron interactions.
2012-01-01
Background This paper lies in the context of modeling the evolution of gene expression away from stationary states, for example in systems subject to external perturbations or during the development of an organism. We base our analysis on experimental data and proceed in a top-down approach, where we start from data on a system's transcriptome, and deduce rules and models from it without a priori knowledge. We focus here on a publicly available DNA microarray time series, representing the transcriptome of Drosophila across evolution from the embryonic to the adult stage. Results In the first step, genes were clustered on the basis of similarity of their expression profiles, measured by a translation-invariant and scale-invariant distance that proved appropriate for detecting transitions between development stages. Average profiles representing each cluster were computed and their time evolution was analyzed using coupled differential equations. A linear and several non-linear model structures involving a transcription and a degradation term were tested. The parameters were identified in three steps: determination of the strongest connections between genes, optimization of the parameters defining these connections, and elimination of the unnecessary parameters using various reduction schemes. Different solutions were compared on the basis of their abilities to reproduce the data, to keep realistic gene expression levels when extrapolated in time, to show the biologically expected robustness with respect to parameter variations, and to contain as few parameters as possible. Conclusions We showed that the linear model did very well in reproducing the data with few parameters, but was not sufficiently robust and yielded unrealistic values upon extrapolation in time. In contrast, the non-linear models all reached the latter two objectives, but some were unable to reproduce the data. A family of non-linear models, constructed from the exponential of linear combinations
NASA Astrophysics Data System (ADS)
Fratanduono, D.
2015-12-01
The thermal history of terrestrial planets depends upon the melt boundary as it represents the largest rheological transition a material can undergo. This change in rheological behavior with solidification corresponds to a dramatic change in the thermal and chemical transport properties. Because of this dramatic change in thermal transport, recent work by Stixrude et al.[1] suggests that the silicate melt curve sets the thermal profile within super-Earths during their early thermal evolution. Here we present recent decaying shock wave experiments studying both enstatite and forsterite. The continuously measured shock pressure and temperature in these studies ranged from 8 to 1.5 Mbar and 20,000-4,000 K, respectively. We find a point on the MgSiO3 liquidus at 6800 K and 285 GPa, which is nearly a factor of two higher pressure than previously measured and provides a strong constraint on the temperature profile within super-Earths. Our shock temperature measurements on forsterite and enstatite provide much needed equation of state information to the planetary impact modeling community since the shock temperature data can be used to constrain the initial entropy state of a growing planet. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. 1. Stixrude, L., Melting in super-earths. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 2014. 372(2014).
Molnar, Denes
2014-04-14
The Section below summarizes research activities and achievements during the first four years of the PI’s Early Career Research Project (ECRP). Two main areas have been advanced: i) radiative 3 ↔ 2 radiative transport, via development of a new computer code MPC/Grid that solves the Boltzmann transport equation in full 6+1D (3X+3V+time) on both single-CPU and parallel computers; ii) development of a self-consistent framework to convert viscous fluids to particles, and application of this framework to relativistic heavy-ion collisions, in particular, determination of the shear viscosity. Year 5 of the ECRP is under a separate award number, and therefore it has its own report document ’Final Technical Report for Year 5 of the Early Career Research Project “Viscosity and equation of state of hot and dense QCDmatter”’ (award DE-SC0008028). The PI’s group was also part of the DOE JET Topical Collaboration, a multi-institution project that overlapped in time significantly with the ECRP. Purdue achievements as part of the JET Topical Collaboration are in a separate report “Final Technical Report summarizing Purdue research activities as part of the DOE JET Topical Collaboration” (award DE-SC0004077).
Progress in vacuum susceptibilities and their applications to the chiral phase transition of QCD
Cui, Zhu-Fang; Hou, Feng-Yao; Shi, Yuan-Mei; Wang, Yong-Long; Zong, Hong-Shi
2015-07-15
The QCD vacuum condensates and various vacuum susceptibilities are all important parameters which characterize the nonperturbative properties of the QCD vacuum. In the QCD sum rules external field formula, various QCD vacuum susceptibilities play important roles in determining the properties of hadrons. In this paper, we review the recent progress in studies of vacuum susceptibilities together with their applications to the chiral phase transition of QCD. The results of the tensor, the vector, the axial–vector, the scalar, and the pseudo-scalar vacuum susceptibilities are shown in detail in the framework of Dyson–Schwinger equations.
Non-linear QCD dynamics and exclusive production in ep collisions
NASA Astrophysics Data System (ADS)
Gonçalves, V. P.; Machado, M. V. T.; Meneses, A. R.
2010-07-01
The exclusive processes in electron-proton ( ep) interactions are an important tool to investigate the QCD dynamics at high energies as they are in general driven by the gluon content of proton which is strongly subject to parton saturation effects. In this paper we compute the cross sections for the exclusive vector meson production as well as the deeply virtual Compton scattering (DVCS) relying on the color dipole approach and considering the numerical solution of the Balitsky-Kovchegov equation including running coupling corrections. We show that the small- x evolution given by this evolution equation is able to describe the DESY-HERA data and is relevant for the physics of the exclusive observables in future electron-proton colliders and in photoproduction processes to be measured in coherent interactions at the LHC.
Precision QCD measurements in DIS at HERA
NASA Astrophysics Data System (ADS)
Britzger, Daniel
2016-08-01
New and recent results on QCD measurements from the H1 and ZEUS experiments at the HERA ep collider are reviewed. The final results on the combined deep-inelastic neutral and charged current cross-sections are presented and their role in the extractions of parton distribution functions (PDFs) is studied. The PDF fits give insight into the compatibility of QCD evolution and heavy flavor schemes with the data as a function of kinematic variables such as the scale Q2. Measurements of jet production cross-sections in ep collisions provide direct proves of QCD and extractions of the strong coupling constants are performed. Charm and beauty cross-section measurements are used for the determination of the heavy quark masses. Their role in PDF fits is investigated. In the regime of diffractive DIS and photoproduction, dijet and prompt photon production cross-sections provide insights into the process of factorization and the nature of the diffractive exchange.
QCD explanation of oscillating hadron and jet multiplicity moments
NASA Astrophysics Data System (ADS)
Buican, M. A.; Förster, C.; Ochs, W.
2003-10-01
Ratios of multiplicity moments, H q (cumulant over factorial moments K q / F q ), have been observed to show an oscillatory behavior with respect to order, q. Recent studies of e + e - annihilations at LEP have shown, moreover, that the amplitude and oscillation length vary strongly with the jet resolution parameter y cut. We study the predictions of the perturbative QCD parton cascade assuming low non-perturbative cut-off (Q_0˜ Λ_{{QCD}}˜ few 100 MeV) and derive the expectations as a function of the CMS energy and jet resolution from threshold to very high energies. We consider numerical solutions of the evolution equations of gluodynamics in double logarithmic and modified leading logarithmic approximations (DLA, MLLA), as well as results from a parton MC with readjusted parameters. The main characteristics are obtained in MLLA, while a more numerically accurate description is obtained by the MC model. A unified description of correlations between hadrons and correlations between jets emerges, in particular for the transition region of small y cut.
Lattice QCD in rotating frames.
Yamamoto, Arata; Hirono, Yuji
2013-08-23
We formulate lattice QCD in rotating frames to study the physics of QCD matter under rotation. We construct the lattice QCD action with the rotational metric and apply it to the Monte Carlo simulation. As the first application, we calculate the angular momenta of gluons and quarks in the rotating QCD vacuum. This new framework is useful to analyze various rotation-related phenomena in QCD.
NASA Astrophysics Data System (ADS)
Beane, Silas
2016-09-01
Over the last several decades, theoretical nuclear physics has been evolving from a very-successful phenomenology of the properties of nuclei, to a first-principles derivation of the properties of visible matter in the Universe from the known underlying theories of Quantum Chromodynamics (QCD) and Electrodynamics. Many nuclear properties have now been calculated using lattice QCD, a method for treating QCD numerically with large computers. In this talk, some of the most recent results in this frontier area of nuclear theory will be reviewed.
Modeling QCD for Hadron Physics
Tandy, P. C.
2011-10-24
We review the approach to modeling soft hadron physics observables based on the Dyson-Schwinger equations of QCD. The focus is on light quark mesons and in particular the pseudoscalar and vector ground states, their decays and electromagnetic couplings. We detail the wide variety of observables that can be correlated by a ladder-rainbow kernel with one infrared parameter fixed to the chiral quark condensate. A recently proposed novel perspective in which the quark condensate is contained within hadrons and not the vacuum is mentioned. The valence quark parton distributions, in the pion and kaon, as measured in the Drell Yan process, are investigated with the same ladder-rainbow truncation of the Dyson-Schwinger and Bethe-Salpeter equations.
Wilsonian matching of effective field theory with underlying QCD
Harada, Masayasu; Yamawaki, Koichi
2001-07-01
We propose a novel way of matching effective field theory with the underlying QCD in the sense of a Wilsonian renormalization group equation (RGE). We derive Wilsonian matching conditions between current correlators obtained by the operator product expansion in QCD and those by the hidden local symmetry (HLS) model. This determines without much ambiguity the bare parameters of the HLS at the cutoff scale in terms of the QCD parameters. Physical quantities for the {pi} and {rho} system are calculated by the Wilsonian RGE{close_quote}s from the bare parameters in remarkable agreement with the experiment.
Lutz, Matthias F. M.; Lange, Jens Sören; Pennington, Michael; Bettoni, Diego; Brambilla, Nora; Crede, Volker; Eidelman, Simon; Gillitzer, Albrecht; Gradl, Wolfgang; Lang, Christian B.; Metag, Volker; Nakano, Takashi; Nieves, Juan; Neubert, Sebastian; Oka, Makoto; Olsen, Stephen L.; Pappagallo, Marco; Paul, Stephan; Pelizäus, Marc; Pilloni, Alessandro; Prencipe, Elisabetta; Ritman, Jim; Ryan, Sinead; Thoma, Ulrike; Uwer, Ulrich; Weise, Wolfram
2016-04-01
We report on the EMMI Rapid Reaction Task Force meeting 'Resonances in QCD', which took place at GSI October 12-14, 2015 (Fig.~1). A group of 26 people met to discuss the physics of resonances in QCD. The aim of the meeting was defined by the following three key questions; what is needed to understand the physics of resonances in QCD?; where does QCD lead us to expect resonances with exotic quantum numbers?; and what experimental efforts are required to arrive at a coherent picture? For light mesons and baryons only those with up, down and strange quark content were considered. For heavy-light and heavy-heavy meson systems, those with charm quarks were the focus.This document summarizes the discussions by the participants, which in turn led to the coherent conclusions we present here.
Rangel, Murilo; /Orsay, LAL
2010-06-01
Experimental studies of soft Quantum Chromodynamics (QCD) at Tevatron are reported in this note. Results on inclusive inelastic interactions, underlying events, double parton interaction and exclusive diffractive production and their implications to the Large Hadron Collider (LHC) physics are discussed.
Skands, Peter Z.; /Fermilab
2005-07-01
Recent developments in QCD phenomenology have spurred on several improved approaches to Monte Carlo event generation, relative to the post-LEP state of the art. In this brief review, the emphasis is placed on approaches for (1) consistently merging fixed-order matrix element calculations with parton shower descriptions of QCD radiation, (2) improving the parton shower algorithms themselves, and (3) improving the description of the underlying event in hadron collisions.
Behavior of universal critical parameters in the QCD phase diagram
NASA Astrophysics Data System (ADS)
Bluhm, Marcus; Nahrgang, Marlene; Bass, Steffen A.; Schäfer, Thomas
2017-01-01
We determine the dependence of important parameters for critical fluctuations on temperature and baryon chemical potential in the QCD phase diagram. The analysis is based on an identification of the fluctuations of the order parameter obtained from the Ising model equation of state and the Ginzburg-Landau effective potential approach. The impact of the mapping from Ising model variables to QCD thermodynamics is discussed.
Infrared Behavior and Fixed Points in Landau-Gauge QCD
NASA Astrophysics Data System (ADS)
Pawlowski, Jan M.; Litim, Daniel F.; Nedelko, Sergei; von Smekal, Lorenz
2004-10-01
We investigate the infrared behavior of gluon and ghost propagators in Landau-gauge QCD by means of an exact renormalization group equation. We explain how, in general, the infrared momentum structure of Green functions can be extracted within this approach. An optimization procedure is devised to remove residual regulator dependences. In Landau-gauge QCD this framework is used to determine the infrared leading terms of the propagators. The results support the Kugo-Ojima confinement scenario. Possible extensions are discussed.
Mapping the QCD Phase Transition with Accreting Compact Stars
Blaschke, D.; Poghosyan, G.; Grigorian, H.
2008-10-29
We discuss an idea for how accreting millisecond pulsars could contribute to the understanding of the QCD phase transition in the high-density nuclear matter equation of state (EoS). It is based on two ingredients, the first one being a ''phase diagram'' of rapidly rotating compact star configurations in the plane of spin frequency and mass, determined with state-of-the-art hybrid equations of state, allowing for a transition to color superconducting quark matter. The second is the study of spin-up and accretion evolution in this phase diagram. We show that the quark matter phase transition leads to a characteristic line in the {omega}-M plane, the phase border between neutron stars and hybrid stars with a quark matter core. Along this line a drop in the pulsar's moment of inertia entails a waiting point phenomenon in the accreting millisecond pulsar (AMXP) evolution: most of these objects should therefore be found along the phase border in the {omega}-M plane, which may be viewed as the AMXP analog of the main sequence in the Hertzsprung-Russell diagram for normal stars. In order to prove the existence of a high-density phase transition in the cores of compact stars we need population statistics for AMXPs with sufficiently accurate determination of their masses, spin frequencies and magnetic fields.
Next-to-leading order QCD factorization for semi-inclusive deep inelastic scattering at twist 4.
Kang, Zhong-Bo; Wang, Enke; Wang, Xin-Nian; Xing, Hongxi
2014-03-14
Within the framework of a high-twist approach, we calculate the next-to-leading order (NLO) perturbative QCD corrections to the transverse momentum broadening in semi-inclusive hadron production in deeply inelastic e+A collisions, as well as lepton pair production in p+A collisions. With explicit calculations of both real and virtual contributions, we verify, for the first time, the factorization theorem at twist 4 in NLO for the nuclear-enhanced transverse momentum weighted differential cross section and demonstrate the universality of the associated twist-4 quark-gluon correlation function. We also identify the QCD evolution equation for the twist-4 quark-gluon correlation function in a large nucleus, which can be solved to determine the scale dependence of the jet transport parameter in the study of jet quenching.
Brodsky, Stanley J.; de Teramond, Guy F.; /SLAC /Southern Denmark U., CP3-Origins /Costa Rica U.
2011-01-10
AdS/QCD, the correspondence between theories in a dilaton-modified five-dimensional anti-de Sitter space and confining field theories in physical space-time, provides a remarkable semiclassical model for hadron physics. Light-front holography allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time. The result is a single-variable light-front Schroedinger equation which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The coordinate z in AdS space is uniquely identified with a Lorentz-invariant coordinate {zeta} which measures the separation of the constituents within a hadron at equal light-front time and determines the off-shell dynamics of the bound state wavefunctions as a function of the invariant mass of the constituents. The hadron eigenstates generally have components with different orbital angular momentum; e.g., the proton eigenstate in AdS/QCD with massless quarks has L = 0 and L = 1 light-front Fock components with equal probability. Higher Fock states with extra quark-anti quark pairs also arise. The soft-wall model also predicts the form of the nonperturbative effective coupling and its {beta}-function. The AdS/QCD model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method to systematically include QCD interaction terms. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates. A method for computing the hadronization of quark and gluon jets at the amplitude level is outlined.
Analytical solutions with the improved (G’/G)-expansion method for nonlinear evolution equations
NASA Astrophysics Data System (ADS)
Kaplan, Melike; Bekir, Ahmet; Akbulut, Arzu
2016-10-01
To seek the exact solutions of nonlinear partial differential equations (NPDEs), the improved (G'/G)-expansion method is proposed in the present work. With the aid of symbolic computation, this effective method is applied to construct exact solutions of the (1+1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and (3+1)- dimensional Kudryashov-Sinelshchikov equation. As a result, new types of exact solutions are obtained.
Nonlinear inhomogeneous Fokker-Planck equations: Entropy and free-energy time evolution.
Sicuro, Gabriele; Rapčan, Peter; Tsallis, Constantino
2016-12-01
We extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck equations. In our approach, the free-energy functional is expressed in terms of an entropic functional and an auxiliary potential, both derived from the coefficients of the equation. With reference to the introduced entropic functional, we discuss the entropy production in a relaxation process towards equilibrium. The properties of the stationary solutions of the considered Fokker-Planck equations are also discussed.
Nucleon Parton Structure from Continuum QCD
NASA Astrophysics Data System (ADS)
Bednar, Kyle; Cloet, Ian; Tandy, Peter
2017-01-01
The parton structure of the nucleon is investigated using QCD's Dyson-Schwinger equations (DSEs). This formalism builds in numerous essential features of QCD, for example, the dressing of parton propagators and dynamical formation of non-pointlike di-quark correlations. All needed elements of the approach, including the nucleon wave function solution from a Poincaré covariant Faddeev equation, are encoded in spectral-type representations in the Nakanishi style. This facilitates calculations and the necessary connections between Euclidean and Minkowski metrics. As a first step results for the nucleon quark distribution functions will be presented. The extension to the transverse momentum-dependent parton distributions (TMDs) also be discussed. Supported by NSF Grant No. PHY-1516138.
Evolutions of Longitudinal Structure Function F L upto Next-to-Next-to-Leading Orders at Small- x
NASA Astrophysics Data System (ADS)
Baruah, Nomita; Sarma, J. K.
2014-07-01
We compute the longitudinal structure function F L of proton from its QCD (Quantum Chromodynamics) evolution equation in next-to-next-to-leading order (NNLO) approximation at small- x. Here we use Taylor series expansion method to solve the evolution equation for small- x and the obtained simple analytical expressions for F L provide t- and x-evolution equations for the computation of the longitudinal structure function. Finally, we compare our results with the recent H1, ZEUS experimental data and results of MSTW, CT10 parameterizations and Block, Donnachie-Landshoff (DL) models. Our results are in good agreement with the data and the related fittings and parameterizations, which can also be described within the framework of perturbative QCD.
FOREWORD: Extreme QCD 2012 (xQCD)
NASA Astrophysics Data System (ADS)
Alexandru, Andrei; Bazavov, Alexei; Liu, Keh-Fei
2013-04-01
The Extreme QCD 2012 conference, held at the George Washington University in August 2012, celebrated the 10th event in the series. It has been held annually since 2003 at different locations: San Carlos (2011), Bad Honnef (2010), Seoul (2009), Raleigh (2008), Rome (2007), Brookhaven (2006), Swansea (2005), Argonne (2004), and Nara (2003). As usual, it was a very productive and inspiring meeting that brought together experts in the field of finite-temperature QCD, both theoretical and experimental. On the experimental side, we heard about recent results from major experiments, such as PHENIX and STAR at Brookhaven National Laboratory, ALICE and CMS at CERN, and also about the constraints on the QCD phase diagram coming from astronomical observations of one of the largest laboratories one can imagine, neutron stars. The theoretical contributions covered a wide range of topics, including QCD thermodynamics at zero and finite chemical potential, new ideas to overcome the sign problem in the latter case, fluctuations of conserved charges and how they allow one to connect calculations in lattice QCD with experimentally measured quantities, finite-temperature behavior of theories with many flavors of fermions, properties and the fate of heavy quarkonium states in the quark-gluon plasma, and many others. The participants took the time to write up and revise their contributions and submit them for publication in these proceedings. Thanks to their efforts, we have now a good record of the ideas presented and discussed during the workshop. We hope that this will serve both as a reminder and as a reference for the participants and for other researchers interested in the physics of nuclear matter at high temperatures and density. To preserve the atmosphere of the event the contributions are ordered in the same way as the talks at the conference. We are honored to have helped organize the 10th meeting in this series, a milestone that reflects the lasting interest in this
Renormalization-group evolution of the B-meson light-cone distribution amplitude.
Lange, Björn O; Neubert, Matthias
2003-09-05
An integro-differential equation governing the evolution of the leading-order B-meson light-cone distribution amplitude is derived. The anomalous dimension in this equation contains a logarithm of the renormalization scale, whose coefficient is identified with the cusp anomalous dimension of Wilson loops. The exact solution of the evolution equation is obtained, from which the asymptotic behavior of the distribution amplitude is derived. These results can be used to resum Sudakov logarithms entering the hard-scattering kernels in QCD factorization theorems for exclusive B decays.
Ultrahigh energy neutrinos and nonlinear QCD dynamics
Machado, Magno V.T.
2004-09-01
The ultrahigh energy neutrino-nucleon cross sections are computed taking into account different phenomenological implementations of the nonlinear QCD dynamics. Based on the color dipole framework, the results for the saturation model supplemented by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution as well as for the Balitskii-Fadin-Kuraev-Lipatov (BFKL) formalism in the geometric scaling regime are presented. They are contrasted with recent calculations using next-to-leading order DGLAP and unified BFKL-DGLAP formalisms.
NASA Astrophysics Data System (ADS)
Nejad, S. Mohammad Moosavi; Khanpour, Hamzeh; Tehrani, S. Atashbar; Mahdavi, Mahdi
2016-10-01
We present a detailed QCD analysis of nucleon structure functions x F3(x ,Q2) , based on Laplace transforms and the Jacobi polynomials approach. The analysis corresponds to the next-to-leading order and next-to-next-to-leading order approximations of perturbative QCD. The Laplace transform technique, as an exact analytical solution, is used for the solution of nonsinglet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at low- and large-x values. The extracted results are used as input to obtain the x and Q2 evolution of x F3(x ,Q2) structure functions using the Jacobi polynomials approach. In our work, the values of the typical QCD scale ΛMS¯ (nf) and the strong coupling constant αs(MZ2) are determined for four quark flavors (nf=4 ) as well. A careful estimation of the uncertainties shall be performed using the Hessian method for the valence-quark distributions, originating from the experimental errors. We compare our valence-quark parton distribution functions sets with those of other collaborations, in particular with the CT14, MMHT14, and NNPDF sets, which are contemporary with the present analysis. The obtained results from the analysis are in good agreement with those from the literature.
Blazey, G.C.
1995-05-01
Selected recent Quantum Chromodynamics (QCD) results from the D0 and CDF experiments at the Fermilab Tevatron are presented and discussed. The inclusive jet and inclusive triple differential dijet cross sections are compared to next-to-leading order QCD calculations. The sensitivity of the dijet cross section to parton distribution functions (for hadron momentum fractions {approximately} 0.01 to {approximately} 0.4) will constrain the gluon distribution of the proton. Two analyses of dijet production at large rapidity separation are presented. The first analysis tests the contributions of higher order processes to dijet production and can be considered a test of BFKL or GLAP parton evolution. The second analysis yields a strong rapidity gap signal consistent with colorless exchange between the scattered partons. The prompt photon inclusive cross section is consistent with next-to-leading order QCD only at the highest transverse momenta. The discrepancy at lower momenta may be indicative of higher order processes impacting a transverse momentum or ``k{sub T}`` to the partonic interaction. The first measurement of the strong coupling constant from the Tevatron is also presented. The coupling constant can be determined from the ratio of W + 1jet to W + 0jet cross sections and a next-to-leading order QCD calculation.
Evolution of higher order nonlinear equation for the dust ion-acoustic waves in nonextensive plasma
Yasmin, S.; Asaduzzaman, M.; Mamun, A. A.
2012-10-15
There are three different types of nonlinear equations, namely, Korteweg-de Vries (K-dV), modified K-dV (mK-dV), and mixed modified K-dV (mixed mK-dV) equations, for the nonlinear propagation of the dust ion-acoustic (DIA) waves. The effects of electron nonextensivity on DIA solitary waves propagating in a dusty plasma (containing negatively charged stationary dust, inertial ions, and nonextensive q distributed electrons) are examined by solving these nonlinear equations. The basic features of mixed mK-dV (higher order nonlinear equation) solitons are found to exist beyond the K-dV limit. The properties of mK-dV solitons are compared with those of mixed mK-dV solitons. It is found that both positive and negative solitons are obtained depending on the q (nonextensive parameter).
Electroweak symmetry breaking via QCD.
Kubo, Jisuke; Lim, Kher Sham; Lindner, Manfred
2014-08-29
We propose a new mechanism to generate the electroweak scale within the framework of QCD, which is extended to include conformally invariant scalar degrees of freedom belonging to a larger irreducible representation of SU(3)c. The electroweak symmetry breaking is triggered dynamically via the Higgs portal by the condensation of the colored scalar field around 1 TeV. The mass of the colored boson is restricted to be 350 GeV≲mS≲3 TeV, with the upper bound obtained from perturbative renormalization group evolution. This implies that the colored boson can be produced at the LHC. If the colored boson is electrically charged, the branching fraction of the Higgs boson decaying into two photons can slightly increase, and moreover, it can be produced at future linear colliders. Our idea of nonperturbative electroweak scale generation can serve as a new starting point for more realistic model building in solving the hierarchy problem.
Small-x Evolution of Structure Functions in the Next-to-Leading Order
Chirilli, Giovanni A.
2009-12-17
The high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the nonlinear Balitsky-Kovchegov (BK) equation. The NLO corrections define the scale of the running-coupling constant in the BK equation and in QCD, its kernel has both conformal and non-conformal parts. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformal N = 4 SYM theory, then we define the 'composite dipole operator' with the rapidity cutoff preserving conformal invariance, and the resulting Moebius invariant kernel for this operator agrees with the forward NLO BFKL calculation.In QCD, the NLO kernel for the composite operators resolves in a sum of the conformal part and the running-coupling part.
Small-x Evolution of Structure Functions in the Next-to-Leading Order
Giovanni Antonio Chirilli
2009-12-01
The high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the nonlinear Balitsky-Kovchegov (BK) equation. The NLO corrections define the scale of the running coupling constant in the BK equation and in QCD, its kernel has both conformal and non-conformal parts. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformal N = 4 SYM theory, then we define the "composite dipole operator" with the rapidity cutoff preserving conformal invariance, and the resulting Möbius invariant kernel for this operator agrees with the forward NLO BFKL calculation. In QCD, the NLO kernel for the composite operators resolves in a sum of the conformal part and the running-coupling part.
Brodsky, Stanley J.; /SLAC
2007-07-06
I discuss a number of novel topics in QCD, including the use of the AdS/CFT correspondence between Anti-de Sitter space and conformal gauge theories to obtain an analytically tractable approximation to QCD in the regime where the QCD coupling is large and constant. In particular, there is an exact correspondence between the fifth-dimension coordinate z of AdS space and a specific impact variable {zeta} which measures the separation of the quark constituents within the hadron in ordinary space-time. This connection allows one to compute the analytic form of the frame-independent light-front wavefunctions of mesons and baryons, the fundamental entities which encode hadron properties and allow the computation of exclusive scattering amplitudes. I also discuss a number of novel phenomenological features of QCD. Initial- and final-state interactions from gluon-exchange, normally neglected in the parton model, have a profound effect in QCD hard-scattering reactions, leading to leading-twist single-spin asymmetries, diffractive deep inelastic scattering, diffractive hard hadronic reactions, the breakdown of the Lam Tung relation in Drell-Yan reactions, and nuclear shadowing and non-universal antishadowing--leading-twist physics not incorporated in the light-front wavefunctions of the target computed in isolation. I also discuss tests of hidden color in nuclear wavefunctions, the use of diffraction to materialize the Fock states of a hadronic projectile and test QCD color transparency, and anomalous heavy quark effects. The presence of direct higher-twist processes where a proton is produced in the hard subprocess can explain the large proton-to-pion ratio seen in high centrality heavy ion collisions.
NASA Astrophysics Data System (ADS)
Li, Zhi-Bin; Liu, Yin-Ping
2004-11-01
In Maple 8, by taking advantage of the package RIF contained in DEtools, we developed a package RAEEM which is a comprehensive and complete implementation of such methods as the tanh-method, the extended tanh-method, the Jacobi elliptic function method and the elliptic equation method. RAEEM can entirely automatically output a series of exact traveling wave solutions, including those of polynomial, exponential, triangular, hyperbolic, rational, Jacobi elliptic, Weierstrass elliptic type. The effectiveness of the package is illustrated by applying it to a large variety of equations. In addition to recovering previously known solutions, we also obtain more general forms of some solutions and new solutions. Program summaryTitle of program: RAEEM Catalogue identifier: ADUP Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUP Program obtained from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers: PC Pentium IV Installations: Copy Operating systems: Windows 98/2000/XP Program language used: Maple 8 Memory required to execute with typical data: depends on the problem, minimum about 8M words No. of bits in a word: 8 No. of lines in distributed program, including test data, etc.: 3163 No. of bytes in distributed program, including the test data, etc.: 26 720 Distribution format: tar.gz Nature of physical problem: Our program provides exact traveling wave solutions, which describe various phenomena in nature, and thus can give more insight into the physical aspects of problems. These solutions may be easily used in further applications. Restriction on the complexity of the problem: The program can handle system of nonlinear evolution equations with any number of independent and dependent variables, in which each equation is a polynomial (or can be converted to a polynomial) in the dependent variables and their derivatives. Typical running time: It depends on the input equations as well as the degrees of the desired polynomial solutions. For
NASA Astrophysics Data System (ADS)
Yan, Zuomao; Lu, Fangxia
2016-08-01
In this paper, we introduce the optimal control problems governed by a new class of impulsive stochastic partial neutral evolution equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, the analytic semigroup theory, fractional powers of closed operators, and suitable fixed point theorems, we prove an existence result of mild solutions for the control systems in the α-norm without the assumptions of compactness. Next, we derive the existence conditions of optimal pairs of these systems. Finally, application to a nonlinear impulsive stochastic parabolic optimal control system is considered.
Nathan Isgur
1997-03-01
The author presents an idiosyncratic view of baryons which calls for a marriage between quark-based and hadronic models of QCD. He advocates a treatment based on valence quark plus glue dominance of hadron structure, with the sea of q pairs (in the form of virtual hadron pairs) as important corrections.
Lincoln, Don
2016-07-12
The strongest force in the universe is the strong nuclear force and it governs the behavior of quarks and gluons inside protons and neutrons. The name of the theory that governs this force is quantum chromodynamics, or QCD. In this video, Fermilabâs Dr. Don Lincoln explains the intricacies of this dominant component of the Standard Model.
Radyushkin, Anatoly V.; Efremov, Anatoly Vasilievich; Ginzburg, Ilya F.
2013-04-01
We discuss some problems concerning the application of perturbative QCD to high energy soft processes. We show that summing the contributions of the lowest twist operators for non-singlet $t$-channel leads to a Regge-like amplitude. Singlet case is also discussed.
Lincoln, Don
2016-06-17
The strongest force in the universe is the strong nuclear force and it governs the behavior of quarks and gluons inside protons and neutrons. The name of the theory that governs this force is quantum chromodynamics, or QCD. In this video, Fermilab’s Dr. Don Lincoln explains the intricacies of this dominant component of the Standard Model.
Brodsky, Stanley J.; Deshpande, Abhay L.; Gao, Haiyan; McKeown, Robert D.; Meyer, Curtis A.; Meziani, Zein-Eddine; Milner, Richard G.; Qiu, Jianwei; Richards, David G.; Roberts, Craig D.
2015-02-26
This White Paper presents the recommendations and scientific conclusions from the Town Meeting on QCD and Hadronic Physics that took place in the period 13-15 September 2014 at Temple University as part of the NSAC 2014 Long Range Planning process. The meeting was held in coordination with the Town Meeting on Phases of QCD and included a full day of joint plenary sessions of the two meetings. The goals of the meeting were to report and highlight progress in hadron physics in the seven years since the 2007 Long Range Plan (LRP07), and present a vision for the future by identifying the key questions and plausible paths to solutions which should define the next decade. The introductory summary details the recommendations and their supporting rationales, as determined at the Town Meeting on QCD and Hadron Physics, and the endorsements that were voted upon. The larger document is organized as follows. Section 2 highlights major progress since the 2007 LRP. It is followed, in Section 3, by a brief overview of the physics program planned for the immediate future. Finally, Section 4 provides an overview of the physics motivations and goals associated with the next QCD frontier: the Electron-Ion-Collider.
Plunkett, R.; The CDF Collaboration
1991-10-01
Results are presented for hadronic jet and direct photon production at {radical}{bar s} = 1800 GeV. The data are compared with next-to-leading QCD calculations. A new limit on the scale of possible composite structure of the quarks is also reported. 12 refs., 4 figs.
Devlin, T.; CDF Collaboration
1996-10-01
The CDF collaboration is engaged in a broad program of QCD measurements at the Fermilab Tevatron Collider. I will discuss inclusive jet production at center-of-mass energies of 1800 GeV and 630 GeV, properties of events with very high total transverse energy and dijet angular distributions.
Andreas S. Kronfeld
2002-09-30
After reviewing some of the mathematical foundations and numerical difficulties facing lattice QCD, I review the status of several calculations relevant to experimental high-energy physics. The topics considered are moments of structure functions, which may prove relevant to search for new phenomena at the LHC, and several aspects of flavor physics, which are relevant to understanding CP and flavor violation.
Phenomenology Using Lattice QCD
NASA Astrophysics Data System (ADS)
Gupta, R.
2005-08-01
This talk provides a brief summary of the status of lattice QCD calculations of the light quark masses and the kaon bag parameter BK. Precise estimates of these four fundamental parameters of the standard model, i.e., mu, md, ms and the CP violating parameter η, help constrain grand unified models and could provide a window to new physics.
Phenomenology Using Lattice QCD
NASA Astrophysics Data System (ADS)
Gupta, R.
This talk provides a brief summary of the status of lattice QCD calculations of the light quark masses and the kaon bag parameter BK. Precise estimates of these four fundamental parameters of the standard model, i.e., mu, md, ms and the CP violating parameter η, help constrain grand unified models and could provide a window to new physics.
An evolution infinity Laplace equation modelling dynamic elasto-plastic torsion
NASA Astrophysics Data System (ADS)
Messelmi, Farid
2016-09-01
We consider in this paper a parabolic partial differential equation involving the infinity Laplace operator and a Leray-Lions operator with no coercitive assumption. We prove the existence and uniqueness of the corresponding approached problem and we show that at the limit the solution solves the parabolic variational inequality arising in the elasto-plastic torsion problem.
QCD propagators and vertices from lattice QCD (in memory of Michael Müller-Preußker)
NASA Astrophysics Data System (ADS)
Sternbeck, André
2017-03-01
We review lattice calculations of the elementary Greens functions of QCD with a special emphasis on the Landau gauge. These lattice results have been of interest to continuum approaches to QCD over the past 20 years. They are used as reference for Dyson-Schwinger- and functional renormalization group equation calculations as well as for hadronic bound state equations. The lattice provides low-energy data for propagators and three-point vertices in Landau gauge at zero and finite temperature even including dynamical fermions. We summarize Michael Müller-Preußker's important contributions to this field and put them into the perspective of his other research interests.
The evolution equation for the flame surface density in turbulent premixed combustion
NASA Technical Reports Server (NTRS)
Trouve, A.; Poinsot, T.
1992-01-01
One central ingredient in flamelet models for turbulent premixed combustion is the flame surface density. This quantity conveys most of the effects of the turbulence on the rate of energy release and is obtained via a modeled transport equation, called the Sigma-equation. Past theoretical work has produced a rigorous approach that leads to an exact, but unclosed, formulation for the turbulent Sigma-equation. In this exact Sigma-equation, it appears that the dynamical properties of the flame surface density are determined by a single parameter, namely the turbulent flame stretch. Unfortunately, the flame surface density and the turbulent flame stretch are not available from experiments and, in the absence of experimental data, little is known on the validity of the closure assumptions used in current flamelet models. Direct Numerical Simulation (DNS) is the obvious, complementary approach to get basic information on these fundamental quantities. Three-dimensional DNS of premixed flames in isotropic turbulent flow is used to estimate the different terms appearing in the Sigma-equation. A new methodology is proposed to provide the source and sink terms for the flame surface density, resolved both temporally and spatially throughout the turbulent flame brush. Using this methodology, the effects of the Lewis number on the rate of production of flame surface area are described in great detail and meaningful comparisons with flamelet models can be performed. The analysis reveals in particular the tendency of the models to overpredict flame surface dissipation as well as their inability to reproduce variations due to thermo-diffusive phenomena. Thanks to the detailed information produced by a DNS-based analysis, this type of comparison not only underscores the shortcomings of current models but also suggests ways to improve them.
The evolution equation for the flame surface density in turbulent premixed combustion
NASA Technical Reports Server (NTRS)
Trouve, Arnaud
1993-01-01
The mean reaction rate in flamelet models for turbulent premixed combustion depends on two basic quantities: a mean chemical rate, called the flamelet speed, and the flame surface density. Our previous work had been primarily focused on the problem of the structure and topology of turbulent premixed flames, and it was then determined that the flamelet speed, when space-averaged, is only weakly sensitive to the turbulent flow field. Consequently, the flame surface density is the key quantity that conveys most of the effects of the turbulence on the rate of energy release. In flamelet models, this quantity is obtained via a modeled transport equation called the Sigma-equation. Past theoretical work has produced a rigorous approach that leads to an exact but unclosed formulation for the turbulent Sigma-equation. In the exact Sigma-equation, it appears that the dynamical properties of the flame surface density are determined by a single parameter, namely the turbulent flame stretch. Unfortunately, the turbulent flame stretch as well as the flame surface density is not available from experiments, and, in the absence of experimental data, little is known on the validity of the closure assumptions used in current flamelet models. Direct Numerical Simulation (DNS) is the alternative approach to get basic information on these fundamental quantities. In the present work, three-dimensional DNS of premixed flames in isotropic turbulent flow is used to estimate the different terms appearing in the Sigma-equation. A new methodology is proposed to provide the source and sink terms for the flame surface density, resolved both temporally and spatially throughout the turbulent flame brush. Using this methodology, our objective is to extract the turbulent flame stretch from the DNS data base and then perform extensive comparisons with flamelet models. Thanks to the detailed information produced by the DNS-based analysis, it is expected that this type of comparison will not only
Viscous QCD matter in a hybrid hydrodynamic+Boltzmann approach
Song Huichao; Bass, Steffen A.; Heinz, Ulrich
2011-02-15
A hybrid transport approach for the bulk evolution of viscous QCD matter produced in ultra-relativistic heavy-ion collisions is presented. The expansion of the dense deconfined phase of the reaction is modeled with viscous hydrodynamics, while the dilute late hadron gas stage is described microscopically by the Boltzmann equation. The advantages of such a hybrid approach lie in the improved capability of handling large dissipative corrections in the late dilute phase of the reaction, including a realistic treatment of the nonequilibrium hadronic chemistry and kinetic freeze-out. By varying the switching temperature at which the hydrodynamic output is converted to particles for further propagation with the Boltzmann cascade we test the ability of the macroscopic hydrodynamic approach to emulate the microscopic evolution during the hadronic stage and extract the temperature dependence of the effective shear viscosity of the hadron resonance gas produced in the collision. We find that the extracted values depend on the prior hydrodynamic history and hence do not represent fundamental transport properties of the hadron resonance gas. We conclude that viscous fluid dynamics does not provide a faithful description of hadron resonance gas dynamics with predictive power, and that both components of the hybrid approach are needed for a quantitative description of the fireball expansion and its freeze-out.
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins
2011-08-12
I review a number of topics where conventional wisdom in hadron physics has been challenged. For example, hadrons can be produced at large transverse momentum directly within a hard higher-twist QCD subprocess, rather than from jet fragmentation. Such 'direct' processes can explain the deviations from perturbative QCD predictions in measurements of inclusive hadron cross sections at fixed x{sub T} = 2p{sub T}/{radical}s, as well as the 'baryon anomaly', the anomalously large proton-to-pion ratio seen in high centrality heavy ion collisions. Initial-state and final-state interactions of the struck quark, the soft-gluon rescattering associated with its Wilson line, lead to Bjorken-scaling single-spin asymmetries, diffractive deep inelastic scattering, the breakdown of the Lam-Tung relation in Drell-Yan reactions, as well as nuclear shadowing and antishadowing. The Gribov-Glauber theory predicts that antishadowing of nuclear structure functions is not universal, but instead depends on the flavor quantum numbers of each quark and antiquark, thus explaining the anomalous nuclear dependence measured in deep-inelastic neutrino scattering. Since shadowing and antishadowing arise from the physics of leading-twist diffractive deep inelastic scattering, one cannot attribute such phenomena to the structure of the nucleus itself. It is thus important to distinguish 'static' structure functions, the probability distributions computed from the square of the target light-front wavefunctions, versus 'dynamical' structure functions which include the effects of the final-state rescattering of the struck quark. The importance of the J = 0 photon-quark QCD contact interaction in deeply virtual Compton scattering is also emphasized. The scheme-independent BLM method for setting the renormalization scale is discussed. Eliminating the renormalization scale ambiguity greatly improves the precision of QCD predictions and increases the sensitivity of searches for new physics at the LHC
NASA Astrophysics Data System (ADS)
Brodsky, Stanley J.
2011-04-01
I review a number of topics where conventional wisdom in hadron physics has been challenged. For example, hadrons can be produced at large transverse momentum directly within a hard QCD subprocess, rather than from jet fragmentation. Such "direct" higher-twist processes can explain the deviations from perturbative QCD predictions in measurements of inclusive hadron cross sections at fixed {xT} = 2{pT}/√ s , as well as the "baryon anomaly, the anomalously large proton-to-pion ratio seen in high centrality heavy ion collisions. Initial-state and final-state interactions of the struck quark, soft-gluon rescattering associated with its Wilson line lead to Bjorken-scaling single-spin asymmetries, diffractive deep inelastic scattering, the breakdown of the Lam-Tung relation in Drell-Yan reactions, as well as nuclear shadowing and antishadowing. The Gribov-Glauber theory predicts that antishadowing of nuclear structure functions is not universal, but instead depends on the flavor quantum numbers of each quark and antiquark, thus explaining the anomalous nuclear dependence measured in deep-inelastic neutrino scattering. Since shadowing and antishadowing arise from the physics of leading-twist diffractive deep inelastic scattering, one cannot attribute such phenomena to the structure of the nucleus itself. It is thus important to distinguish "static" structure functions, the probability distributions computed from the square of the target light-front wavefunctions, versus "dynamical" structure functions which include the effects of the final-state rescattering of the struck quark. The importance of the J = 0 photon-quark QCD contact interaction in deeply virtual Compton scattering is also emphasized. The scheme-independent BLM method for setting the renormalization scale is discussed. The elimination of the renormalization scale ambiguity would greatly improve the precision of QCD predictions and increase the sensitivity of searches for new physics at the LHC. Other novel
MAGNETIC FIELDS FROM QCD PHASE TRANSITIONS
Tevzadze, Alexander G.; Kisslinger, Leonard; Kahniashvili, Tina; Brandenburg, Axel
2012-11-01
We study the evolution of QCD phase transition-generated magnetic fields (MFs) in freely decaying MHD turbulence of the expanding universe. We consider an MF generation model that starts from basic non-perturbative QCD theory and predicts stochastic MFs with an amplitude of the order of 0.02 {mu}G and small magnetic helicity. We employ direct numerical simulations to model the MHD turbulence decay and identify two different regimes: a 'weakly helical' turbulence regime, when magnetic helicity increases during decay, and 'fully helical' turbulence, when maximal magnetic helicity is reached and an inverse cascade develops. The results of our analysis show that in the most optimistic scenario the magnetic correlation length in the comoving frame can reach 10 kpc with the amplitude of the effective MF being 0.007 nG. We demonstrate that the considered model of magnetogenesis can provide the seed MF for galaxies and clusters.
Optical analogues of the Newton-Schrödinger equation and boson star evolution
NASA Astrophysics Data System (ADS)
Roger, Thomas; Maitland, Calum; Wilson, Kali; Westerberg, Niclas; Vocke, David; Wright, Ewan M.; Faccio, Daniele
2016-11-01
Many gravitational phenomena that lie at the core of our understanding of the Universe have not yet been directly observed. An example in this sense is the boson star that has been proposed as an alternative to some compact objects currently interpreted as being black holes. In the weak field limit, these stars are governed by the Newton-Schrodinger equation. Here we present an optical system that, under appropriate conditions, identically reproduces such equation in two dimensions. A rotating boson star is experimentally and numerically modelled by an optical beam propagating through a medium with a positive thermal nonlinearity and is shown to oscillate in time while also stable up to relatively high densities. For higher densities, instabilities lead to an apparent breakup of the star, yet coherence across the whole structure is maintained. These results show that optical analogues can be used to shed new light on inaccessible gravitational objects.
Optical analogues of the Newton–Schrödinger equation and boson star evolution
Roger, Thomas; Maitland, Calum; Wilson, Kali; Westerberg, Niclas; Vocke, David; Wright, Ewan M.; Faccio, Daniele
2016-01-01
Many gravitational phenomena that lie at the core of our understanding of the Universe have not yet been directly observed. An example in this sense is the boson star that has been proposed as an alternative to some compact objects currently interpreted as being black holes. In the weak field limit, these stars are governed by the Newton–Schrodinger equation. Here we present an optical system that, under appropriate conditions, identically reproduces such equation in two dimensions. A rotating boson star is experimentally and numerically modelled by an optical beam propagating through a medium with a positive thermal nonlinearity and is shown to oscillate in time while also stable up to relatively high densities. For higher densities, instabilities lead to an apparent breakup of the star, yet coherence across the whole structure is maintained. These results show that optical analogues can be used to shed new light on inaccessible gravitational objects. PMID:27841261
Optical analogues of the Newton-Schrödinger equation and boson star evolution.
Roger, Thomas; Maitland, Calum; Wilson, Kali; Westerberg, Niclas; Vocke, David; Wright, Ewan M; Faccio, Daniele
2016-11-14
Many gravitational phenomena that lie at the core of our understanding of the Universe have not yet been directly observed. An example in this sense is the boson star that has been proposed as an alternative to some compact objects currently interpreted as being black holes. In the weak field limit, these stars are governed by the Newton-Schrodinger equation. Here we present an optical system that, under appropriate conditions, identically reproduces such equation in two dimensions. A rotating boson star is experimentally and numerically modelled by an optical beam propagating through a medium with a positive thermal nonlinearity and is shown to oscillate in time while also stable up to relatively high densities. For higher densities, instabilities lead to an apparent breakup of the star, yet coherence across the whole structure is maintained. These results show that optical analogues can be used to shed new light on inaccessible gravitational objects.
Dynamics of Vapour Bubbles in Nucleate Boiling. 1; Basic Equations of Bubble Evolution
NASA Technical Reports Server (NTRS)
Buyevich, Yu A.; Webbon, Bruce W.; Callaway, Robert (Technical Monitor)
1995-01-01
We consider the behaviour of a vapour bubble formed at a nucleation site on a heated horizontal wall. There is no forced convection of an ambient liquid, and the bubble is presumably separated from the wall by a thin liquid microlayer. The energy conservation law results in a variational equation for the mechanical energy of the whole system consisting of the bubble and liquid. It leads to a set of two strongly nonlinear equations which govern bubble expansion and motion of its centre of mass. A supplementary equation to find out the vapour temperature follows from consideration of heat transfer to the bubble, both from the bulk of surrounding liquid and through the microlayer. The average thickness of the microlayer is shown to increase monotonously with time as the bubble meniscus spreads along the wall. Bubble expansion is driven by the pressure head between vapour inside and liquid far away from the bubble, with due allowance for surface tension and gravity effects. It is resisted by inertia of liquid being placed into motion as the bubble grows. The inertia originates also a force that presses the bubble to the wall. This force is counteracted by the buoyancy and an effective surface tension force that tends to transform the bubble into a sphere. The analysis brings about quite a new formulation of the familiar problem of bubble growth and detachment under conditions of nucleate pool boiling.
AdS/QCD and Light Front Holography: A New Approximation to QCD
Brodsky, Stanley J.; de Teramond, Guy
2010-02-15
The combination of Anti-de Sitter space (AdS) methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states. Starting from the bound-state Hamiltonian equation of motion in QCD, we derive relativistic light-front wave equations in terms of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti-de Sitter (AdS) space. Its eigenvalues give the hadronic spectrum, and its eigenmodes represent the probability distribution of the hadronic constituents at a given scale. Applications to the light meson and baryon spectra are presented. The predicted meson spectrum has a string-theory Regge form M{sup 2} = 4{kappa}{sup 2}(n+L+S/2); i.e., the square of the eigenmass is linear in both L and n, where n counts the number of nodes of the wavefunction in the radial variable {zeta}. The space-like pion form factor is also well reproduced. One thus obtains a remarkable connection between the description of hadronic modes in AdS space and the Hamiltonian formulation of QCD in physical space-time quantized on the light-front at fixed light-front time {tau}. The model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms.
QCD bulk thermodynamics and conserved charge fluctuations with HISQ fermions
NASA Astrophysics Data System (ADS)
Schmidt, Christian; pre="(for" post="" affil="1,
2013-04-01
After briefly reviewing recent progress by the HotQCD collaboration in studying the 2+1 flavor QCD equation of state, we will focus on results on fluctuations of conserved charges by the BNL-Bielefeld and HotQCD collaborations. Higher order cumulants of the net-charge distributions are increasingly dominated by a universal scaling behavior, which arises due to a critical point of QCD in the chiral limit. Considering cumulants up to the 6th order, we observe that they generically behave as expected from universal scaling laws, which is quite different from cumulants calculated within the hadron resonance gas model. Taking ratios of these cumulants, we obtain volume independent results that can be compared to the experimental measurements. We will argue that the freeze-out chemical potentials and the freeze-out temperature, usually obtained by a HRG model fit to the measured hadronic yields, can also be obtained in a model independent way from ab-initio lattice QCD calculations by utilizing observables related to conserved charge fluctuations. Further, we will show that the freeze-out strangeness and electric charge chemical potentials can be fixed by imposing strangeness neutrality and isospin asymmetry constraints in the lattice QCD calculations, in order to accommodate conditions met in heavy ion collisions. All results have been obtained with the highly improved staggered quark action (HISQ) and almost physical quark masses on lattices with temporal extent of Nτ = 6, 8, 10, 12.
Electromigration-induced step meandering on vicinal surfaces: Nonlinear evolution equation
NASA Astrophysics Data System (ADS)
Dufay, Matthieu; Debierre, Jean-Marc; Frisch, Thomas
2007-01-01
We study the effect of a constant electrical field applied on vicinal surfaces such as the Si(111) surface. An electrical field parallel to the steps induces a meandering instability with a nonzero phase shift. Using the Burton-Cabrera-Frank model, we extend the linear stability analysis performed by Liu, Weeks, and Kandel [Phys. Rev. Lett. 81, 2743 (1998)] to the nonlinear regime for which the meandering amplitude is large. We derive an amplitude equation for the step dynamics using a highly nonlinear expansion method. We investigate numerically two limiting regimes (small and large attachment lengths) which both reveal long-time coarsening dynamics.
A non-local evolution equation model of cell–cell adhesion in higher dimensional space
Dyson, Janet; Gourley, Stephen A.; Webb, Glenn F.
2013-01-01
A model for cell–cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell–cell adhesion, J. Theor. Biol. 243 (2006), pp. 98–113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dimensional infinite domain. It has a non-local flux term which models the component of cell motion attributable to cells having formed bonds with other nearby cells. Using the theory of fractional powers of analytic semigroup generators and working in spaces with bounded uniformly continuous derivatives, the local existence of classical solutions is proved. Positivity and boundedness of solutions is then established, leading to global existence of solutions. Finally, the asymptotic behaviour of solutions about the spatially uniform state is considered. The model is illustrated by simulations that can be applied to in vitro wound closure experiments. AMS Classifications: 35A01; 35B09; 35B40; 35K57; 92C17 PMID:23289870
Dudek, Jozef J.; Edwards, Robert G.
2012-03-21
In this study, we present the first comprehensive study of hybrid baryons using lattice QCD methods. Using a large basis of composite QCD interpolating fields we extract an extensive spectrum of baryon states and isolate those of hybrid character using their relatively large overlap onto operators which sample gluonic excitations. We consider the spectrum of Nucleon and Delta states at several quark masses finding a set of positive parity hybrid baryons with quantum numbers $N_{1/2^+},\\,N_{1/2^+},\\,N_{3/2^+},\\, N_{3/2^+},\\,N_{5/2^+},\\,$ and $\\Delta_{1/2^+},\\, \\Delta_{3/2^+}$ at an energy scale above the first band of `conventional' excited positive parity baryons. This pattern of states is compatible with a color octet gluonic excitation having $J^{P}=1^{+}$ as previously reported in the hybrid meson sector and with a comparable energy scale for the excitation, suggesting a common bound-state construction for hybrid mesons and baryons.
NASA Astrophysics Data System (ADS)
Dudek, Jozef J.
2016-03-01
I describe how hadron-hadron scattering amplitudes are related to the eigenstates of QCD in a finite cubic volume. The discrete spectrum of such eigenstates can be determined from correlation functions computed using lattice QCD, and the corresponding scattering amplitudes extracted. I review results from the Hadron Spectrum Collaboration who have used these finite volume methods to study ππ elastic scattering, including the ρ resonance, as well as coupled-channel πK, ηK scattering. The very recent extension to the case where an external current acts is also presented, considering the reaction πγ* → ππ, from which the unstable ρ → πγ transition form factor is extracted. Ongoing calculations are advertised and the outlook for finite volume approaches is presented.
Kovacs, E.; CDF Collaboration
1996-02-01
We present results for the inclusive jet cross section and the dijet mass distribution. The inclusive cross section and dijet mass both exhibit significant deviations from the predictions of NLO QCD for jets with E{sub T}>200 GeV, or dijet masses > 400 GeV/c{sup 2}. We show that it is possible, within a global QCD analysis that includes the CDF inclusive jet data, to modify the gluon distribution at high x. The resulting increase in the jet cross-section predictions is 25-35%. Owing to the presence of k{sub T} smearing effects, the direct photon data does not provide as strong a constraint on the gluon distribution as previously thought. A comparison of the CDF and UA2 jet data, which have a common range in x, is plagued by theoretical and experimental uncertainties, and cannot at present confirm the CDF excess or the modified gluon distribution.
Jozef Dudek
2007-08-05
Charmonium is an attractive system for the application of lattice QCD methods. While the sub-threshold spectrum has been considered in some detail in previous works, it is only very recently that excited and higher-spin states and further properties such as radiative transitions and two-photon decays have come to be calculated. I report on this recent progress with reference to work done at Jefferson Lab.
Flaugher, B.
1992-09-01
Measurement of scaling violations, the inclusive photon and diphoton cross sections as well as the photon-jet and jet-jet angular distributions are discussed and compared to leading order and next-to-leading order QCD. A study of four-jet events is described, with a limit on the cross section for double parton scattering. The multiplicity of jets in W boson events is compared to theoretical predictions.
Hadronic Resonances from Lattice QCD
John Bulava; Robert Edwards; George Fleming; K. Jimmy Juge; Adam C. Lichtl; Nilmani Mathur; Colin Morningstar; David Richards; Stephen J. Wallace
2007-06-16
The determination of the pattern of hadronic resonances as predicted by Quantum Chromodynamics requires the use of non-perturbative techniques. Lattice QCD has emerged as the dominant tool for such calculations, and has produced many QCD predictions which can be directly compared to experiment. The concepts underlying lattice QCD are outlined, methods for calculating excited states are discussed, and results from an exploratory Nucleon and Delta baryon spectrum study are presented.
Hadronic Resonances from Lattice QCD
Lichtl, Adam C.; Bulava, John; Morningstar, Colin; Edwards, Robert; Mathur, Nilmani; Richards, David; Fleming, George; Juge, K. Jimmy; Wallace, Stephen J.
2007-10-26
The determination of the pattern of hadronic resonances as predicted by Quantum Chromodynamics requires the use of non-perturbative techniques. Lattice QCD has emerged as the dominant tool for such calculations, and has produced many QCD predictions which can be directly compared to experiment. The concepts underlying lattice QCD are outlined, methods for calculating excited states are discussed, and results from an exploratory Nucleon and Delta baryon spectrum study are presented.
C. Mesropian
2002-07-12
The Tevatron hadron collider provides the unique opportunity to study Quantum Chromodynamics, QCD, at the highest energies. The results summarized in this talk, although representing different experimental objects, as hadronic jets and electromagnetic clusters, serve to determine the fundamental input ingredients of QCD as well as to search for new physics. The authors present results from QCD studies at the Tevatron from Run 1 data, including jet and direct photon production, and a measurement of the strong coupling constant.
I. Gorelov
2001-12-28
Experimental results on QCD measurements obtained in recent analyses and based on data collected with CDF Detector from the Run 1b Tevatron running cycle are presented. The scope of the talk includes major QCD topics: a measurement of the strong coupling constant {alpha}{sub s}, extracted from inclusive jet spectra and the underlying event energy contribution to a jet cone. Another experimental object of QCD interest, prompt photon production, is also discussed and the updated measurements by CDF of the inclusive photon cross section at 630 GeV and 1800 GeV, and the comparison with NLO QCD predictions is presented.
NASA Astrophysics Data System (ADS)
Lou, Sen-yue
1998-05-01
To study a nonlinear partial differential equation (PDE), the Painleve expansion developed by Weiss, Tabor and Carnevale (WTC) is one of the most powerful methods. In this paper, using any singular manifold, the expansion series in the usual Painleve analysis is shown to be resummable in some different ways. A simple nonstandard truncated expansion with a quite universal reduction function is used for many nonlinear integrable and nonintegrable PDEs such as the Burgers, Korteweg de-Vries (KdV), Kadomtsev-Petviashvli (KP), Caudrey-Dodd-Gibbon-Sawada-Kortera (CDGSK), Nonlinear Schrödinger (NLS), Davey-Stewartson (DS), Broer-Kaup (BK), KdV-Burgers (KdVB), λf4 , sine-Gordon (sG) etc.
Gravitational waves from the cosmological QCD transition
NASA Astrophysics Data System (ADS)
Mourão Roque, V. R. C.; Roque, G. Lugones o.; Lugones, G.
2014-09-01
We determine the minimum fluctuations in the cosmological QCD phase transition that could be detectable by the eLISA/NGO gravitational wave observatory. To this end, we performed several hydrodynamical simulations using a state-of-the-art equation of state derived from lattice QCD simulations. Based on the fact that the viscosity per entropy density of the quark gluon plasma obtained from heavy-ion collision experiments at the RHIC and the LHC is extremely small, we considered a non-viscous fluid in our simulations. Several previous works about this transition considered a first order transition that generates turbulence which follows a Kolmogorov power law. We show that for the QCD crossover transition the turbulent spectrum must be very different because there is no viscosity and no source of continuous energy injection. As a consequence, a large amount of kinetic energy accumulates at the smallest scales. From the hydrodynamic simulations, we have obtained the spectrum of the gravitational radiation emitted by the motion of the fluid, finding that, if typical velocity and temperature fluctuations have an amplitude Δ v /c ≳ 10-2 and/or Δ T/T_c ≳ 10-3, they would be detected by eLISA/NGO at frequencies larger than ˜ 10-4 Hz.
Hybrid model for QCD deconfining phase boundary
NASA Astrophysics Data System (ADS)
Srivastava, P. K.; Singh, C. P.
2012-06-01
Intensive search for a proper and realistic equations of state (EOS) is still continued for studying the phase diagram existing between quark gluon plasma (QGP) and hadron gas (HG) phases. Lattice calculations provide such EOS for the strongly interacting matter at finite temperature (T) and vanishing baryon chemical potential (μB). These calculations are of limited use at finite μB due to the appearance of notorious sign problem. In the recent past, we had constructed a hybrid model description for the QGP as well as HG phases where we make use of a new excluded-volume model for HG and a thermodynamically-consistent quasiparticle model for the QGP phase and used them further to get QCD phase boundary and a critical point. Since then many lattice calculations have appeared showing various thermal and transport properties of QCD matter at finite T and μB=0. We test our hybrid model by reproducing the entire data for strongly interacting matter and predict our results at finite μB so that they can be tested in future. Finally we demonstrate the utility of the model in fixing the precise location, the order of the phase transition and the nature of CP existing on the QCD phase diagram. We thus emphasize the suitability of the hybrid model as formulated here in providing a realistic EOS for the strongly interacting matter.
ERIC Educational Resources Information Center
Mayr, Ernst
1978-01-01
Traces the history of evolution theory from Lamarck and Darwin to the present. Discusses natural selection in detail. Suggests that, besides biological evolution, there is also a cultural evolution which is more rapid than the former. (MA)
Narayanan, Siva
2016-01-01
It is important to evaluate how the value of medicine is assessed, as it may have important implications for health technology and reimbursement assessments. The value equation could comprise ‘incremental benefit/outcome’ (relative results of care in terms of patient health, comparing the innovation to best available alternative(s)) in the numerator and ‘cost’ (relative costs involved in the full cycle of care (or a defined period) for the patient's medical condition, incorporating the relevant cost-offsets due to displacement of best available alternative(s)) in the denominator. This ‘relative value’ combined with the overall net budget impact (of including the drug in the formulary or reimbursed drug list) at the concerned population level in the given institution/region/country may better inform the usefulness of the new therapeutic option to the healthcare system. As product value messages are created, anticipating external stakeholder questions and information needs, including addressing three main categories of ‘uncertainties’, namely the scientific uncertainties, usage uncertainties, and financial uncertainties, could facilitate demonstration of optimal product value and help informed decision-making to benefit all stakeholders involved in the process. PMID:27489585
Narayanan, Siva
2016-01-01
It is important to evaluate how the value of medicine is assessed, as it may have important implications for health technology and reimbursement assessments. The value equation could comprise 'incremental benefit/outcome' (relative results of care in terms of patient health, comparing the innovation to best available alternative(s)) in the numerator and 'cost' (relative costs involved in the full cycle of care (or a defined period) for the patient's medical condition, incorporating the relevant cost-offsets due to displacement of best available alternative(s)) in the denominator. This 'relative value' combined with the overall net budget impact (of including the drug in the formulary or reimbursed drug list) at the concerned population level in the given institution/region/country may better inform the usefulness of the new therapeutic option to the healthcare system. As product value messages are created, anticipating external stakeholder questions and information needs, including addressing three main categories of 'uncertainties', namely the scientific uncertainties, usage uncertainties, and financial uncertainties, could facilitate demonstration of optimal product value and help informed decision-making to benefit all stakeholders involved in the process.
Small-x evolution of structure functions in the next-to-leading order
Giovanni A. Chirilli
2010-01-01
The high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the non-linear Balitsky-Kovchegov (BK) equation. In QCD the NLO kernel has both conformal and non-conformal parts. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformal N = 4 SYM theory, then we define the "composite dipole operator", and the resulting Mobius invariant kernel for this operator agrees with the forward NLO BFKL calculation.
QCD dynamics in mesons at soft and hard scales
Nguyen, T.; Souchlas, N. A.; Tandy, P. C.
2010-07-27
Using a ladder-rainbow kernel previously established for the soft scale of light quark hadrons, we explore, within a Dyson-Schwinger approach, phenomena that mix soft and hard scales of QCD. The difference between vector and axial vector current correlators is examined to estimate the four quark chiral condensate and the leading distance scale for the onset of non-perturbative phenomena in QCD. The valence quark distributions, in the pion and kaon, defined in deep inelastic scattering, and measured in the Drell Yan process, are investigated with the same ladder-rainbow truncation of the Dyson-Schwinger and Bethe-Salpeter equations.
Two-flavor QCD thermodynamics using anisotropic lattices
NASA Astrophysics Data System (ADS)
Levkova, Ludmila; Manke, Thomas; Mawhinney, Robert
2006-04-01
Numerical simulations of full QCD on anisotropic lattices provide a convenient way to study QCD thermodynamics with fixed physics scales and reduced lattice spacing errors. We report results from calculations with two flavors of dynamical staggered fermions, where all bare parameters and the renormalized anisotropy are kept constant and the temperature is changed in small steps by varying only the number of time slices. Including results from zero-temperature scale-setting simulations, which determine the Karsch coefficients, allows for the calculation of the equation of state at finite temperatures.
R. Skartlien; E. Sollum; A. Akselsen; P. Meakin; B. Grimes; J. Sjoblom
2012-12-01
Lattice Boltzmann simulations were used to study the coalescence kinetics in emulsions with amphiphilic surfactant, under neutrally buoyant conditions, and with a significant kinematic viscosity contrast between the phases (emulating water in oil emulsions). The 3D simulation domain was large enough (256 3rd power -- 10 7th power grid points) to obtain good statistics with droplet numbers ranging from a few thousand at early times to a few hundred near equilibrium. Increased surfactant contents slowed down the coalescence rate between droplets due to the Gibbs-Marangoni effect, and the coalescence was driven by a quasi-turbulent velocity field. The kinetic energy decayed at a relatively slow rate at early times, due to conversion of interfacial energy to kinetic energy in the flow during coalescence. Phenomenological, coupled differential equations for the mean droplet diameter D(t) and the number density nd(t) were obtained from the simulation data and from film draining theories. Local (in time) power law exponents for the growth of the mean diameter (and for the concomitant decrease of nd) were established in terms of the instantaneous values of the kinetic energy, coalescence probability, Gibbs elasticity, and interfacial area. The model studies indicated that true power laws for the growth of the droplet size and decrease of the number of droplets with time may not be justified, since the exponents derived using the phenomenological model were time dependent. In contrast to earlier simulation results for symmetric blends with surfactant, we found no evidence for stretched logarithmic scaling of the formD -- [ln (ct)]a for the morphology length, or exponential scalings associated with arrested growth, on the basis of the phenomenological model.
Multi-meson systems in lattice QCD / Many-body QCD
Detmold, William
2013-08-31
Nuclear physics entails the study of the properties and interactions of hadrons, such as the proton and neutron, and atomic nuclei and it is central to our understanding of our world at the smallest scales. The underlying basis for nuclear physics is provided by the Standard Model of particle physics which describes how matter interacts through the strong, electromagnetic and weak (electroweak) forces. This theory was developed in the 1970s and provides an extremely successful description of our world at the most fundamental level to which it has been probed. The Standard Model has been, and continues to be, subject to stringent tests at particle accelerators around the world, so far passing without blemish. However, at the relatively low energies that are relevant for nuclear physics, calculations involving the strong interaction, governed by the equations of Quantum Chromodynamics (QCD), are enormously challenging, and to date, the only systematic way to perform them is numerically, using a framework known as lattice QCD (LQCD). In this approach, one discretizes space-time and numerically solves the equations of QCD on a space-time lattice; for realistic calculations, this requires highly optimized algorithms and cutting-edge high performance computing (HPC) resources. Progress over the project period is discussed in detail in the following subsections
QCD coupling constants and VDM
Erkol, G.; Ozpineci, A.; Zamiralov, V. S.
2012-10-23
QCD sum rules for coupling constants of vector mesons with baryons are constructed. The corresponding QCD sum rules for electric charges and magnetic moments are also derived and with the use of vector-meson-dominance model related to the coupling constants. The VDM role as the criterium of reciprocal validity of the sum rules is considered.
Recent Developments in Perturbative QCD
Dixon, Lance J.; /SLAC
2005-07-11
I review recent progress in perturbative QCD on two fronts: extending next-to-next-to-leading order QCD corrections to a broader range of collider processes, and applying twistor-space methods (and related spinoffs) to computations of multi-parton scattering amplitudes.
QCD: Questions, challenges, and dilemmas
Bjorken, J.
1996-11-01
An introduction to some outstanding issues in QCD is presented, with emphasis on work by Diakonov and co-workers on the influence of the instanton vacuum on low-energy QCD observables. This includes the calculation of input valence-parton distributions for deep-inelastic scattering. 35 refs., 3 figs.
NASA Astrophysics Data System (ADS)
Güijosa, Alberto
2016-10-01
In the nearly 20 years that have elapsed since its discovery, the gauge-gravity correspondence has become established as an efficient tool to explore the physics of a large class of strongly-coupled field theories. A brief overview is given here of its formulation and a few of its applications, emphasizing attempts to emulate aspects of the strong-coupling regime of quantum chromodynamics (QCD). To the extent possible, the presentation is self-contained, and does not presuppose knowledge of string theory.
Sakai, Tadakatsu; Sugimoto, Shigeki
2005-12-02
We propose a holographic dual of QCD with massless flavors on the basis of a D4/D8-brane configuration within a probe approximation. We are led to a five-dimensional Yang-Mills theory on a curved space-time along with a Chern-Simons five-form on it, both of which provide us with a unifying framework to study the massless pion and an infinite number of massive vector mesons. We make sample computations of the physical quantities that involve the mesons and compare them with the experimental data. It is found that most of the results of this model are compatible with the experiments.
Nuclear reactions from lattice QCD
NASA Astrophysics Data System (ADS)
Briceño, Raúl A.; Davoudi, Zohreh; Luu, Thomas C.
2015-02-01
One of the overarching goals of nuclear physics is to rigorously compute properties of hadronic systems directly from the fundamental theory of strong interactions, quantum chromodynamics (QCD). In particular, the hope is to perform reliable calculations of nuclear reactions which will impact our understanding of environments that occur during big bang nucleosynthesis, the evolution of stars and supernovae, and within nuclear reactors and high energy/density facilities. Such calculations, being truly ab initio, would include all two-nucleon and three-nucleon (and higher) interactions in a consistent manner. Currently, lattice quantum chromodynamics (LQCD) provides the only reliable option for performing calculations of some of the low-energy hadronic observables. With the aim of bridging the gap between LQCD and nuclear many-body physics, the Institute for Nuclear Theory held a workshop on Nuclear Reactions from LQCD on March 2013. In this review article, we report on the topics discussed in this workshop and the path planned to move forward in the upcoming years.
Lattice QCD results on cumulant ratios at freeze-out
NASA Astrophysics Data System (ADS)
Karsch, Frithjof
2017-01-01
Ratios of cumulants of net proton-number fluctuations measured by the STAR Collaboration show strong deviations from a skellam distribution, which should describe thermal properties of cumulant ratios, if proton-number fluctuations are generated in equilibrium and a hadron resonance gas (HRG) model would provide a suitable description of thermodynamics at the freeze-out temperature. We present some results on 6 th order cumulants entering the calculation of the QCD equation of state at non-zero values of the baryon chemical potential (μB ) and discuss limitations on the applicability of HRG thermodynamics deduced from a comparison between QCD and HRG model calculations of cumulants of conserved charge fluctuations. We show that basic features of the μB -dependence of skewness and kurtosis ratios of net proton-number fluctuations measured by the STAR Collaboration resemble those expected from a QCD calculation of the corresponding net baryon-number cumulant ratios.
None
2016-07-12
Modern QCD - Lecture 1 Starting from the QCD Lagrangian we will revisit some basic QCD concepts and derive fundamental properties like gauge invariance and isospin symmetry and will discuss the Feynman rules of the theory. We will then focus on the gauge group of QCD and derive the Casimirs CF and CA and some useful color identities.
Dynamics for QCD on an Infinite Lattice
NASA Astrophysics Data System (ADS)
Grundling, Hendrik; Rudolph, Gerd
2017-02-01
We prove the existence of the dynamics automorphism group for Hamiltonian QCD on an infinite lattice in R^3, and this is done in a C*-algebraic context. The existence of ground states is also obtained. Starting with the finite lattice model for Hamiltonian QCD developed by Kijowski, Rudolph (cf. J Math Phys 43:1796-1808 [15], J Math Phys 46:032303 [16]), we state its field algebra and a natural representation. We then generalize this representation to the infinite lattice, and construct a Hilbert space which has represented on it all the local algebras (i.e., kinematics algebras associated with finite connected sublattices) equipped with the correct graded commutation relations. On a suitably large C*-algebra acting on this Hilbert space, and containing all the local algebras, we prove that there is a one parameter automorphism group, which is the pointwise norm limit of the local time evolutions along a sequence of finite sublattices, increasing to the full lattice. This is our global time evolution. We then take as our field algebra the C*-algebra generated by all the orbits of the local algebras w.r.t. the global time evolution. Thus the time evolution creates the field algebra. The time evolution is strongly continuous on this choice of field algebra, though not on the original larger C*-algebra. We define the gauge transformations, explain how to enforce the Gauss law constraint, show that the dynamics automorphism group descends to the algebra of physical observables and prove that gauge invariant ground states exist.
Dudek, Jozef J.; Edwards, Robert G.
2012-03-21
In this study, we present the first comprehensive study of hybrid baryons using lattice QCD methods. Using a large basis of composite QCD interpolating fields we extract an extensive spectrum of baryon states and isolate those of hybrid character using their relatively large overlap onto operators which sample gluonic excitations. We consider the spectrum of Nucleon and Delta states at several quark masses finding a set of positive parity hybrid baryons with quantum numbersmore » $$N_{1/2^+},\\,N_{1/2^+},\\,N_{3/2^+},\\, N_{3/2^+},\\,N_{5/2^+},\\,$$ and $$\\Delta_{1/2^+},\\, \\Delta_{3/2^+}$$ at an energy scale above the first band of `conventional' excited positive parity baryons. This pattern of states is compatible with a color octet gluonic excitation having $$J^{P}=1^{+}$$ as previously reported in the hybrid meson sector and with a comparable energy scale for the excitation, suggesting a common bound-state construction for hybrid mesons and baryons.« less
NASA Astrophysics Data System (ADS)
Majumder, D. P.; Dhar, A. K.
2015-08-01
A fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves as first pointed out by Dysthe (1979) is derived for gravity waves propagating at the interface of two superposed fluids of infinite depth in the presence of air flowing over water and a basic current shear. A stability analysis is then made for a uniform Stokes gravity wave train. Graphs are plotted for the maximum growth rate of instability and for wave number at marginal stability against wave steepness for different values of air flow velocity and basic current shears. Significant deviations are noticed from the results obtained from the third order evolution equation, which is the nonlinear Schrödinger equation.
NASA Astrophysics Data System (ADS)
Lu, Yanfei; Lekszycki, Tomasz
2016-10-01
During fracture healing, a series of complex coupled biological and mechanical phenomena occurs. They include: (i) growth and remodelling of bone, whose Young's modulus varies in space and time; (ii) nutrients' diffusion and consumption by living cells. In this paper, we newly propose to model these evolution phenomena. The considered features include: (i) a new constitutive equation for growth simulation involving the number of sensor cells; (ii) an improved equation for nutrient concentration accounting for the switch between Michaelis-Menten kinetics and linear consumption regime; (iii) a new constitutive equation for Young's modulus evolution accounting for its dependence on nutrient concentration and variable number of active cells. The effectiveness of the model and its predictive capability are qualitatively verified by numerical simulations (using COMSOL) describing the healing of bone in the presence of damaged tissue between fractured parts.
QCD and Light-Front Holography
Brodsky, Stanley J.; de Teramond, Guy F.; /Costa Rica U.
2010-10-27
The soft-wall AdS/QCD model, modified by a positive-sign dilaton metric, leads to a remarkable one-parameter description of nonperturbative hadron dynamics. The model predicts a zero-mass pion for zero-mass quarks and a Regge spectrum of linear trajectories with the same slope in the leading orbital angular momentum L of hadrons and the radial quantum number N. Light-Front Holography maps the amplitudes which are functions of the fifth dimension variable z of anti-de Sitter space to a corresponding hadron theory quantized on the light front. The resulting Lorentz-invariant relativistic light-front wave equations are functions of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. The result is to a semi-classical frame-independent first approximation to the spectra and light-front wavefunctions of meson and baryon light-quark bound states, which in turn predict the behavior of the pion and nucleon form factors. The theory implements chiral symmetry in a novel way: the effects of chiral symmetry breaking increase as one goes toward large interquark separation, consistent with spectroscopic data, and the the hadron eigenstates generally have components with different orbital angular momentum; e.g., the proton eigenstate in AdS/QCD with massless quarks has L = 0 and L = 1 light-front Fock components with equal probability. The soft-wall model also predicts the form of the non-perturbative effective coupling {alpha}{sub s}{sup AdS} (Q) and its {beta}-function which agrees with the effective coupling {alpha}{sub g1} extracted from the Bjorken sum rule. The AdS/QCD model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms. A new perspective on quark and gluon condensates is also reviewed.
On the possible role of zonal dynamics in the formation and evolution of F3 layers over equator
NASA Astrophysics Data System (ADS)
Mridula, N.; Pant, Tarun Kumar
2015-11-01
In the present study, occurrences of F3 layer over Thiruvananthapuram (8.5°N; 77°E; dip latitude ~0.5°N), a dip equatorial station in India have been investigated using ionosonde data for the years 2004-2007. The F3 layers appearing in the ionograms during the pre noon hours only have been included in the analysis. The result indicates that a weak EIA resulting in low ionospheric height and high ionization density prevails before the occurrence of F3 layer and serves as an essential condition for its occurrence. The relative Slant Total Electron Content (rSTEC) measured using collocated ground based coherent low earth orbiting (LEO) radio beacon receiver has also been used along with electron densities measured by CHAMP satellite for the year 2006 and 2007 to illustrate this difference in the evolution of Equatorial Ionization Anomaly (EIA) on F3 and non F3 days. A new mechanism for F3 generation has been proposed. It has been shown that the coupling of the thermospheric zonal wind jet over equator and enhanced ionospheric density at lower heights over Indian longitude can account for the generation of F3 layer through ion-drag. The vertical wind associated with the thermospheric heating resulting from ion-drag causes the generation of an additional eastward field which, along with the prevailing F-region electric field, leads to the upward excursion of the F3 layer.
Theta angle in holographic QCD
NASA Astrophysics Data System (ADS)
Järvinen, Matti
2017-03-01
V-QCD is a class of effective holographic models for QCD which fully includes the backreaction of quarks to gluon dynamics. The physics of the θ-angle and the axial anomaly can be consistently included in these models. We analyze their phase diagrams over ranges of values of the quark mass, Nf/Nc, and θ, computing observables such as the topological susceptibility and the meson masses. At small quark mass, where effective chiral Lagrangians are reliable, they agree with the predictions of V-QCD.
Lattice QCD and Nuclear Physics
Konstantinos Orginos
2007-03-01
A steady stream of developments in Lattice QCD have made it possible today to begin to address the question of how nuclear physics emerges from the underlying theory of strong interactions. Central role in this understanding play both the effective field theory description of nuclear forces and the ability to perform accurate non-perturbative calculations in lo w energy QCD. Here I present some recent results that attempt to extract important low energy constants of the effective field theory of nuclear forces from lattice QCD.
Akbar, M Ali; Mohd Ali, Norhashidah Hj; Mohyud-Din, Syed Tauseef
2013-01-01
Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics. In the present paper, the alternative (G'/G)-expansion method has been further modified by introducing the generalized Riccati equation to construct new exact solutions. In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way. These solutions may be imperative and significant for the explanation of some practical physical phenomena. It is shown that the modified alternative (G'/G)-expansion method an efficient and advance mathematical tool for solving nonlinear partial differential equations in mathematical physics.
NLO evolution of color dipoles in N=4 SYM
Chirilli, Giovanni A.; Balitsky, Ian
2009-07-04
Here, high-energy behavior of amplitudes in a gauge theory can be reformulated in terms of the evolution of Wilson-line operators. In the leading logarithmic approximation it is given by the conformally invariant BK equation for the evolution of color dipoles. In QCD, the next-to-leading order BK equation has both conformal and non-conformal parts, the latter providing the running of the coupling constant. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformalmore » $${\\cal N}$$=4 SYM theory. We define the "composite dipole operator" with the rapidity cutoff preserving conformal invariance.« less
NASA Technical Reports Server (NTRS)
Emukashvily, I. M.
1982-01-01
An extension of the method of moments is developed for the numerical integration of the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes. The number density function n sub k (x,t) in each separate droplet packet between droplet mass grid points (x sub k, x sub k+1) is represented by an expansion in orthogonal polynomials with a given weighting function. In this way droplet number concentrations, liquid water contents and other moments in each droplet packet are conserved and the problem of solving the kinetic equations is replaced by one of solving a set of coupled differential equations for the number density function moments. The method is tested against analytic solutions of the corresponding kinetic equations. Numerical results are obtained for different coalescence/breakup and condensation/evaporation kernels and for different initial droplet spectra. Also droplet mass grid intervals, weighting functions, and time steps are varied.
Sekhar Chivukula
2016-07-12
The symmetries of a quantum field theory can be realized in a variety of ways. Symmetries can be realized explicitly, approximately, through spontaneous symmetry breaking or, via an anomaly, quantum effects can dynamically eliminate a symmetry of the theory that was presentÂ at the classical level. Â Quantum Chromodynamics (QCD),Â the modern theoryÂ of the strong interactions, exemplify each ofÂ these possibilities.Â The interplayÂ of these effects determine theÂ spectrum of particles that we observeÂ and, ultimately, account forÂ 99% of the mass of ordinary matter.Â
NASA Astrophysics Data System (ADS)
Sarcevic, Ina; Tan, Chung-I.
2000-07-01
The Table of Contents for the full book PDF is as follows: * Preface * Monday morning session: Hadronic Final States - Conveners: E. de Wolf and J. W. Gary * Session Chairman: J. W. Gary * Inclusive Jets at the Tevatron * Forward Jets, Dijets, and Subjets at the Tevatron * Inclusive Hadron Production and Dijets at HERA * Recent Opal Results on Photon Structure and Interactions * Review of Two-Photon Physics at LEP * Session Chairman: E. de Wolf * An Intriguing Area-Law-Based Hadron Production Scheme in e+e- Annihilation and Its Possible Extensions * Hyperfine Splitting in Hadron Production at High Energies * Event Selection Effects on Multiplicities in Quark and Gluon Jets * Quark and Gluon Jet Properties at LEP * Rapidity Gaps in Quark and Gluon Jets -- A Perturbative Approach * Monday afternoon session: Diffractive and Small-x - Conveners: M. Derrick and A. White * Session Chairman: A. White * Structure Functions: Low x, High y, Low Q2 * The Next-to-Leading Dynamics of the BFKL Pomeron * Renormalization Group Improved BFKL Equation * Session Chairman: G. Briskin * New Experimental Results on Diffraction at HERA * Diffractive Parton Distributions in Light-Cone QCD * The Logarithmic Derivative of the F2 Structure Function and Saturation * Spin Dependence of Diffractive DIS * Monday evening session * Session Chairman: M. Braun * Tests of QCD with Particle Production at HERA: Review and Outlook * Double Parton Scattering and Hadron Structure in Transverse Space * The High Density Parton Dynamics from Eikonal and Dipole Pictures * Hints of Higher Twist Effects in the Slope of the Proton Structure Function * Tuesday morning session: Correlations and Fluctuations - Conveners: R. Hwa and M. Tannenbaum * Session Chairman: A. Giovannini -- Fluctuations and Correlations * Bose-Einstein Results from L3 * Short-Range and Long-Range Correlations in DIS at HERA * Coior Mutation Model, Intermittency, and Erraticity * QCD Queuing and Hadron Multiplicity * Soft and Semi
LATTICE QCD AT FINITE TEMPERATURE.
PETRECZKY, P.
2005-03-12
I review recent progress in lattice QCD at finite temperature. Results on the transition temperature will be summarized. Recent progress in understanding in-medium modifications of interquark forces and quarkonia spectral functions at finite temperatures is discussed.
RECENT LATTICE RESULTS ON FINITE TEMPERATURE AND DENSITY QCD, PART 1.
KARSCH,F.
2007-07-09
We discuss recent progress made studies of bulk thermodynamics of strongly interacting matter through lattice simulations of QCD with an almost physical light and strange quark mass spectrum. We present results on the QCD equation of state at vanishing and non-vanishing quark chemical potential and show first results on baryon number and strangeness fluctuations, which might be measured in event-by-event fluctuations in low energy runs at RHIC as well as at FAIR.
NASA Astrophysics Data System (ADS)
Düll, Wolf-Patrick; Schneider, Guido; Wayne, C. Eugene
2016-05-01
In 1968 V.E. Zakharov derived the Nonlinear Schrödinger equation for the two-dimensional water wave problem in the absence of surface tension, that is, for the evolution of gravity driven surface water waves, in order to describe slow temporal and spatial modulations of a spatially and temporarily oscillating wave packet. In this paper we give a rigorous proof that the wave packets in the two-dimensional water wave problem in a canal of finite depth can be approximated over a physically relevant timespan by solutions of the Nonlinear Schrödinger equation.
NASA Astrophysics Data System (ADS)
Ren, Yong; Sakthivel, R.
2012-07-01
In this paper, we study a class of second-order neutral stochastic evolution equations with infinite delay and Poisson jumps (SNSEEIPs), in which the initial value belongs to the abstract space B. We establish the existence and uniqueness of mild solutions for SNSEEIPs under non-Lipschitz condition with Lipschitz condition being considered as a special case by means of the successive approximation. Furthermore, we give the continuous dependence of solutions on the initial data by means of a corollary of the Bihari inequality. An application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given to illustrate the theory.
The Emergence of Hadrons from QCD Color
NASA Astrophysics Data System (ADS)
Brooks, William; Color Dynamics in Cold Matter (CDCM) Collaboration
2015-10-01
The formation of hadrons from energetic quarks, the dynamical enforcement of QCD confinement, is not well understood at a fundamental level. In Deep Inelastic Scattering, modifications of the distributions of identified hadrons emerging from nuclei of different sizes reveal a rich variety of spatial and temporal characteristics of the hadronization process, including its dependence on spin, flavor, energy, and hadron mass and structure. The EIC will feature a wide range of kinematics, allowing a complete investigation of medium-induced gluon bremsstrahlung by the propagating quarks, leading to partonic energy loss. This fundamental process, which is also at the heart of jet quenching in heavy ion collisions, can be studied for light and heavy quarks at the EIC through observables quantifying hadron ``attenuation'' for a variety of hadron species. Transverse momentum broadening of hadrons, which is sensitive to the nuclear gluonic field, will also be accessible, and can be used to test our understanding from pQCD of how this quantity evolves with pathlength, as well as its connection to partonic energy loss. The evolution of the forming hadrons in the medium will shed new light on the dynamical origins of the forces between hadrons, and thus ultimately on the nuclear force. Supported by the Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT) of Chile.
High-Energy QCD Asymptotics of Photon--Photon Collisions
Brodsky, Stanley J.
2002-07-26
The high-energy behavior of the total cross section for highly virtual photons, as predicted by the BFKL equation at next-to-leading order (NLO) in QCD, is discussed. The NLO BFKL predictions, improved by the BLM optimal scale setting, are in good agreement with recent OPAL and L3 data at CERN LEP2. NLO BFKL predictions for future linear colliders are presented.
Towards the QCD phase diagram from analytical continuation
NASA Astrophysics Data System (ADS)
Bellwied, R.; Borsányi, S.; Fodor, Z.; Günther, J.; Katz, S. D.; Pásztor, A.; Ratti, C.; Szabó, K. K.
2016-12-01
We calculate the QCD cross-over temperature, the equation of state and fluctuations of conserved charges at finite density by analytical continuation from imaginary to real chemical potentials. Our calculations are based on new continuum extrapolated lattice simulations using the 4stout staggered actions with a lattice resolution up to Nt = 16. The simulation parameters are tuned such that the strangeness neutrality is maintained, as it is in heavy ion collisions.
Light-Front Holography and Non-Perturbative QCD
Brodsky, Stanley J.; de Teramond, Guy F.; /Costa Rica U.
2009-12-09
The combination of Anti-de Sitter space (AdS) methods with light-front holography leads to a semi-classical first approximation to the spectrum and wavefunctions of meson and baryon light-quark bound states. Starting from the bound-state Hamiltonian equation of motion in QCD, we derive relativistic light-front wave equations in terms of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti-de Sitter (AdS) space. Its eigenvalues give the hadronic spectrum, and its eigenmodes represent the probability distribution of the hadronic constituents at a given scale. Applications to the light meson and baryon spectra are presented. The predicted meson spectrum has a string-theory Regge form M{sup 2} = 4{kappa}{sup 2}(n + L + S = 2); i.e., the square of the eigenmass is linear in both L and n, where n counts the number of nodes of the wavefunction in the radial variable {zeta}. The space-like pion form factor is also well reproduced. One thus obtains a remarkable connection between the description of hadronic modes in AdS space and the Hamiltonian formulation of QCD in physical space-time quantized on the light-front at fixed light-front time {tau}. The model can be systematically improved by using its complete orthonormal solutions to diagonalize the full QCD light-front Hamiltonian or by applying the Lippmann-Schwinger method in order to systematically include the QCD interaction terms.
NASA Astrophysics Data System (ADS)
Winckler, N.; Rybalchenko, A.; Shevelko, V. P.; Al-Turany, M.; Kollegger, T.; Stöhlker, Th.
2017-02-01
A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.
NASA Astrophysics Data System (ADS)
Nicolaidis, A.; Bordes, G.
1986-05-01
We examine available experimental distributions of transverse energy and transverse momentum, obtained at the CERN pp¯ collider, in the context of quantum chromodynamics. We consider the following. (i) The hadronic transverse energy released during W+/- production. This hadronic transverse energy is made out of two components: a soft component which we parametrize using minimum-bias events and a semihard component which we calculate from QCD. (ii) The transverse momentum of the produced W+/-. If the transverse momentum (or the transverse energy) results from a single gluon jet we use the formalism of Dokshitzer, Dyakonov, and Troyan, while if it results from multiple-gluon emission we use the formalism of Parisi and Petronzio. (iii) The relative transverse momentum of jets. While for W+/- production quarks play an essential role, jet production at moderate pT and present energies is dominated by gluon-gluon scattering and therefore we can study the Sudakov form factor of the gluon. We suggest also how through a Hankel transform of experimental data we can have direct access to the Sudakov form factors of quarks and gluons.
NASA Astrophysics Data System (ADS)
Brandt, Bastian B.; Lohmayer, Robert; Wettig, Tilo
2016-11-01
We explore an alternative discretization of continuum SU( N c ) Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer. In this discretization the self-interactions of the gauge field are induced by a path integral over N b auxiliary boson fields, which are coupled linearly to the gauge field. The main progress compared to earlier approaches is that N b can be as small as N c . In the present paper we (i) extend the proof that the continuum limit of the new discretization reproduces Yang-Mills theory in two dimensions from gauge group U( N c ) to SU( N c ), (ii) derive refined bounds on N b for non-integer values, and (iii) perform a perturbative calculation to match the bare parameter of the induced gauge theory to the standard lattice coupling. In follow-up papers we will present numerical evidence in support of the conjecture that the induced gauge theory reproduces Yang-Mills theory also in three and four dimensions, and explore the possibility to integrate out the gauge fields to arrive at a dual formulation of lattice QCD.
Gupta, R.
1994-12-31
This talk contains an analysis of quenched chiral perturbation theory and its consequences. The chiral behavior of a number of quantities such as the pion mass m{sub pi}{sup 2}, the Bernard-Golterman ratios R and {sub X}, the masses of nucleons, and the kaon B-parameter are examined to see if the singular terms induced by the additional Goldstone boson, {eta}{prime}, are visible in present data. The overall conclusion (different from that presented at the lattice meeting) of this analysis is that even though there are some caveats attached to the indications of the extra terms induced by {eta}{prime} loops, the standard expressions break down when extrapolating the quenched data with m{sub q} < m{sub s}/2 to physical light quarks. I then show that due to the single and double poles in the quenched {eta}{prime}, the axial charge of the proton cannot be calculated using the Adler-Bell-Jackiw anomaly condition. I conclude with a review of the status of the calculation of light quark masses from lattice QCD.
LATTICE QCD AT FINITE TEMPERATURE AND DENSITY.
BLUM,T.; CREUTZ,M.; PETRECZKY,P.
2004-02-24
With the operation of the RHIC heavy ion program, the theoretical understanding of QCD at finite temperature and density has become increasingly important. Though QCD at finite temperature has been extensively studied using lattice Monte-Carlo simulations over the past twenty years, most physical questions relevant for RHIC (and future) heavy ion experiments remain open. In lattice QCD at finite temperature and density there have been at least two major advances in recent years. First, for the first time calculations of real time quantities, like meson spectral functions have become available. Second, the lattice study of the QCD phase diagram and equation of state have been extended to finite baryon density by several groups. Both issues were extensively discussed in the course of the workshop. A real highlight was the study of the QCD phase diagram in (T, {mu})-plane by Z. Fodor and S. Katz and the determination of the critical end-point for the physical value of the pion mass. This was the first time such lattice calculations at, the physical pion mass have been performed. Results by Z Fodor and S. Katz were obtained using a multi-parameter re-weighting method. Other determinations of the critical end point were also presented, in particular using a Taylor expansion around {mu} = 0 (Bielefeld group, Ejiri et al.) and using analytic continuation from imaginary chemical potential (Ph. de Forcrand and O. Philipsen). The result based on Taylor expansion agrees within errors with the new prediction of Z. Fodor and S. Katz, while methods based on analytic continuation still predict a higher value for the critical baryon density. Most of the thermodynamics studies in full QCD (including those presented at this workshop) have been performed using quite coarse lattices, a = 0.2-0.3 fm. Therefore one may worry about cutoff effects in different thermodynamic quantities, like the transition temperature T{sub tr}. At the workshop U. Heller presented a study of the transition
Brodsky, S
2004-01-15
Measurements from HERMES, SMC, and Jlab show a significant single-spin asymmetry in semi-inclusive pion leptoproduction {gamma}*(q)p {yields} {pi}X when the proton is polarized normal to the photon-to-pion production plane. Hwang, Schmidt, and I [1] have shown that final-state interactions from gluon exchange between the outgoing quark and the target spectator system lead to such single-spin asymmetries at leading twist in perturbative QCD; i.e., the rescattering corrections are not power-law suppressed at large photon virtuality Q{sup 2} at fixed x{sub bj}. The existence of such single-spin asymmetries (the Sivers effect) requires a phase difference between two amplitudes coupling the proton target with J{sub p}{sup z} = {+-} 1/2 to the same final-state, the same amplitudes which are necessary to produce a nonzero proton anomalous magnetic moment. The single-spin asymmetry which arises from such final-state interactions is in addition to the Collins effect which measures the transversity distribution {delta}q(x, Q). The Sivers effect also leads to a leading-twist target single-spin asymmetry for jet production in electroproduction where the thrust axis is used to define the production plane. More generally, Hoyer, Marchal, Peigne, Sannino, and I [2] have shown that one cannot neglect the interactions which occur between the times of the currents in the current correlator even in light-cone gauge. For example, the final-state interactions lead to the Bjorken-scaling diffractive component {gamma}*p {yields} pX of deep inelastic scattering. Since the gluons exchanged in the final state carry negligible k{sup +}, the Pomeron structure function closely resembles that of the primary gluon. The diffractive scattering of the fast outgoing quarks on spectators in the target in turn causes shadowing in the DIS cross section. These effects highlight the unexpected importance of final- and initial-state interactions in QCD observables, they lead to leading-twist single
Recent QCD results from the Tevatron
Pickarz, Henryk; CDF and DO collaboration
1997-02-01
Recent QCD results from the CDF and D0 detectors at the Tevatron proton-antiproton collider are presented. An outlook for future QCD tests at the Tevatron collider is also breifly discussed. 27 refs., 11 figs.
Twisted mass QCD for weak matrix elements
NASA Astrophysics Data System (ADS)
Pena, Carlos
2006-12-01
I report on the application of tmQCD techniques to the computation of hadronic matrix elements of four-fermion operators. Emphasis is put on the computation of BK in quenched QCD performed by the ALPHA Collaboration. The extension of tmQCD strategies to the study of neutral B- meson mixing is briefly discussed. Finally, some remarks are made concerning proposals to apply tmQCD to the computation of K → ππ amplitudes.
Light-Front Holography and Novel Effects in QCD
Brodsky, Stanley J.; de Teramond, Guy F.
2008-12-18
The correspondence between theories in anti-de Sitter space and conformal field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD. Light-front holography allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. We identify the AdS coordinate z with an invariant light-front coordinate {zeta} which separates the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single-variable light-front Schroedinger equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. The mapping of electromagnetic and gravitational form factors in AdS space to their corresponding expressions in light-front theory confirms this correspondence. Some novel features of QCD are discussed, including the consequences of confinement for quark and gluon condensates and the behavior of the QCD coupling in the infrared. The distinction between static structure functions such as the probability distributions computed from the square of the light-front wavefunctions versus dynamical structure functions which include the effects of rescattering is emphasized. A new method for computing the hadronization of quark and gluon jets at the amplitude level, an event amplitude generator, is outlined.
Quantum chromodynamics (QCD) and collider physics
Ellis, R.K. ); Stirling, W.J. )
1990-08-14
This report discusses: fundamentals of perturbative QCD; QCD in e{sup +}e{sup {minus}} {yields} hadrons; deep inelastic scattering and parton distributions; the QCD parton model in hadron-hadron collisions; large p{sub T} jet production in hadron-hadron collisions; the production of vector bosons in hadronic collisions; and the production of heavy quarks.
NASA Astrophysics Data System (ADS)
Kwieciński, Jan; Maul, Martin
2003-02-01
In this paper we derive an integral equation for the evolution of unintegrated (longitudinally) polarized quark and gluon parton distributions. The conventional Catani-Ciafaloni-Fiorani-Marchesini (CCFM) framework is modified at small x in order to incorporate the QCD expectations concerning the double ln2(1/x) resummation at low x for the integrated distributions. Complete Altarelli-Parisi splitting functions are included that makes the formalism compatible with the leading order Altarelli-Parisi evolution at large and moderately small values of x. The obtained modified polarized CCFM equation is shown to be partially diagonalized by the Fourier-Bessel transformation. Results of the numerical solution for this modifed polarized CCFM equation for the nonsinglet quark distributions are presented.
QCD inequalities for hadron interactions.
Detmold, William
2015-06-05
We derive generalizations of the Weingarten-Witten QCD mass inequalities for particular multihadron systems. For systems of any number of identical pseudoscalar mesons of maximal isospin, these inequalities prove that near threshold interactions between the constituent mesons must be repulsive and that no bound states can form in these channels. Similar constraints in less symmetric systems are also extracted. These results are compatible with experimental results (where known) and recent lattice QCD calculations, and also lead to a more stringent bound on the nucleon mass than previously derived, m_{N}≥3/2m_{π}.
Hadron scattering, resonances, and QCD
Briceno, Raul
2016-12-01
The non-perturbative nature of quantum chromodynamics (QCD) has historically left a gap in our understanding of the connection between the fundamental theory of the strong interactions and the rich structure of experimentally observed phenomena. For the simplest properties of stable hadrons, this is now circumvented with the use of lattice QCD (LQCD). In this talk I discuss a path towards a rigorous determination of few-hadron observables from LQCD. I illustrate the power of the methodology by presenting recently determined scattering amplitudes in the light-meson sector and their resonance content.
The supercritical pomeron in QCD.
White, A. R.
1998-06-29
Deep-inelastic diffractive scaling violations have provided fundamental insight into the QCD pomeron, suggesting a single gluon inner structure rather than that of a perturbative two-gluon bound state. This talk outlines a derivation of a high-energy, transverse momentum cut-off, confining solution of QCD. The pomeron, in first approximation, is a single reggeized gluon plus a ''wee parton'' component that compensates for the color and particle properties of the gluon. This solution corresponds to a super-critical phase of Reggeon Field Theory.
Lattice QCD: Status and Prospect
Ukawa, Akira
2006-02-08
A brief review is given of the current status and near-future prospect of lattice QCD studies of the Standard Model. After summarizing a bit of history, we describe current attempts toward inclusion of dynamical up, down and strange quarks. Recent results on the light hadron mass spectrum as well as those on the heavy quark quantities are described. Recent work on lattice pentaquark search is summarized. We touch upon the PACS-CS Project for building our next machine for lattice QCD, and conclude with a summary of computer situation and the physics possibilities over the next several years.
Yun, J.C.
1990-10-10
In this paper we report recent QCD analysis with the new data taken from CDF detector. CDF recorded an integrated luminosity of 4.4 nb{sup {minus}1} during the 1988--1989 run at center of mass system (CMS) energy of 1.8 TeV. The major topics of this report are inclusive jet, dijet, trijet and direct photon analysis. These measurements are compared of QCD predictions. For the inclusive jet an dijet analysis, tests of quark compositeness are emphasized. 11 refs., 6 figs.
Glueball decay in holographic QCD
Hashimoto, Koji; Tan, C.-I; Terashima, Seiji
2008-04-15
Using holographic QCD based on D4-branes and D8-anti-D8-branes, we have computed couplings of glueballs to light mesons. We describe glueball decay by explicitly calculating its decay widths and branching ratios. Interestingly, while glueballs remain less well understood both theoretically and experimentally, our results are found to be consistent with the experimental data for the scalar glueball candidate f{sub 0}(1500). More generally, holographic QCD predicts that decay of any glueball to 4{pi}{sup 0} is suppressed, and that mixing of the lightest glueball with qq mesons is small.
J.J. Sakurai Prize for Theoretical Particle Physics: 40 Years of Lattice QCD
NASA Astrophysics Data System (ADS)
Lepage, Peter
2016-03-01
Lattice QCD was invented in 1973-74 by Ken Wilson, who passed away in 2013. This talk will describe the evolution of lattice QCD through the past 40 years with particular emphasis on its first years, and on the past decade, when lattice QCD simulations finally came of age. Thanks to theoretical breakthroughs in the late 1990s and early 2000s, lattice QCD simulations now produce the most accurate theoretical calculations in the history of strong-interaction physics. They play an essential role in high-precision experimental studies of physics within and beyond the Standard Model of Particle Physics. The talk will include a non-technical review of the conceptual ideas behind this revolutionary development in (highly) nonlinear quantum physics, together with a survey of its current impact on theoretical and experimental particle physics, and prospects for the future. Work supported by the National Science Foundation.
General QED/QCD aspects of simple systems
Telegdi, V.L.; Brodsky, S.J.
1989-09-01
This paper discusses the following topics: renormalization theory; the Kinoshita-Lee-Nauenberg theorem; the Yennie-Frautschi-Suura relation; scale invariance at large momentum transfer; scaling and scaling violation at large momentum transfers; low-energy theorem in Compton scattering; does the perturbation series in QED converge; renormalization of the weak angle /Theta//sub w/; the Nambu-Bethe-Salpeter (NBS) equation; the decay rate of /sup 3/S, positronium; radiative corrections to QCD Born cross section; and progress on the relativistic 2-body equation.
NASA Astrophysics Data System (ADS)
Dey, Bijoy K.; Askar, Attila; Rabitz, H.
1998-11-01
An alternative method of quantum dynamics is presented. The method is based on the hydrodynamical formulation of the time-dependent Schrödinger equation originally given by David Bohm in his quest for establishing a hidden variable alternative to the quantum mechanics. A new alternating direction implicit technique has been employed to decouple many-dimensional hydrodynamical equations into a set of one-dimensional equations which have been solved numerically by adopting a recently developed flux corrected transport algorithm. We apply the method to describe the dynamics of a quantum particle in three spatial dimensions where analytical solutions are known.
Small-x evolution in the next-to-leading order
Giovanni Antonio Chirilli
2009-12-01
After a brief introduction to Deep Inelastic Scattering in the Bjorken limit and in the Regge Limit we discuss the operator product expansion in terms of non local string operator and in terms of Wilson lines. We will show how the high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the non-linear Balitsky-Kovchegov (BK) equation. In order to see if this equation is relevant for existing or future deep inelastic scattering (DIS) accelerators (like Electron Ion Collider (EIC) or Large Hadron electron Collider (LHeC)) one needs to know the next-to-leading order (NLO) corrections. In addition, the NLO corrections define the scale of the running-coupling constant in the BK equation and therefore determine the magnitude of the leading-order cross sections. In Quantum Chromodynamics (QCD), the next-to-leading order BK equation has both conformal and non-conformal parts. The NLO kernel for the composite operators resolves in a sum of the conformal part and the running-coupling part. The QCD and kernel of the BK equation is presented.
Boz, Tamer; Skullerud, Jon-Ivar; Giudice, Pietro; Hands, Simon; Williams, Anthony G.
2016-01-22
QCD at high chemical potential has interesting properties such as deconfinement of quarks. Two-color QCD, which enables numerical simulations on the lattice, constitutes a laboratory to study QCD at high chemical potential. Among the interesting properties of two-color QCD at high density is the diquark condensation, for which we present recent results obtained on a finer lattice compared to previous studies. The quark propagator in two-color QCD at non-zero chemical potential is referred to as the Gor’kov propagator. We express the Gor’kov propagator in terms of form factors and present recent lattice simulation results.
Michael Pennington
2011-05-01
The Schwinger-Dyson, Bethe-Salpeter system of equations are the link between coloured quarks and gluons, and colourless hadrons and their properties. This talk reviews some aspects of these studies from the infrared behaviour of ghosts to the prediction of electromagnetic form-factors.
Pennington, M. R.
2011-05-23
The Schwinger-Dyson, Bethe-Salpeter system of equations are the link between coloured quarks and gluons, and colourless hadrons and their properties. This talk reviews some aspects of these studies from the infrared behaviour of ghosts to the prediction of electromagnetic form-factors.
Controlling quark mass determinations non-perturbatively in three-flavour QCD
NASA Astrophysics Data System (ADS)
Campos, Isabel; Fritzsch, Patrick; Pena, Carlos; Preti, David; Ramos, Alberto; Vladikas, Anastassios
2017-03-01
The determination of quark masses from lattice QCD simulations requires a non-perturbative renormalization procedure and subsequent scale evolution to high energies, where a conversion to the commonly used \\overline {{{MS}}} scheme can be safely established. We present our results for the non-perturbative running of renormalized quark masses in Nf = 3 QCD between the electroweak and a hadronic energy scale, where lattice simulations are at our disposal. Recent theoretical advances in combination with well-established techniques allows to follow the scale evolution to very high statistical accuracy, and full control of systematic effects.
Recent progress in lattice QCD
Sharpe, S.R.
1992-12-01
A brief overview of the status of lattice QCD is given, with emphasis on topics relevant to phenomenology. The calculation of the light quark spectrum, the lattice prediction of {alpha} {sub {ovr MS}} (M {sub Z}), and the calculation of f{sub B} are discussed. 3 figs., 3 tabs., 40 refs.
Lattice QCD in Background Fields
William Detmold, Brian Tiburzi, Andre Walker-Loud
2009-06-01
Electromagnetic properties of hadrons can be computed by lattice simulations of QCD in background fields. We demonstrate new techniques for the investigation of charged hadron properties in electric fields. Our current calculations employ large electric fields, motivating us to analyze chiral dynamics in strong QED backgrounds, and subsequently uncover surprising non-perturbative effects present at finite volume.
Meson Resonances from Lattice QCD
Edwards, Robert G.
2016-06-01
There has been recent, significant, advances in the determination of the meson spectrum of QCD. Current efforts have focused on the development and application of finite-volume formalisms that allow for the determination of scattering amplitudes as well as resonance behavior in coupled channel systems. I will review some of these recent developments, and demonstrate the viability of the method in meson systems.
Basics of QCD perturbation theory
Soper, D.E.
1997-06-01
This is an introduction to the use of QCD perturbation theory, emphasizing generic features of the theory that enable one to separate short-time and long-time effects. The author also covers some important classes of applications: electron-positron annihilation to hadrons, deeply inelastic scattering, and hard processes in hadron-hadron collisions. 31 refs., 38 figs.
QCD Phase Transitions, Volume 15
Schaefer, T.; Shuryak, E.
1999-03-20
The title of the workshop, ''The QCD Phase Transitions'', in fact happened to be too narrow for its real contents. It would be more accurate to say that it was devoted to different phases of QCD and QCD-related gauge theories, with strong emphasis on discussion of the underlying non-perturbative mechanisms which manifest themselves as all those phases. Before we go to specifics, let us emphasize one important aspect of the present status of non-perturbative Quantum Field Theory in general. It remains true that its studies do not get attention proportional to the intellectual challenge they deserve, and that the theorists working on it remain very fragmented. The efforts to create Theory of Everything including Quantum Gravity have attracted the lion share of attention and young talent. Nevertheless, in the last few years there was also a tremendous progress and even some shift of attention toward emphasis on the unity of non-perturbative phenomena. For example, we have seen some efforts to connect the lessons from recent progress in Supersymmetric theories with that in QCD, as derived from phenomenology and lattice. Another example is Maldacena conjecture and related development, which connect three things together, string theory, super-gravity and the (N=4) supersymmetric gauge theory. Although the progress mentioned is remarkable by itself, if we would listen to each other more we may have chance to strengthen the field and reach better understanding of the spectacular non-perturbative physics.
Heavy quark production and QCD
Purohit, M.V.
1988-12-01
Recent results on charm and beauty production in fixed target experiments are reviewed. Particular emphasis is placed on the recent results, on the trend favored by the data, on companies with the recently improved QCD predictions and on what may be expected in the near future. 35 refs., 5 figs.
New results in perturbative QCD
Ellis, R.K.
1985-11-01
Three topics in perturbative QCD important for Super-collider physics are reviewed. The topics are: (2 2) jet phenomena calculated in O( sT); new techniques for the calculation of tree graphs; and colour coherence in jet phenomena. 31 refs., 6 figs.
Strings, quarkonium and nuclear physics in lattice QCD
NASA Astrophysics Data System (ADS)
Stewart, Christopher Robert
2000-11-01
Quantum Chromodynamics, QCD, is currently accepted as the correct theory of quark and gluon interactions, a theory that embodies many of our modern notions about the links between mathematical symmetry and physical reality. It is also, for many interesting phenomena, a strongly-coupled theory. Traditional perturbation theory can not be applied to low-energy QCD; new, non-perturbative methods are required. Lattice QCD is the most successful non-perturbative, first-principles approach to investigations of QCD physics. The QCD field equations are discretised on a space-time grid, making them well-suited to numerical simulation. We have performed lattice simulations to investigate three separate problems in low-energy QCD. First, the nature of the strong nuclear force was examined through the simpler system of two interacting heavy-light mesons. The inter-meson binding potential was extracted from lattice simulations, and was in quantitative agreement with the Yukawa model of pion exchange. Next we investigated the phenomenon of string-breaking. The QCD static-quark potential is confining-the gluon field between spatially separated quarks forms a narrow flux `string', with energy that increases linearly with the quark separation. For large separations, the field energy is sufficient for the system to decay into a static-light meson pair. To date, evidence for this `string-breaking' effect has been elusive. We presented a lattice operator that produces the desired effect, even in the absence of light sea-quarks. This has implications for current string- breaking investigations. Finally, we attempted precision simulations of the charmonium ( cc¯) meson family using a non-relativistic effective theory of heavy-quark interactions known as NRQCD. The charm quark is a challenge for lattice simulations-large discrepancies exist between experimental measurements and lattice results for the charmonium spectrum. We performed NRQCD simulations of the charmonium system to examine
NASA Astrophysics Data System (ADS)
Dhar, A. K.; Mondal, J.
2015-05-01
Fourth order nonlinear evolution equations, which are a good starting point for the study of nonlinear water waves, are derived for deep water surface capillary gravity waves in the presence of second waves in which air is blowing over water. Here it is assumed that the space variation of the amplitude takes place only in a direction along which the group velocity projection of the two waves overlap. A stability analysis is made for a uniform wave train in the presence of a second wave train. Graphs are plotted for the maximum growth rate of instability wave number at marginal stability and wave number separation of fastest growing sideband component against wave steepness. Significant improvements are noticed from the results obtained from the two coupled third order nonlinear Schrödinger equations.
Dynamical model for longitudinal wave functions in light-front holographic QCD
Chabysheva, Sophia S.; Hiller, John R.
2013-10-15
We construct a Schrödinger-like equation for the longitudinal wave function of a meson in the valence qq{sup -bar} sector, based on the ’t Hooft model for large-N two-dimensional QCD, and combine this with the usual transverse equation from light-front holographic QCD, to obtain a model for mesons with massive quarks. The computed wave functions are compared with the wave function ansatz of Brodsky and de Téramond and used to compute decay constants and parton distribution functions. The basis functions used to solve the longitudinal equation may be useful for more general calculations of meson states in QCD. -- Highlights: •Provide relativistic quark model based on light-front holographic QCD. •Incorporate dependence on quark mass. •Consistent with the Brodsky–de Téramond quark-wave-function ansatz. •Compute meson decay constants and parton distribution functions. •Illustrate use of basis functions that could be convenient for more general numerical calculations in light-front QCD.
NASA Astrophysics Data System (ADS)
Chen, Jinbing
2010-08-01
Each soliton equation in the Korteweg-de Vries (KdV) hierarchy, the 2+1 dimensional breaking soliton equation, and the 2+1 dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation are reduced to two or three Neumann systems on the tangent bundle TSN -1 of the unit sphere SN -1. The Lax-Moser matrix for the Neumann systems of degree N -1 is deduced in view of the Mckean-Trubowitz identity and a bilinear generating function, whose favorite characteristic accounts for the problem of the genus of Riemann surface matching to the number of elliptic variables. From the Lax-Moser matrix, the constrained Hamiltonians in the sense of Dirac-Poisson bracket for all the Neumann systems are written down in a uniform recursively determined by integrals of motion. The involution of integrals of motion and constrained Hamiltonians is completed on TSN -1 by using a Lax equation and their functional independence is displayed over a dense open subset of TSN -1 by a direct calculation, which contribute to the Liouville integrability of a family of Neumann systems in a new systematical way. We also construct the hyperelliptic curve of Riemann surface and the Abel map straightening out the restricted Neumann flows that naturally leads to the Jacobi inversion problem on the Jacobian with the aid of the holomorphic differentials, from which some finite-gap solutions expressed by Riemann theta functions for the 2+1 dimensional breaking soliton equation, the 2+1 dimensional CDGKS equation, the KdV, and the fifth-order KdV equations are presented by means of the Riemann theorem.
NASA Technical Reports Server (NTRS)
Nakagawa, Y.
1981-01-01
The method described as the method of nearcharacteristics by Nakagawa (1980) is renamed the method of projected characteristics. Making full use of properties of the projected characteristics, a new and simpler formulation is developed. As a result, the formulation for the examination of the general three-dimensional problems is presented. It is noted that since in practice numerical solutions must be obtained, the final formulation is given in the form of difference equations. The possibility of including effects of viscous and ohmic dissipations in the formulation is considered, and the physical interpretation is discussed. A systematic manner is then presented for deriving physically self-consistent, time-dependent boundary equations for MHD initial boundary problems. It is demonstrated that the full use of the compatibility equations (differential equations relating variations at two spatial locations and times) is required in determining the time-dependent boundary conditions. In order to provide a clear physical picture as an example, the evolution of axisymmetric global magnetic field by photospheric differential rotation is considered.
Phases of QCD, thermal quasiparticles, and dilepton radiation from a fireball
NASA Astrophysics Data System (ADS)
Renk, Thorsten; Schneider, Roland; Weise, Wolfram
2002-07-01
We calculate dilepton production rates from a fireball adapted to the kinematical conditions realized in ultrarelativistic heavy-ion collisions over a broad range of beam energies. The freeze-out state of the fireball is fixed by hadronic observables. We use this information combined with the initial geometry of the collision region to follow the space-time evolution of the fireball. Assuming entropy conservation, its bulk thermodynamic properties can then be uniquely obtained once the equation of state (EOS) is specified. The high-temperature quark-gluon plasma (QGP) phase is modeled by a nonperturbative quasiparticle model that incorporates a phenomenological confinement description, adapted to lattice QCD results. For the hadronic phase, we interpolate the EOS into the region where a resonance gas approach seems applicable, keeping track of a possible overpopulation of the pion phase space. In this way, the fireball evolution is specified without reference to dilepton data, thus eliminating it as an adjustable parameter in the rate calculations. Dilepton emission in the QGP phase is then calculated within the quasiparticle model. In the hadronic phase, both temperature and finite baryon density effects on the photon spectral function are incorporated. Existing dilepton data from CERES at 158 and 40 A GeV Pb-Au collisions are well described, and a prediction for the PHENIX setup at RHIC for (s)=200A GeV is given.
Vector meson electroproduction in QCD
NASA Astrophysics Data System (ADS)
Lu, Juan; Cai, Xian-Hao; Zhou, Li-Juan
2012-08-01
Based on the generalized QCD vector meson dominance model, we study the electroproduction of a vector meson off a proton in the QCD inspired eikonalized model. Numerical calculations for the total cross section σtot and differential cross section dσ/dt are performed for ρ, ω and varphi meson electroproduction in this paper. Since gluons interact among themselves (self-interaction), two gluons can form a glueball with quantum numbers IG, JPC = 0+,2++, decay width Γt ≈ 100 MeV, and mass of mG = 2.23 GeV. The three gluons can form a three-gluon colorless bound state with charge conjugation quantum number C = -1, called the Odderon. The mediators of interactions between projectiles (the quark and antiquark pair fluctuated from the virtual photon) and the proton target (a three-quark system) are the tensor glueball and the Odderon. Our calculated results in the tensor glueball and Odderon exchange model fit to the existing data successfully, which evidently shows that our present QCD mechanism is a good description of meson electroproduction off a proton. It should be emphasized that our mechanism is different from the theoretical framework of Block et al. We also believe that the present study and its success are important for the investigation of other vector meson electro- and photoproduction at high energies, as well as for searching for new particles such as tensor glueballs and Odderons, which have been predicted by QCD and the color glass condensate model (CGC). Therefore, in return, it can test the validity of QCD and the CGC model.
NASA Astrophysics Data System (ADS)
Morrison, J. P.; Saquet, N.; Grant, E. R.
2012-01-01
Coupled rate equation calculations demonstrate that the variational rate theory models for the three-body electron-electron-ion scattering dynamics associated with ultracold plasma evolution scale with density in accordance with the classical mechanics of a Coulomb system. Completeness of scaling requires a broad domain of Rydberg levels over which a quasi-equilibrium can be established. For given initial conditions, the predicted evolution of electron temperature with time changes with the choice of nmax, i.e. the highest Rydberg orbital populated by three-body recombination. But, if the criterion that defines nmax scales with density, then the results scale. Molecular dynamics calculations distinguish bound Rydberg states by an electron-ion distance criterion, Rmax, which is represented in scaled coordinates by Rmax = rmaxaws, where aws represents the Wigner-Seitz radius and rmax is chosen arbitrarily. The rate equation calculations best conform with the output of molecular dynamics simulations for values of nmax defined by a thermal criterion, n_max=\\sqrt{ {R}/k_BT_e}. In a hydrogenic limit, the thermal criterion equates with a scaled distance criterion when rmax = Γe/2, where Γe = e2/4πɛ0awskBTe describes the degree of electron correlation. Molecular dynamics simulations conventionally attenuate the Coulomb potential by means of a term, C, PE_{ij}=q_iq_j/4\\pi \\epsilon _0\\sqrt{R_{ij}^2+(Ca_{ws})^2}. Reference to rate equation calculations suggests a connection between the soft-core term, C, and nmin, the lowest Rydberg level considered in the relaxation of the plasma to a quasi-steady state.
Small-x Evolution in the Next-to-Leading Order
Ian Balitsky
2009-10-01
The high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the non-linear BK equation. The NLO corrections define the scale of the running-coupling constant in the BK equation and in QCD, its kernel has both conformal and non-conformal parts. To separate the conformally invariant effects from the running-coupling effects, we calculate the NLO evolution of the color dipoles in the conformal N=4 SYM theory, then we define the 'composite dipole operator' with the rapidity cutoff preserving conformal invariance, and the resulting Möbius invariant kernel for this operator agrees with the forward NLO BFKL calculation.
2005-05-06
and node counts for a codimension-n problem of solving the eikonal equation |∇φ| = 1, (8) with a boundary point at xb = (0.5, 0.5, . . . , 0.5) with...unorganized points using variational level set method. Comp. Vis. and Image Under., 80:295–319, 2000. [40] Hongkai Zhao. A fast sweeping method for eikonal equations. Math. Comp., 74(250):603–627 (electronic), 2005. 21 ...nature. Secondly, they re- quire a backtracking along characteristics and an interpolation at an arbitrary point within the domain. This
QCD on the Light-Front. A Systematic Approach to Hadron Physics
NASA Astrophysics Data System (ADS)
Brodsky, Stanley J.; de Téramond, Guy F.; Dosch, Hans Günter
2014-06-01
Light-front Hamiltonian theory, derived from the quantization of the QCD Lagrangian at fixed light-front time x + = x 0 + x 3, provides a rigorous frame-independent framework for solving nonperturbative QCD. The eigenvalues of the light-front QCD Hamiltonian H LF predict the hadronic mass spectrum, and the corresponding eigensolutions provide the light-front wavefunctions which describe hadron structure, providing a direct connection to the QCD Lagrangian. In the semiclassical approximation the valence Fock-state wavefunctions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schrödinger equation, with an effective confining potential U which systematically incorporates the effects of higher quark and gluon Fock states. Remarkably, the potential U has a unique form of a harmonic oscillator potential if one requires that the chiral QCD action remains conformally invariant. A mass gap and the color confinement scale also arises when one extends the formalism of de Alfaro, Fubini and Furlan to light-front Hamiltonian theory. In the case of mesons, the valence Fock-state wavefunctions of H LF for zero quark mass satisfy a single-variable relativistic equation of motion in the invariant variable , which is conjugate to the invariant mass squared . The result is a nonperturbative relativistic light-front quantum mechanical wave equation which incorporates color confinement and other essential spectroscopic and dynamical features of hadron physics, including a massless pion for zero quark mass and linear Regge trajectories with the same slope in the radial quantum number n and orbital angular momentum L. Only one mass parameter appears. The corresponding light-front Dirac equation provides a dynamical and spectroscopic model of nucleons. The same light-front equations arise from the holographic mapping of the soft-wall model modification of AdS5 space with a unique dilaton profile to QCD
Nonperturbative comparison of QCD effective charges
Aguilar, A. C.; Binosi, D.; Papavassiliou, J.; Rodriguez-Quintero, J.
2009-10-15
We study the nonperturbative behavior of two versions of the QCD effective charge, one obtained from the pinch technique gluon self-energy, and one from the ghost-gluon vertex. Despite their distinct theoretical origin, due to a fundamental identity relating various ingredients appearing in their respective definitions, the two effective charges are almost identical in the entire range of physical momenta, and coincide exactly in the deep infrared, where they freeze at a common finite value. Specifically, the dressing function of the ghost propagator is related to the two form factors in the Lorentz decomposition of a certain Green's function, appearing in a variety of field-theoretic contexts. The central identity, which is valid only in the Landau gauge, is derived from the Schwinger-Dyson equations governing the dynamics of the aforementioned quantities. The renormalization procedure that preserves the validity of the identity is carried out, and various relevant kinematic limits and physically motivated approximations are studied in detail. A crucial ingredient in this analysis is the infrared finiteness of the gluon propagator, which is inextricably connected with the aforementioned freezing of the effective charges. Some important issues related to the consistent definition of the effective charge in the presence of such a gluon propagator are resolved. We finally present a detailed numerical study of a special set of Schwinger-Dyson equations, whose solutions determine the nonperturbative dynamics of the quantities composing the two effective charges.
anQCD: Fortran programs for couplings at complex momenta in various analytic QCD models
NASA Astrophysics Data System (ADS)
Ayala, César; Cvetič, Gorazd
2016-02-01
We provide three Fortran programs which evaluate the QCD analytic (holomorphic) couplings Aν(Q2) for complex or real squared momenta Q2. These couplings are holomorphic analogs of the powers a(Q2)ν of the underlying perturbative QCD (pQCD) coupling a(Q2) ≡αs(Q2) / π, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2 δanQCD), and Massive Perturbation Theory (MPT). The index ν can be noninteger. The provided programs do basically the same job as the Mathematica package anQCD.m published by us previously (Ayala and Cvetič, 2015), but are now written in Fortran.
LATTICE QCD AT FINITE DENSITY.
SCHMIDT, C.
2006-07-23
I discuss different approaches to finite density lattice QCD. In particular, I focus on the structure of the phase diagram and discuss attempts to determine the location of the critical end-point. Recent results on the transition line as function of the chemical potential (T{sub c}({mu}{sub q})) are reviewed. Along the transition line, hadronic fluctuations have been calculated; which can be used to characterize properties of the Quark Gluon plasma and eventually can also help to identify the location of the critical end-point in the QCD phase diagram on the lattice and in heavy ion experiments. Furthermore, I comment on the structure of the phase diagram at large {mu}{sub q}.
Precision QCD measurements at HERA
NASA Astrophysics Data System (ADS)
Pirumov, Hayk
2014-11-01
A review of recent experimental results on perturbative QCD from the HERA experiments H1 and ZEUS is presented. All inclusive deep inelastic cross sections measured by the H1 and ZEUS collaborations in neutral and charged current unpolarised ep scattering are combined. They span six orders of magnitude in negative four-momentum-transfer squared, Q2, and in Bjorken x. This data set is used as the sole input to NLO and NNLO QCD analyses to determine new sets of parton distributions, HERAPDF2.0, with small experimental uncertainties and an estimate of model and parametrisation uncertainties. Also shown are new results on inclusive jet, dijet and trijet differential cross sections measured in neutral current deep inelastic scattering. The precision jet data is used to extract the strong coupling αs at NLO with small experimental errors.
Dru Renner
2012-04-01
Precision computation of hadronic physics with lattice QCD is becoming feasible. The last decade has seen precent-level calculations of many simple properties of mesons, and the last few years have seen calculations of baryon masses, including the nucleon mass, accurate to a few percent. As computational power increases and algorithms advance, the precise calculation of a variety of more demanding hadronic properties will become realistic. With this in mind, I discuss the current lattice QCD calculations of generalized parton distributions with an emphasis on the prospects for well-controlled calculations for these observables as well. I will do this by way of several examples: the pion and nucleon form factors and moments of the nucleon parton and generalized-parton distributions.
Innovations in Lattice QCD Algorithms
Konstantinos Orginos
2006-06-25
Lattice QCD calculations demand a substantial amount of computing power in order to achieve the high precision results needed to better understand the nature of strong interactions, assist experiment to discover new physics, and predict the behavior of a diverse set of physical systems ranging from the proton itself to astrophysical objects such as neutron stars. However, computer power alone is clearly not enough to tackle the calculations we need to be doing today. A steady stream of recent algorithmic developments has made an important impact on the kinds of calculations we can currently perform. In this talk I am reviewing these algorithms and their impact on the nature of lattice QCD calculations performed today.
NASA Astrophysics Data System (ADS)
Niemi, H.; Eskola, K. J.; Paatelainen, R.; Tuominen, K.
2016-12-01
We compute the initial energy densities produced in ultrarelativistic heavy-ion collisions from NLO perturbative QCD using a saturation conjecture to control soft particle production, and describe the subsequent space-time evolution of the system with hydrodynamics, event by event. The resulting centrality dependence of the low-pT observables from this pQCD + saturation + hydro ("EKRT") framework are then compared simultaneously to the LHC and RHIC measurements. With such an analysis we can test the initial state calculation, and constrain the temperature dependence of the shear viscosity-to-entropy ratio η / s of QCD matter. Using these constraints from the current RHIC and LHC measurements we then predict the charged hadron multiplicities and flow coefficients for the 5 TeV Pb + Pb collisions.
Coherence and Incoherence in QCD Jets Dynamics (QCD Jets and Branching Processes)
NASA Astrophysics Data System (ADS)
Giovannini, A.; Ugoccioni, R.
The interpretation of QCD jets as Markov branching processes obtained by solving Konishi Ukawa Veneziano equations [1] in the leading logarithmic approximation with a fixed cut-off regularization prescription [2] is reviewed, and its impact in multiparticle dynamics critically examined. Independent intermediate gluon sources (clans) are generated through quark bremsstrahlung, each source then decays into final partons according to a cascading mechanism dominated by gluon self-interaction. At the hadron level, approximate universal regularities are expected in the different components (or substructures) of the various classes of high-energy collisions. The general behavior of collective variables of final multiplicity distributions is reproduced in terms of the weighted superposition of the above-mentioned regularities controlling the component behaviors of each collision. Predictions of signals of new physics at LHC [3] are reviewed, and perspective of the 1/N expansion approach [4] indicated.
Yamamoto, Arata
2016-07-29
We propose the lattice QCD calculation of the Berry phase, which is defined by the ground state of a single fermion. We perform the ground-state projection of a single-fermion propagator, construct the Berry link variable on a momentum-space lattice, and calculate the Berry phase. As the first application, the first Chern number of the (2+1)-dimensional Wilson fermion is calculated by the Monte Carlo simulation.
Lattice QCD: A Brief Introduction
NASA Astrophysics Data System (ADS)
Meyer, H. B.
A general introduction to lattice QCD is given. The reader is assumed to have some basic familiarity with the path integral representation of quantum field theory. Emphasis is placed on showing that the lattice regularization provides a robust conceptual and computational framework within quantum field theory. The goal is to provide a useful overview, with many references pointing to the following chapters and to freely available lecture series for more in-depth treatments of specifics topics.
Hadron physics from lattice QCD
NASA Astrophysics Data System (ADS)
Bietenholz, Wolfgang
2016-07-01
We sketch the basic ideas of the lattice regularization in Quantum Field Theory, the corresponding Monte Carlo simulations, and applications to Quantum Chromodynamics (QCD). This approach enables the numerical measurement of observables at the non-perturbative level. We comment on selected results, with a focus on hadron masses and the link to Chiral Perturbation Theory. At last, we address two outstanding issues: topological freezing and the sign problem.
DeGrand, T.
1997-06-01
These lectures provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1: Basic techniques for QCD and results for hadron spectroscopy using the simplest discretizations; lecture 2: Improved actions--what they are and how well they work; lecture 3: SLAC physics from the lattice-structure functions, the mass of the glueball, heavy quarks and {alpha}{sub s} (M{sub z}), and B-{anti B} mixing. 67 refs., 36 figs.
NASA Astrophysics Data System (ADS)
Crutcher, Sihon H.; Osei, Albert; Biswas, Anjan
2012-06-01
Maxwell's equations for a metallic and nonlinear Kerr interface waveguide at the nanoscale can be approximated to a (1+1) D Nonlinear Schrodinger type model equation (NLSE) with appropriate assumptions and approximations. Theoretically, without losses or perturbations spatial plasmon solitons profiles are easily produced. However, with losses, the amplitude or beam profile is no longer stationary and adiabatic parameters have to be considered to understand propagation. For this model, adiabatic parameters are calculated considering losses resulting in linear differential coupled integral equations with constant definite integral coefficients not dependent on the transverse and longitudinal coordinates. Furthermore, by considering another configuration, a waveguide that is an M-NL-M (metal-nonlinear Kerr-metal) that tapers, the tapering can balance the loss experienced at a non-tapered metal/nonlinear Kerr interface causing attenuation of the beam profile, so these spatial plasmon solitons can be produced. In this paper taking into consideration the (1+1)D NLSE model for a tapered waveguide, we derive a one soliton solution based on He's Semi-Inverse Variational Principle (HPV).
Thermal relaxation, electrical conductivity, and charge diffusion in a hot QCD medium
NASA Astrophysics Data System (ADS)
Mitra, Sukanya; Chandra, Vinod
2016-08-01
The response of electromagnetic (EM) fields that are produced in noncentral heavy-ion collisions to electromagnetically charged quark gluon plasma can be understood in terms of charge transport and charge diffusion in the hot QCD medium. This article presents a perspective on these processes by investigating the temperature behavior of the related transport coefficients, viz. electrical conductivity and the charge diffusion coefficients along with charge susceptibility. In the process of estimating them, thermal relaxation times for quarks and gluons have been determined first. These transport coefficients have been studied by solving the relativistic transport equation in the Chapman-Enskog method. For the analysis, 2 →2 , quark-quark, quark-gluon and gluon-gluon scattering processes are taken into account along with an effective description of hot QCD equations of state (EOSs) in terms of temperature dependent effective fugacities of quasiquarks (antiquarks) and quasigluons. Both improved perturbative hot QCD EOSs at high temperature and a lattice QCD EOS are included for the analysis. The hot QCD medium effects entering through the quasiparticle momentum distributions along with an effective coupling, are seen to have significant impact on the temperature behavior of these transport parameters along with the thermal relaxation times for the quasigluons and quasiquarks.
None
2016-07-12
Modern QCD - Lecture 2 We will start discussing the matter content of the theory and revisit the experimental measurements that led to the discovery of quarks. We will then consider a classic QCD observable, the R-ratio, and use it to illustrate the appearance of UV divergences and the need to renormalize the coupling constant of QCD. We will then discuss asymptotic freedom and confinement. Finally, we will examine a case where soft and collinear infrared divergences appear, will discuss the soft approximation in QCD and will introduce the concept of infrared safe jets.
QCD nature of dark energy at finite temperature: Cosmological implications
NASA Astrophysics Data System (ADS)
Azizi, K.; Katırcı, N.
2016-05-01
The Veneziano ghost field has been proposed as an alternative source of dark energy, whose energy density is consistent with the cosmological observations. In this model, the energy density of the QCD ghost field is expressed in terms of QCD degrees of freedom at zero temperature. We extend this model to finite temperature to search the model predictions from late time to early universe. We depict the variations of QCD parameters entering the calculations, dark energy density, equation of state, Hubble and deceleration parameters on temperature from zero to a critical temperature. We compare our results with the observations and theoretical predictions existing at different eras. It is found that this model safely defines the universe from quark condensation up to now and its predictions are not in tension with those of the standard cosmology. The EoS parameter of dark energy is dynamical and evolves from -1/3 in the presence of radiation to -1 at late time. The finite temperature ghost dark energy predictions on the Hubble parameter well fit to those of Λ CDM and observations at late time.
Geiger, K.; Longacre, R.; Srivastava, D.K.
1999-02-01
VNI is a general-purpose Monte-Carlo event-generator, which includes the simulation of lepton-lepton, lepton-hadron, lepton-nucleus, hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. It uses the real-time evolution of parton cascades in conjunction with a self-consistent hadronization scheme, as well as the development of hadron cascades after hadronization. The causal evolution from a specific initial state (determined by the colliding beam particles) is followed by the time-development of the phase-space densities of partons, pre-hadronic parton clusters, and final-state hadrons, in position-space, momentum-space and color-space. The parton-evolution is described in terms of a space-time generalization of the familiar momentum-space description of multiple (semi)hard interactions in QCD, involving 2 {r_arrow} 2 parton collisions, 2 {r_arrow} 1 parton fusion processes, and 1 {r_arrow} 2 radiation processes. The formation of color-singlet pre-hadronic clusters and their decays into hadrons, on the other hand, is treated by using a spatial criterion motivated by confinement and a non-perturbative model for hadronization. Finally, the cascading of produced prehadronic clusters and of hadrons includes a multitude of 2 {r_arrow} n processes, and is modeled in parallel to the parton cascade description. This paper gives a brief review of the physics underlying VNI, as well as a detailed description of the program itself. The latter program description emphasizes easy-to-use pragmatism and explains how to use the program (including simple examples), annotates input and control parameters, and discusses output data provided by it.
Bulk viscosity of anisotropically expanding hot QCD plasma
Chandra, Vinod
2011-11-01
The bulk viscosity, {zeta} and its ratio with the shear viscosity, {zeta}/{eta} have been studied in an anisotropically expanding pure glue plasma in the presence of turbulent color fields. It has been shown that the anisotropy in the momentum distribution function of gluons, which has been determined from a linearized transport equation eventually leads to the bulk viscosity. For the isotropic (equilibrium) state, a recently proposed quasiparticle model of pure SU(3) lattice QCD equation of state has been employed where the interactions are encoded in the effective fugacity. It has been argued that the interactions present in the equation of state, significantly contribute to the bulk viscosity. Its ratio with the shear viscosity is significant even at 1.5T{sub c}. Thus, one needs to take in account the effects of the bulk viscosity while studying the hydrodynamic expansion of quark-gluon plasma in the Relativistic Heavy Ion Collider and the Large Hadron Collider.
NASA Astrophysics Data System (ADS)
Bejger, M.; Blaschke, D.; Haensel, P.; Zdunik, J. L.; Fortin, M.
2017-03-01
Aims: We explore the implications of a strong first-order phase transition region in the dense matter equation of state in the interiors of rotating neutron stars, and the resulting creation of two disjoint families of neutron-star configurations (the so-called high-mass twins). Methods: We numerically obtained rotating, axisymmetric, and stationary stellar configurations in the framework of general relativity, and studied their global parameters and stability. Results: The instability induced by the equation of state divides stable neutron star configurations into two disjoint families: neutron stars (second family) and hybrid stars (third family), with an overlapping region in mass, the high-mass twin-star region. These two regions are divided by an instability strip. Its existence has interesting astrophysical consequences for rotating neutron stars. We note that it provides a natural explanation for the rotational frequency cutoff in the observed distribution of neutron star spins, and for the apparent lack of back-bending in pulsar timing. It also straightforwardly enables a substantial energy release in a mini-collapse to another neutron-star configuration (core quake), or to a black hole.
Modified block BiCGSTAB for lattice QCD
NASA Astrophysics Data System (ADS)
Nakamura, Y.; Ishikawa, K.-I.; Kuramashi, Y.; Sakurai, T.; Tadano, H.
2012-01-01
We present results for application of block BiCGSTAB algorithm modified by the QR decomposition and the SAP preconditioner to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD on 32×64 and 64 4 lattices at almost physical quark masses. The QR decomposition improves convergence behaviors in the block BiCGSTAB algorithm suppressing deviation between true residual and recursive one. The SAP preconditioner applied to the domain-decomposed lattice helps us minimize communication overhead. We find remarkable cost reduction thanks to cache tuning and reduction of number of iterations.
Quark-gluon vertex model and lattice-QCD data
Bhagwat, M.S.; Tandy, P.C.
2004-11-01
A model for the dressed-quark-gluon vertex, at zero gluon momentum, is formed from a nonperturbative extension of the two Feynman diagrams that contribute at one loop in perturbation theory. The required input is an existing ladder-rainbow model Bethe-Salpeter kernel from an approach based on the Dyson-Schwinger equations; no new parameters are introduced. The model includes an Ansatz for the triple-gluon vertex. Two of the three vertex amplitudes from the model provide a pointwise description of the recent quenched-lattice-QCD data. An estimate of the effects of quenching is made.
Viscous quark-gluon plasma model through fluid QCD approach
Djun, T. P.; Soegijono, B.; Mart, T.; Handoko, L. T. E-mail: Laksana.tri.handoko@lipi.go.id
2014-09-25
A Lagrangian density for viscous quark-gluon plasma has been constructed within the fluid-like QCD framework. Gauge symmetry is preserved for all terms inside the Lagrangian, except for the viscous term. The transition mechanism from point particle field to fluid field, and vice versa, are discussed. The energy momentum tensor that is relevant to the gluonic plasma having the nature of fluid bulk of gluon sea is derived within the model. By imposing conservation law in the energy momentum tensor, shear viscosity appears as extractable from the equation.
Transverse Momentum-Dependent Parton Distributions From Lattice QCD
Michael Engelhardt, Bernhard Musch, Philipp Haegler, Andreas Schaefer
2012-12-01
Starting from a definition of transverse momentum-dependent parton distributions for semi-inclusive deep inelastic scattering and the Drell-Yan process, given in terms of matrix elements of a quark bilocal operator containing a staple-shaped Wilson connection, a scheme to determine such observables in lattice QCD is developed and explored. Parametrizing the aforementioned matrix elements in terms of invariant amplitudes permits a simple transformation of the problem to a Lorentz frame suited for the lattice calculation. Results for the Sivers and Boer-Mulders transverse momentum shifts are presented, focusing in particular on their dependence on the staple extent and the Collins-Soper evolution parameter.
JIMWLK evolution in the Gaussian approximation
NASA Astrophysics Data System (ADS)
Iancu, E.; Triantafyllopoulos, D. N.
2012-04-01
We demonstrate that the Balitsky-JIMWLK equations describing the high-energy evolution of the n-point functions of the Wilson lines (the QCD scattering amplitudes in the eikonal approximation) admit a controlled mean field approximation of the Gaussian type, for any value of the number of colors N c . This approximation is strictly correct in the weak scattering regime at relatively large transverse momenta, where it re-produces the BFKL dynamics, and in the strong scattering regime deeply at saturation, where it properly describes the evolution of the scattering amplitudes towards the respective black disk limits. The approximation scheme is fully specified by giving the 2-point function (the S-matrix for a color dipole), which in turn can be related to the solution to the Balitsky-Kovchegov equation, including at finite N c . Any higher n-point function with n ≥ 4 can be computed in terms of the dipole S-matrix by solving a closed system of evolution equations (a simplified version of the respective Balitsky-JIMWLK equations) which are local in the transverse coordinates. For simple configurations of the projectile in the transverse plane, our new results for the 4-point and the 6-point functions coincide with the high-energy extrapolations of the respective results in the McLerran-Venugopalan model. One cornerstone of our construction is a symmetry property of the JIMWLK evolution, that we notice here for the first time: the fact that, with increasing energy, a hadron is expanding its longitudinal support symmetrically around the light-cone. This corresponds to invariance under time reversal for the scattering amplitudes.
NASA Astrophysics Data System (ADS)
Rashid, Shahid
1990-07-01
The kinematically based concept of quasi-free electron states developed by Rashid (1988) is extended to obtain a coupling/decoupling technique capable of separating dynamical and kinematical factors. This method is then applied to a reduced form of the Boltzmann equation (assuming that the electrons are in quantum states with quasi-four-momentum, as in an intense laser field). The solution obtained is applicable to the relativistic case and consists of the product of (1) the initial distribution function and (2) a time-evolving part dependent on the differential cross section of the plasma-heating scattering process. The significance of the present analysis for laser-fusion studies is briefly indicated.
Gunion, J.F.
1980-05-01
A critical review of the applications of QCD to low- and high-p/sub T/ interactions of two photons is presented. The advantages of the two-photon high-p/sub T/ tests over corresponding hadronic beam and/or target tests of QCD are given particular emphasis.
Lattice QCD and High Baryon Density State
Nagata, Keitaro; Nakamura, Atsushi; Motoki, Shinji; Nakagawa, Yoshiyuki; Saito, Takuya
2011-10-21
We report our recent studies on the finite density QCD obtained from lattice QCD simulation with clover-improved Wilson fermions of two flavor and RG-improved gauge action. We approach the subject from two paths, i.e., the imaginary and chemical potentials.
Solvable models and hidden symmetries in QCD
Yepez-Martinez, Tochtli; Hess, P. O.; Civitarese, O.; Lerma H., S.
2010-12-23
We show that QCD Hamiltonians at low energy exhibit an SU(2) structure, when only few orbital levels are considered. In case many orbital levels are taken into account we also find a semi-analytic solution for the energy levels of the dominant part of the QCD Hamiltonian. The findings are important to propose the structure of phenomenological models.
Holographic QCD for H-dibaryon (uuddss)
NASA Astrophysics Data System (ADS)
Suganuma, Hideo; Matsumoto, Kohei
2017-03-01
The H-dibaryon (uuddss) is studied in holographic QCD for the first time. In holographic QCD, four-dimensional QCD, i.e., SU(Nc) gauge theory with chiral quarks, can be formulated with S1-compactified D4/D8/\\overline {{{D8}}} -brane system. In holographic QCD with large (Nc, all the baryons appear as topological chiral solitons of Nambu-Goldstone bosons and (axial) vector mesons, and the H-dibaryon can be described as an SO(3)-type topological soliton with B = 2. We derive the low-energy effective theory to describe the H-dibaryon in holographic QCD. The H-dibaryon mass is found to be twice of the B = 1 hedgehog-baryon mass, MH ≃ 2.00MB=1HH, and is estimated about 1.7GeV, which is smaller than mass of two nucleons (flavor-octet baryons), in the chiral limit.
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD.
Ryttov, Thomas A
2016-08-12
We suggest how to consistently calculate the anomalous dimension γ_{*} of the ψ[over ¯]ψ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the n+1 loop beta function and n loop anomalous dimension are known, then γ_{*} can be calculated exactly and fully scheme independently in a Banks-Zaks expansion through O(Δ_{f}^{n}), where Δ_{f}=N[over ¯]_{f}-N_{f}, N_{f} is the number of flavors, and N[over ¯]_{f} is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory, the calculation preserves supersymmetry order by order in Δ_{f}. We then compute γ_{*} through O(Δ_{f}^{2}) for supersymmetric QCD in the dimensional reduction scheme and find that it matches the exact known result. We find that γ_{*} is astonishingly well described in perturbation theory already at the few loops level throughout the entire conformal window. We finally compute γ_{*} through O(Δ_{f}^{3}) for QCD and a variety of other nonsupersymmetric fermionic gauge theories. Small values of γ_{*} are observed for a large range of flavors.
Nucleon Structure from Lattice QCD
Haegler, Philipp
2011-10-24
Hadron structure calculations in lattice QCD have seen substantial progress during recent years. We illustrate the achievements that have been made by discussing latest lattice results for a limited number of important observables related to nucleon form factors and generalized parton distributions. A particular focus is placed on the decomposition of the nucleon spin 1/2 in terms of quark spin and orbital angular momentum contributions. Results and limitations of the necessary chiral extrapolations based on ChPT will be briefly discussed.
Tetraquark states from lattice QCD
Mathur, Nilmani
2011-10-24
Recently there have been considerable interests in studying hadronic states beyond the usual two and three quark configurations. With the renewed experimental interests in {sigma}(600) and the inability of quark model to incorporate too many light scalar mesons, it is quite appropriate to study hadronic states with four quark configurations. Moreover, some of the newly observed charmed hadrons may well be described by four quark configurations. Lattice QCD is perhaps the most desirable tool to adjudicate the theoretical controversy of the scalar mesons and to interpret the structures of the newly observed charmed states. Here we briefly reviewed the lattice studies of four-quark hadrons.
Nuclear Physics from Lattice QCD
William Detmold, Silas Beane, Konstantinos Orginos, Martin Savage
2011-01-01
We review recent progress toward establishing lattice Quantum Chromodynamics as a predictive calculational framework for nuclear physics. A survey of the current techniques that are used to extract low-energy hadronic scattering amplitudes and interactions is followed by a review of recent two-body and few-body calculations by the NPLQCD collaboration and others. An outline of the nuclear physics that is expected to be accomplished with Lattice QCD in the next decade, along with estimates of the required computational resources, is presented.
"Quantum Field Theory and QCD"
Jaffe, Arthur M.
2006-02-25
This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
Balitsky, I.I.; Braun, V.M.; Koike, Y.; Tanaka, K. |||
1996-10-01
We prove that the twist-3 chiral-odd parton distributions obey simple Gribov-Lipatov-Altarelli-Parisi evolution equations in the limit {ital N}{sub {ital c}}{r_arrow}{infinity} and give analytic results for the corresponding anomalous dimensions. To this end we introduce an evolution equation for the corresponding three-particle twist-3 parton correlation functions and find an exact analytic solution. For large values of {ital n} (operator dimension) we are further able to collect all corrections subleading in {ital N}{sub {ital c}}, so our final results are valid to {ital O}{bold (}(1/{ital N}{sup 2}{sub {ital c}})ln({ital n})/{ital n}{bold )} accuracy. {copyright} {ital 1996 The American Physical Society.}
Applications of AdS/QCD and Light-Front Holography to Baryon Physics
Brodsky, Stanley J.; de Teramond, Guy F.; /Costa Rica U.
2011-08-22
The correspondence between theories in anti-de Sitter space and field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD which has scale invariance at short distances and color confinement at large distances. These equations, for both mesons and baryons, give a very good representation of the observed hadronic spectrum, including a zero mass pion. Light-front holography allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. The meson and baryon wavefunctions derived from light-front holography and AdS/QCD also have remarkable phenomenological features, including predictions for the electromagnetic form factors and decay constants. The approach can be systematically improved using light-front Hamiltonian methods. Some novel features of QCD for baryon physics are also discussed.
The QCD/SM working group: Summary report
W. Giele et al.
2004-01-12
Quantum Chromo-Dynamics (QCD), and more generally the physics of the Standard Model (SM), enter in many ways in high energy processes at TeV Colliders, and especially in hadron colliders (the Tevatron at Fermilab and the forthcoming LHC at CERN), First of all, at hadron colliders, QCD controls the parton luminosity, which rules the production rates of any particle or system with large invariant mass and/or large transverse momentum. Accurate predictions for any signal of possible ''New Physics'' sought at hadron colliders, as well as the corresponding backgrounds, require an improvement in the control of uncertainties on the determination of PDF and of the propagation of these uncertainties in the predictions. Furthermore, to fully exploit these new types of PDF with uncertainties, uniform tools (computer interfaces, standardization of the PDF evolution codes used by the various groups fitting PDF's) need to be proposed and developed. The dynamics of colour also affects, both in normalization and shape, various observables of the signals of any possible ''New Physics'' sought at the TeV scale, such as, e.g. the production rate, or the distributions in transverse momentum of the Higgs boson. Last, but not least, QCD governs many backgrounds to the searches for this ''New Physics''. Large and important QCD corrections may come from extra hard parton emission (and the corresponding virtual corrections), involving multi-leg and/or multi-loop amplitudes. This requires complex higher order calculations, and new methods have to be designed to compute the required multi-legs and/or multi-loop corrections in a tractable form. In the case of semi-inclusive observables, logarithmically enhanced contributions coming from multiple soft and collinear gluon emission require sophisticated QCD resummation techniques. Resummation is a catch-all name for efforts to extend the predictive power of QCD by summing the large logarithmic corrections to all orders in perturbation theory. In
Theta dependence in holographic QCD
NASA Astrophysics Data System (ADS)
Bartolini, Lorenzo; Bigazzi, Francesco; Bolognesi, Stefano; Cotrone, Aldo L.; Manenti, Andrea
2017-02-01
We study the effects of the CP-breaking topological θ-term in the large N c QCD model by Witten, Sakai and Sugimoto with N f degenerate light flavors. We first compute the ground state energy density, the topological susceptibility and the masses of the lowest lying mesons, finding agreement with expectations from the QCD chiral effective action. Then, focusing on the N f = 2 case, we consider the baryonic sector and determine, to leading order in the small θ regime, the related holographic instantonic soliton solutions. We find that while the baryon spectrum does not receive O(θ ) corrections, this is not the case for observables like the electromagnetic form factor of the nucleons. In particular, it exhibits a dipole term, which turns out to be vector-meson dominated. The resulting neutron electric dipole moment, which is exactly the opposite as that of the proton, is of the same order of magnitude of previous estimates in the literature. Finally, we compute the CP-violating pion-nucleon coupling constant {overline{g}}_{π NN} , finding that it is zero to leading order in the large N c limit.
Smith, W.H.
1997-06-01
These lectures describe QCD physics studies over the period 1992--1996 from data taken with collisions of 27 GeV electrons and positrons with 820 GeV protons at the HERA collider at DESY by the two general-purpose detectors H1 and ZEUS. The focus of these lectures is on structure functions and jet production in deep inelastic scattering, photoproduction, and diffraction. The topics covered start with a general introduction to HERA and ep scattering. Structure functions are discussed. This includes the parton model, scaling violation, and the extraction of F{sub 2}, which is used to determine the gluon momentum distribution. Both low and high Q{sup 2} regimes are discussed. The low Q{sup 2} transition from perturbative QCD to soft hadronic physics is examined. Jet production in deep inelastic scattering to measure {alpha}{sub s}, and in photoproduction to study resolved and direct photoproduction, is also presented. This is followed by a discussion of diffraction that begins with a general introduction to diffraction in hadronic collisions and its relation to ep collisions, and moves on to deep inelastic scattering, where the structure of diffractive exchange is studied, and in photoproduction, where dijet production provides insights into the structure of the Pomeron. 95 refs., 39 figs.
High energy scattering in QCD and in quantum gravity
NASA Astrophysics Data System (ADS)
Lipatov, L. N.
2014-06-01
The theory of the high energy scattering in QCD is based on the BFKL equation for the Pomeron wave function and on its generalization for composite multi-gluon states in the crossing channel. At a large number of colors the equations for the gluon composite states have remarkable mathematical properties including their Möbius invariance, holomorphic separability, duality symmetry and integrability. High energy QCD interactions local in the particle rapidities are formulated in the form of the gauge invariant effective action. In the maximally extended N = 4 super-symmetry the Pomeron turns out to be dual to the reggeized graviton in the 10-dimensional anti-de-Sitter space. As a result, the Gribov calculus for the Pomeron interactions should be reformulated here as a generally covariant effective field theory for the reggeized gravitons. We construct the corresponding effective action, which gives a possibility to calculate their trajectory and couplings. The graviton trajectory in the leading order contains an ultraviolet divergency meaning the presence of the double-logarithmic (DL) terms. We sum the DL contributions in all orders of the perturbation theory in the Einstein-Hilbert gravity and in its super-symmetric generalizations. In the N = 8 super gravity the ratio of the scattering amplitude in the DL approximation to the Born expression tends to zero at large energies.
Vranas, P
2007-06-18
Quantum Chromodynamics is the theory of nuclear and sub-nuclear physics. It is a celebrated theory and one of its inventors, F. Wilczek, has termed it as '... our most perfect physical theory'. Part of this is related to the fact that QCD can be numerically simulated from first principles using the methods of lattice gauge theory. The computational demands of QCD are enormous and have not only played a role in the history of supercomputers but are also helping define their future. Here I will discuss the intimate relation of QCD and massively parallel supercomputers with focus on the Blue Gene supercomputer and QCD thermodynamics. I will present results on the performance of QCD on the Blue Gene as well as physics simulation results of QCD at temperatures high enough that sub-nuclear matter transitions to a plasma state of elementary particles, the quark gluon plasma. This state of matter is thought to have existed at around 10 microseconds after the big bang. Current heavy ion experiments are in the quest of reproducing it for the first time since then. And numerical simulations of QCD on the Blue Gene systems are calculating the theoretical values of fundamental parameters so that comparisons of experiment and theory can be made.
AdS/QCD at finite density and temperature
Kim, Y.
2012-07-15
We review some basics of AdS/QCD following a non-standard path and list a few results from AdS/QCD or holographic QCD. The non-standard path here is to use the analogy of the way one obtains an effective model of QCD like linear sigma model and the procedure to construct an AdS/QCD model based on the AdS/CFT dictionary.
Khodadi, M. Sepangi, H.R.
2014-07-15
We study the phase transition from quark–gluon plasma to hadrons in the early universe in the context of non-equilibrium thermodynamics. According to the standard model of cosmology, a phase transition associated with chiral symmetry breaking after the electro-weak transition has occurred when the universe was about 1–10 μs old. We focus attention on such a phase transition in the presence of a viscous relativistic cosmological background fluid in the framework of non-detailed balance Hořava–Lifshitz cosmology within an effective model of QCD. We consider a flat Friedmann–Robertson–Walker universe filled with a non-causal and a causal bulk viscous cosmological fluid respectively and investigate the effects of the running coupling constants of Hořava–Lifshitz gravity, λ, on the evolution of the physical quantities relevant to a description of the early universe, namely, the temperature T, scale factor a, deceleration parameter q and dimensionless ratio of the bulk viscosity coefficient to entropy density (ξ)/s . We assume that the bulk viscosity cosmological background fluid obeys the evolution equation of the steady truncated (Eckart) and full version of the Israel–Stewart fluid, respectively. -- Highlights: •In this paper we have studied quark–hadron phase transition in the early universe in the context of the Hořava–Lifshitz model. •We use a flat FRW universe with the bulk viscosity cosmological background fluid obeying the evolution equation of the steady truncated (Eckart) and full version of the Israel–Stewart fluid, respectively.
Death to perturbative QCD in exclusive processes?
Eckardt, R.; Hansper, J.; Gari, M.F.
1994-04-01
The authors discuss the question of whether perturbative QCD is applicable in calculations of exclusive processes at available momentum transfers. They show that the currently used method of determining hadronic quark distribution amplitudes from QCD sum rules yields wave functions which are completely undetermined because the polynomial expansion diverges. Because of the indeterminacy of the wave functions no statement can be made at present as to whether perturbative QCD is valid. The authors emphasize the necessity of a rigorous discussion of the subject and the importance of experimental data in the range of interest.
The QCD vacuum, hadrons and superdense matter
Shuryak, E.
1986-01-01
This is probably the only textbook available that gathers QCD, many-body theory and phase transitions in one volume. The presentation is pedagogical and readable. Contents: The QCD Vacuum: Introduction; QCD on the Lattice Topological Effects in Gauges Theories. Correlation Functions and Microscopic Excitations: Introduction; Operator Product Expansion; The Sum Rules beyond OPE; Nonpower Contributions to Correlators and Instantons; Hadronic Spectroscopy on the Lattice. Dense Matter: Hadronic Matter; Asymptotically Dense Quark-Gluon Plasma; Instantons in Matter; Lattice Calculations at Finite Temperature; Phase Transitions; Macroscopic Excitations and Experiments: General Properties of High Energy Collisions; ''Barometers'', ''Thermometers'', Interferometric ''Microscope''; Experimental Perspectives.
Excited light isoscalar mesons from lattice QCD
Christopher Thomas
2011-07-01
I report a recent lattice QCD calculation of an excited spectrum of light isoscalar mesons, something that has up to now proved challenging for lattice QCD. With novel techniques we extract an extensive spectrum with high statistical precision, including spin-four states and, for the first time, light isoscalars with exotic quantum numbers. In addition, the hidden flavour content of these mesons is determined, providing a window on annihilation dynamics in QCD. I comment on future prospects including applications to the study of resonances.
Shape of mesons in holographic QCD
Torabian, Mahdi; Yee, Ho-Ung
2009-10-15
Based on the expectation that the constituent quark model may capture the right physics in the large N limit, we point out that the orbital angular momentum of the quark-antiquark pair inside light mesons of low spins in the constituent quark model may provide a clue for the holographic dual string model of large N QCD. Our discussion, relying on a few suggestive assumptions, leads to a necessity of world-sheet fermions in the bulk of dual strings that can incorporate intrinsic spins of fundamental QCD degrees of freedom. We also comment on the interesting issue of the size of mesons in holographic QCD.
Light-front Holography - A New Approach to Relativistic Hadron Dynamics and Nonperturbative QCD
de Teramond, Guy F.; Brodsky, Stanley J.
2012-06-20
The holographic mapping of gravity in AdS space to QCD, quantized at fixed light-front time, provides a precise relation between the bound-state amplitudes in the fifth dimension of AdS space and the boost-invariant light-front wavefunctions describing the internal structure of hadrons in physical space-time. In particular, the elastic and transition form factors of the pion and the nucleons are well described in this framework. The light-front AdS/QCD holographic approach thus gives a frame-independent first approximation of the color-confining dynamics, spectroscopy, and excitation spectra of relativistic light-quark bound states in QCD. More generally, we show that the valence Fock-state wavefunctions of the eigensolutions of the light-front QCD Hamiltonian satisfy a single-variable relativistic equation of motion, analogous to the nonrelativistic radial Schroedinger equation, with an effective confining potential which systematically incorporates the effects of higher quark and gluon Fock states. The proposed method to compute the effective interaction thus resembles the two-particle-irreducible functional techniques used in quantum field theory.
NASA Astrophysics Data System (ADS)
Lebed, Richard F.
1999-09-01
These lectures are designed to introduce the methods and results of large N c QCD in a presentation intended for nuclear and particle physicists alike. Beginning with definitions and motivations of the approach, we demonstrate that all quark and gluon Feynman diagrams are organized into classes based on powers of 1/N c. We then show that this result can be translated into definite statements about mesons and baryons containing arbitrary numbers of constituents. In the mesons, numerous well-known phenomenological properties follow as immediate consequences of simply counting powers of N c, while for the baryons, quantitative large N c analyses of masses and other properties are seen to agree with experiment, even when large” N c is set equal to its observed value of 3. Large N c reasoning is also used to explain some simple features of nuclear interactions.
QCD tests with polarized beams
Maruyama, Takashi; SLD Collaboration
1996-09-01
The authors present three QCD studies performed by the SLD experiment at SLAC, utilizing the highly polarized SLC electron beam. They examined particle production differences in light quark and antiquark hemispheres, and observed more high momentum baryons and K{sup {minus}}`s than antibaryons and K{sup +}`s in quark hemispheres, consistent with the leading particle hypothesis. They performed a search for jet handedness in light q- and {anti q}-jets. Assuming Standard Model values of quark polarization in Z{sup 0} decays, they have set an improved upper limit on the analyzing power of the handedness method. They studied the correlation between the Z{sup 0} spin and the event-plane orientation in polarized Z{sup 0} decays into three jets.
SAITO,N.
1999-12-09
In this lecture I give a pedagogical introduction to the Perturbative QCD to understand the short-distance dynamics of the strong interaction. Starting with fundamental concepts such as the color degree of freedom of QCD, non-abelian gauge field theory, renormalization group equation etc., I explain a basic idea of the perturbative QCD and apply this idea to the e{sup +}e{sup {minus}} processes and the structure functions. The notion of mass singularity and the necessity of its factorization is discussed in some detail.
Opportunities, challenges, and fantasies in lattice QCD
NASA Astrophysics Data System (ADS)
Wilczek, Frank
2003-05-01
Some important problems in quantitative QCD will certainly yield to hard work and adequate investment of resources, others appear difficult but may be accessible, and still others will require essentially new ideas. Here I identify several examples in each class.
Simplifying Multi-Jet QCD Computation
Peskin, Michael E.; /SLAC
2011-11-04
These lectures give a pedagogical discussion of the computation of QCD tree amplitudes for collider physics. The tools reviewed are spinor products, color ordering, MHV amplitudes, and the Britto-Cachazo-Feng-Witten recursion formula.
Scheme variations of the QCD coupling
NASA Astrophysics Data System (ADS)
Boito, Diogo; Jamin, Matthias; Miravitllas, Ramon
2017-03-01
The Quantum Chromodynamics (QCD) coupling αs is a central parameter in the Standard Model of particle physics. However, it depends on theoretical conventions related to renormalisation and hence is not an observable quantity. In order to capture this dependence in a transparent way, a novel definition of the QCD coupling, denoted by â, is introduced, whose running is explicitly renormalisation scheme invariant. The remaining renormalisation scheme dependence is related to transformations of the QCD scale Λ, and can be parametrised by a single parameter C. Hence, we call â the C-scheme coupling. The dependence on C can be exploited to study and improve perturbative predictions of physical observables. This is demonstrated for the QCD Adler function and hadronic decays of the τ lepton.
Excited light meson spectroscopy from lattice QCD
Christopher Thomas, Hadron Spectrum Collaboration
2012-04-01
I report on recent progress in calculating excited meson spectra using lattice QCD, emphasizing results and phenomenology. With novel techniques we can now extract extensive spectra of excited mesons with high statistical precision, including spin-four states and those with exotic quantum numbers. As well as isovector meson spectra, I will present new calculations of the spectrum of excited light isoscalar mesons, something that has up to now been a challenge for lattice QCD. I show determinations of the flavor content of these mesons, including the eta-eta' mixing angle, providing a window on annihilation dynamics in QCD. I will also discuss recent work on using lattice QCD to map out the energy-dependent phase shift in pi-pi scattering and future applications of the methodology to the study of resonances and decays.
Strange Baryon Physics in Full Lattice QCD
Huey-Wen Lin
2007-11-01
Strange baryon spectra and form factors are key probes to study excited nuclear matter. The use of lattice QCD allows us to test the strength of the Standard Model by calculating strange baryon quantities from first principles.
Superfluid helium II as the QCD vacuum
NASA Astrophysics Data System (ADS)
Zhitnitsky, Ariel
2017-03-01
We study the winding number susceptibility
None
2016-07-12
Modern QCD - Lecture 4 We will consider some processes of interest at the LHC and will discuss the main elements of their cross-section calculations. We will also summarize the current status of higher order calculations.
Novel QCD effects in nuclear collisions
Brodsky, S.J.
1991-12-01
Heavy ion collisions can provide a novel environment for testing fundamental dynamical processes in QCD, including minijet formation and interactions, formation zone phenomena, color filtering, coherent co-mover interactions, and new higher twist mechanisms which could account for the observed excess production and anomalous nuclear target dependence of heavy flavor production. The possibility of using light-cone thermodynamics and a corresponding covariant temperature to describe the QCD phases of the nuclear fragmentation region is also briefly discussed.
Some new/old approaches to QCD
Gross, D.J.
1992-11-01
In this lecture I shall discuss some recent attempts to revive some old ideas to address the problem of solving QCD. I believe that it is timely to return to this problem which has been woefully neglected for the last decade. QCD is a permanent part of the theoretical landscape and eventually we will have to develop analytic tools for dealing with the theory in the infra-red. Lattice techniques are useful but they have not yet lived up to their promise. Even if one manages to derive the hadronic spectrum numerically, to an accuracy of 10% or even 1%, we will not be truly satisfied unless we have some analytic understanding of the results. Also, lattice Monte-Carlo methods can only be used to answer a small set of questions. Many issues of great conceptual and practical interest-in particular the calculation of scattering amplitudes, are thus far beyond lattice control. Any progress in controlling QCD in an explicit analytic, fashion would be of great conceptual value. It would also be of great practical aid to experimentalists, who must use rather ad-hoc and primitive models of QCD scattering amplitudes to estimate the backgrounds to interesting new physics. I will discuss an attempt to derive a string representation of QCD and a revival of the large N approach to QCD. Both of these ideas have a long history, many theorist-years have been devoted to their pursuit-so far with little success. I believe that it is time to try again. In part this is because of the progress in the last few years in string theory. Our increased understanding of string theory should make the attempt to discover a stringy representation of QCD easier, and the methods explored in matrix models might be employed to study the large N limit of QCD.
Lattice and Phase Diagram in QCD
Lombardo, Maria Paola
2008-10-13
Model calculations have produced a number of very interesting expectations for the QCD Phase Diagram, and the task of a lattice calculations is to put these studies on a quantitative grounds. I will give an overview of the current status of the lattice analysis of the QCD phase diagram, from the quantitative results of mature calculations at zero and small baryochemical potential, to the exploratory studies of the colder, denser phase.
Some New/Old Approaches to QCD
DOE R&D Accomplishments Database
Gross, D. J.
1992-11-01
In this lecture I shall discuss some recent attempts to revive some old ideas to address the problem of solving QCD. I believe that it is timely to return to this problem which has been woefully neglected for the last decade. QCD is a permanent part of the theoretical landscape and eventually we will have to develop analytic tools for dealing with the theory in the infra-red. Lattice techniques are useful but they have not yet lived up to their promise. Even if one manages to derive the hadronic spectrum numerically, to an accuracy of 10% or even 1%, we will not be truly satisfied unless we have some analytic understanding of the results. Also, lattice Monte-Carlo methods can only be used to answer a small set of questions. Many issues of great conceptual and practical interest-in particular the calculation of scattering amplitudes, are thus far beyond lattice control. Any progress in controlling QCD in an explicit analytic, fashion would be of great conceptual value. It would also be of great practical aid to experimentalists, who must use rather ad-hoc and primitive models of QCD scattering amplitudes to estimate the backgrounds to interesting new physics. I will discuss an attempt to derive a string representation of QCD and a revival of the large N approach to QCD. Both of these ideas have a long history, many theorist-years have been devoted to their pursuit-so far with little success. I believe that it is time to try again. In part this is because of the progress in the last few years in string theory. Our increased understanding of string theory should make the attempt to discover a stringy representation of QCD easier, and the methods explored in matrix models might be employed to study the large N limit of QCD.
QCD and hard diffraction at the LHC
Albrow, Michael G.; /Fermilab
2005-09-01
As an introduction to QCD at the LHC the author gives an overview of QCD at the Tevatron, emphasizing the high Q{sup 2} frontier which will be taken over by the LHC. After describing briefly the LHC detectors the author discusses high mass diffraction, in particular central exclusive production of Higgs and vector boson pairs. The author introduces the FP420 project to measure the scattered protons 420m downstream of ATLAS and CMS.
NASA Astrophysics Data System (ADS)
Pelinovsky, Efim; Chaikovskaia, Natalya; Rodin, Artem
2015-04-01
The paper presents the analysis of the formation and evolution of shock wave in shallow water with no restrictions on its amplitude in the framework of the nonlinear shallow water equations. It is shown that in the case of large-amplitude waves appears a new nonlinear effect of reflection from the shock front of incident wave. These results are important for the assessment of coastal flooding by tsunami waves and storm surges. Very often the largest number of victims was observed on the coastline where the wave moved breaking. Many people, instead of running away, were just looking at the movement of the "raging wall" and lost time. This fact highlights the importance of researching the problem of security and optimal behavior of people in situations with increased risk. Usually there is uncertainty about the exact time, when rogue waves will impact. This fact limits the ability of people to adjust their behavior psychologically to the stressful situations. It concerns specialists, who are busy both in the field of flying activity and marine service as well as adults, young people and children, who live on the coastal zone. The rogue wave research is very important and it demands cooperation of different scientists - mathematicians and physicists, as well as sociologists and psychologists, because the final goal of efforts of all scientists is minimization of the harm, brought by rogue waves to humanity.
Windows on the axion. [quantum chromodynamics (QCD)
NASA Technical Reports Server (NTRS)
Turner, Michael S.
1989-01-01
Peccei-Quinn symmetry with attendant axion is a most compelling, and perhaps the most minimal, extension of the standard model, as it provides a very elegant solution to the nagging strong CP-problem associated with the theta vacuum structure of QCD. However, particle physics gives little guidance as to the axion mass; a priori, the plausible values span the range: 10(-12)eV is approx. less than m(a) which is approx. less than 10(6)eV, some 18 orders-of-magnitude. Laboratory experiments have excluded masses greater than 10(4)eV, leaving unprobed some 16 orders-of-magnitude. Axions have a host of interesting astrophysical and cosmological effects, including, modifying the evolution of stars of all types (our sun, red giants, white dwarfs, and neutron stars), contributing significantly to the mass density of the Universe today, and producting detectable line radiation through the decays of relic axions. Consideration of these effects has probed 14 orders-of-magnitude in axion mass, and has left open only two windows for further exploration: 10(-6)eV is approx. less than m(a) is approx. less than 10(-3)eV and 1eV is approx. less than m(a) is approx. less than 5eV (hadronic axions only). Both these windows are accessible to experiment, and a variety of very interesting experiments, all of which involve heavenly axions, are being planned or are underway.
Recent progress in backreacted bottom-up holographic QCD
Järvinen, Matti
2016-01-22
Recent progress in constructing holographic models for QCD is discussed, concentrating on the bottom-up models which implement holographically the renormalization group flow of QCD. The dynamics of gluons can be modeled by using a string-inspired model termed improved holographic QCD, and flavor can be added by introducing space filling branes in this model. The flavor fully backreacts to the glue in the Veneziano limit, giving rise to a class of models which are called V-QCD. The phase diagrams and spectra of V-QCD are in good agreement with results for QCD obtained by other methods.
Simple analytic QCD model with perturbative QCD behavior at high momenta
Contreras, Carlos; Espinosa, Olivier; Cvetic, Gorazd; Martinez, Hector E.
2010-10-01
Analytic QCD models are those where the QCD running coupling has the physically correct analytic behavior, i.e., no Landau singularities in the Euclidean regime. We present a simple analytic QCD model in which the discontinuity function of the running coupling at high momentum scales is the same as in perturbative QCD (just like in the analytic QCD model of Shirkov and Solovtsov), but at low scales it is replaced by a delta function which parametrizes the unknown behavior there. We require that the running coupling agree to a high degree with the perturbative coupling at high energies, which reduces the number of free parameters of the model from four to one. The remaining parameter is fixed by requiring the reproduction of the correct value of the semihadronic tau decay ratio.
The renormalization scale-setting problem in QCD
Wu, Xing-Gang; Brodsky, Stanley J.; Mojaza, Matin
2013-09-01
A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scale ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending
Interquark potential with finite quark mass from lattice QCD.
Kawanai, Taichi; Sasaki, Shoichi
2011-08-26
We present an investigation of the interquark potential determined from the q ̄q Bethe-Salpeter (BS) amplitude for heavy quarkonia in lattice QCD. The q ̄q potential at finite quark mass m(q) can be calculated from the equal-time and Coulomb gauge BS amplitude through the effective Schrödinger equation. The definition of the potential itself requires information about a kinetic mass of the quark. We then propose a self-consistent determination of the quark kinetic mass on the same footing. To verify the proposed method, we perform quenched lattice QCD simulations with a relativistic heavy-quark action at a lattice cutoff of 1/a≈2.1 GeV in a range 1.0≤m(q)≤3.6 GeV. Our numerical results show that the q ̄q potential in the m(q)→∞ limit is fairly consistent with the conventional one obtained from Wilson loops. The quark-mass dependence of the q ̄q potential and the spin-spin potential are also examined.
Spin-2 form factors at three loop in QCD
NASA Astrophysics Data System (ADS)
Ahmed, Taushif; Das, Goutam; Mathews, Prakash; Rana, Narayan; Ravindran, V.
2015-12-01
Spin-2 fields are often candidates in physics beyond the Standard Model namely the models with extra-dimensions where spin-2 Kaluza-Klein gravitons couple to the fields of the Standard Model. Also, in the context of Higgs searches, spin-2 fields have been studied as an alternative to the scalar Higgs boson. In this article, we present the complete three loop QCD radiative corrections to the spin-2 quark-antiquark and spin-2 gluon-gluon form factors in SU(N) gauge theory with n f light flavors. These form factors contribute to both quark-antiquark and gluon-gluon initiated processes involving spin-2 particle in the hadronic reactions at the LHC. We have studied the structure of infrared singularities in these form factors up to three loop level using Sudakov integro-differential equation and found that the anomalous dimensions originating from soft and collinear regions of the loop integrals coincide with those of the electroweak vector boson and Higgs form factors confirming the universality of the infrared singularities in QCD amplitudes.
Interquark Potential with Finite Quark Mass from Lattice QCD
Kawanai, Taichi; Sasaki, Shoichi
2011-08-26
We present an investigation of the interquark potential determined from the qq Bethe-Salpeter (BS) amplitude for heavy quarkonia in lattice QCD. The qq potential at finite quark mass m{sub q} can be calculated from the equal-time and Coulomb gauge BS amplitude through the effective Schroedinger equation. The definition of the potential itself requires information about a kinetic mass of the quark. We then propose a self-consistent determination of the quark kinetic mass on the same footing. To verify the proposed method, we perform quenched lattice QCD simulations with a relativistic heavy-quark action at a lattice cutoff of 1/a{approx_equal}2.1 GeV in a range 1.0{<=}m{sub q}{<=}3.6 GeV. Our numerical results show that the qq potential in the m{sub q}{yields}{infinity} limit is fairly consistent with the conventional one obtained from Wilson loops. The quark-mass dependence of the qq potential and the spin-spin potential are also examined.
Re+e- and an effective QCD charge
NASA Astrophysics Data System (ADS)
Gomez, J. D.; Natale, A. A.
2016-01-01
We consider the electron-positron annihilation process into hadrons Re+e- up to O (αs3), and we adopt the smearing method suggest by Poggio, Quinn, and Weinberg to confront the experimental data with theory. As a theoretical model, we use a QCD coupling constant frozen in the low-energy regime, where this coupling can be parametrized in terms of an effective dynamical gluon mass (mg) which is determined through Schwinger-Dyson equations. In order to find the best fit between experimental data and theory, we perform a χ2 study, that, within the uncertainties of the approach, has a minimum value when mg/ΛQCD is in the range 1.2-1.4. These values are in agreement with other phenomenological determinations of this ratio and lead to an infrared effective charge αs(0 )≈0.7 . We comment how this effective charge may affect the global duality mass scale that indicates the frontier between perturbative and nonperturbative physics.
Kurbel, Sven
2014-01-07
Based on avian and mammalian fossils found in the northeastern Chinese province of Liaoning and physiological traits linked to homeothermy, a hypothesis of evolution of homeothermic animals is proposed. It is based on the importance of muscle function in cold environment, as a strong selection pressure that favors endothermic metabolism during periods of cold climates. The presented hypothesis postulates that in progressively cooling environment, animals will develop thermal insulation, increased basal metabolism if food is available, and torpor when food is scarce. Since late Permian, Triassic and Cretaceous global temperatures were high, an exceptional place that gradually became cold was needed for the homeothermy evolution. South China Craton is here proposed as a plausible candidate for that role since it drifted across the Paleo-Tethys ocean, from equator to high northern latitudes in a journey that lasted from 250 to 200Myr ago. After this small continent collided with North China Craton some 200Myr ago, the already cold-adapted animals had spread to large, mostly empty spaces on the North China Craton, due to their evolutionary advantage of making active living in the cold environment. The most advantageous early homeothermic animals went further north to the cold Liaoning to start an oasis that delivered modern birds during next 50Myr. Modern mammals possibly evolved somewhere in the cold vicinity. This made Liaoning and similarly cold places the cradles of early birds and early mammals since for the following millions of years these places remained too cold for poikilotherms to enter and warm enough for homeotherms to dwell, until the Cretaceous-Paleogene extinction event and subsequent global cooling that diminished poikilotherms. Homeothermy was probably even more important as a survival advantage in cooler climates of Paleogene, when mammals and birds became dominant animals. This interpretation is probably supported by a recent report that a small
QCD as a topologically ordered system
Zhitnitsky, Ariel R.
2013-09-15
We argue that QCD belongs to a topologically ordered phase similar to many well-known condensed matter systems with a gap such as topological insulators or superconductors. Our arguments are based on an analysis of the so-called “deformed QCD” which is a weakly coupled gauge theory, but nevertheless preserves all the crucial elements of strongly interacting QCD, including confinement, nontrivial θ dependence, degeneracy of the topological sectors, etc. Specifically, we construct the so-called topological “BF” action which reproduces the well known infrared features of the theory such as non-dispersive contribution to the topological susceptibility which cannot be associated with any propagating degrees of freedom. Furthermore, we interpret the well known resolution of the celebrated U(1){sub A} problem where the would be η{sup ′} Goldstone boson generates its mass as a result of mixing of the Goldstone field with a topological auxiliary field characterizing the system. We then identify the non-propagating auxiliary topological field of the BF formulation in deformed QCD with the Veneziano ghost (which plays the crucial role in resolution of the U(1){sub A} problem). Finally, we elaborate on relation between “string-net” condensation in topologically ordered condensed matter systems and long range coherent configurations, the “skeletons”, studied in QCD lattice simulations. -- Highlights: •QCD may belong to a topologically ordered phase similar to condensed matter (CM) systems. •We identify the non-propagating topological field in deformed QCD with the Veneziano ghost. •Relation between “string-net” condensates in CM systems and the “skeletons” in QCD lattice simulations is studied.
Hadronic and nuclear interactions in QCD
Not Available
1982-01-01
Despite the evidence that QCD - or something close to it - gives a correct description of the structure of hadrons and their interactions, it seems paradoxical that the theory has thus far had very little impact in nuclear physics. One reason for this is that the application of QCD to distances larger than 1 fm involves coherent, non-perturbative dynamics which is beyond present calculational techniques. For example, in QCD the nuclear force can evidently be ascribed to quark interchange and gluon exchange processes. These, however, are as complicated to analyze from a fundamental point of view as is the analogous covalent bond in molecular physics. Since a detailed description of quark-quark interactions and the structure of hadronic wavefunctions is not yet well-understood in QCD, it is evident that a quantitative first-principle description of the nuclear force will require a great deal of theoretical effort. Another reason for the limited impact of QCD in nuclear physics has been the conventional assumption that nuclear interactions can for the most part be analyzed in terms of an effective meson-nucleon field theory or potential model in isolation from the details of short distance quark and gluon structure of hadrons. These lectures, argue that this view is untenable: in fact, there is no correspondence principle which yields traditional nuclear physics as a rigorous large-distance or non-relativistic limit of QCD dynamics. On the other hand, the distinctions between standard nuclear physics dynamics and QCD at nuclear dimensions are extremely interesting and illuminating for both particle and nuclear physics.
The gauge invariant quark Green's function in two-dimensional QCD
Sazdjian, H.
2010-12-22
The gauge invariant quark Green's function, defined with a path-ordered phase factor along a straight-line, is studied in two-dimensional QCD in the large-N{sub c} limit by means of an exact integrodifferential equation. It is found to be infrared finite with singularities represented by an infinite number of threshold type branch points with a power of -3/2, starting at positive mass squared values. The Green's function is analytically determined.
QCD bound states and their response to extremes of temperature and density.
Maris, P.
1998-06-09
We describe the application of Dyson-Schwinger equations to the calculation of hadron observable. The studies at zero temperature (T) and quark chemical potential ({mu}) provide a springboard for the extension to finite-(T, {mu}). Our exemplars highlight that much of hadronic physics can be understood as simply a manifestation of the nonperturbative, momentum-dependent dressing of the elementary Schwinger functions in QCD.
Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization
NASA Astrophysics Data System (ADS)
Nedelko, Sergei N.; Voronin, Vladimir V.
2017-03-01
An approach to QCD vacuum as a medium describable in terms of statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields is reviewed. These fields play the role of the confining medium for color charged fields as well as underline the mechanism of realization of chiral SUL(Nf) × SUR(Nf) and UA(1) symmetries. Hadronization formalism based on this ensemble leads to manifestly defined quantum effective meson action. Strong, electromagnetic and weak interactions of mesons are represented in the action in terms of nonlocal n-point interaction vertices given by the quark-gluon loops averaged over the background ensemble. Systematic results for the mass spectrum and decay constants of radially excited light, heavy-light mesons and heavy quarkonia are presented. Relationship of this approach to the results of functional renormalization group and Dyson-Schwinger equations, and the picture of harmonic confinement is briefly outlined.
Nonperturbative Quark Mass and Coupling Renormalization in Two Flavor QCD
NASA Astrophysics Data System (ADS)
Blum, Thomas Charles
1995-01-01
Nonperturbative bare quark mass and coupling renormalization is studied for two flavor quantum chromodynamics (QCD). In particular, the beta function for the case of Kogut-Susskind quarks is determined over the parameter space of existing lattice (spectrum) simulations from the existing spectrum data. This beta function is combined with a series of finite temperature lattice simulations (N_{t} = 4 ) to calculate the interaction measure, varepsilon-3p, which together with the pressure yields the thermal equation of state. A method of computing the asymmetry, or Karsch, coefficients, is also given. These coefficients give the parameter renormalizations for anisotropic lattices. However, for the three points in parameter space that we studied (one using Wilson fermions and two using Kogut-Susskind fermions), a clear determination of the asymmetry coefficients could not be made because of the remarkable fact that ratios of masses measured in different directions on lattices with anisotropic couplings were Euclidean invariant.
Spin jumping in the context of a QCD effective model
NASA Astrophysics Data System (ADS)
de Gracia, G. B.
2017-03-01
The tensor formulation for the effective theory of QCD vector resonances, whose model we denote by TEVR, is given by an antisymmetric tensor field and describes spin 1 particles. Our goal is to show, by different approaches, that the Abelian version of this model presents the so-called “spin jumping” when we consider its massless limit. Classically we find, by the use of the equations of motion and the Hamiltonian constraint analysis, that the massive phase of the model describes spin 1 particles while its massless phase describes spin 0 particles. From the quantum point of view, we derive these conclusions via tree-level unitarity analysis and the master action approach.
Transverse momentum-dependent parton distribution functions from lattice QCD
Michael Engelhardt, Philipp Haegler, Bernhard Musch, John Negele, Andreas Schaefer
2012-12-01
Transverse momentum-dependent parton distributions (TMDs) relevant for semi-inclusive deep inelastic scattering (SIDIS) and the Drell-Yan process can be defined in terms of matrix elements of a quark bilocal operator containing a staple-shaped Wilson connection. Starting from such a definition, a scheme to determine TMDs in lattice QCD is developed and explored. Parametrizing the aforementioned matrix elements in terms of invariant amplitudes permits a simple transformation of the problem to a Lorentz frame suited for the lattice calculation. Results for the Sivers and Boer-Mulders transverse momentum shifts are obtained using ensembles at the pion masses 369MeV and 518MeV, focusing in particular on the dependence of these shifts on the staple extent and a Collins-Soper-type evolution parameter quantifying proximity of the staples to the light cone.
Exploring hyperons and hypernuclei with lattice QCD
Beane, S.R.; Bedaque, P.F.; Parreno, A.; Savage, M.J.
2003-01-01
In this work we outline a program for lattice QCD that wouldprovide a first step toward understanding the strong and weakinteractions of strange baryons. The study of hypernuclear physics hasprovided a significant amount of information regarding the structure andweak decays of light nuclei containing one or two Lambda's, and Sigma's.From a theoretical standpoint, little is known about the hyperon-nucleoninteraction, which is required input for systematic calculations ofhypernuclear structure. Furthermore, the long-standing discrepancies inthe P-wave amplitudes for nonleptonic hyperon decays remain to beunderstood, and their resolution is central to a better understanding ofthe weak decays of hypernuclei. We present a framework that utilizesLuscher's finite-volume techniques in lattice QCD to extract thescattering length and effective range for Lambda-N scattering in both QCDand partially-quenched QCD. The effective theory describing thenonleptonic decays of hyperons using isospin symmetry alone, appropriatefor lattice calculations, is constructed.
'T hooft anomaly matching for QCD
Terning, John
1998-03-03
I present a set of theories which display non-trivial 'tHooft anomaly matching for QCD with F flavors. The matching theories arenon-Abelian gauge theories with "dual" quarks and baryons, rather thanthe purely confining theories of baryons that 't Hooft originallysearched for. The matching gauge groups are required to have an Fpm 6dimensional representation. Such a correspondence is reminiscent ofSeiberg's duality for supersymmetric (SUSY) QCD, and these theories arecandidates for non-SUSY duality. However anomaly matching by itself isnot sufficiently restrictive, and duality for QCD cannot be establishedat present. At the very least, the existence of multiple anomaly matchingsolutions should provide a note of caution regarding conjectured non-SUSYdualities.
New View of the QCD Phase Diagram
McLerran,L.
2009-07-09
Quarkyonic matter is confining but can have densities much larger than 3QCD. Its existence isargued in the large Nc limit of QCD and implies that there are at least three phases of QCD with greatly different bulk properties. These are a Confined Phase of hadrons, a Deconfined Phase ofquarks and gluons, and the Quarkyonic Phase. In the Quarkyonic Phase, the baryon density isaccounted for by a quasi-free gas of quarks, and the the antiquarks and gluons are confined intomesons, glueballs. Quarks near the Fermi surface also are treated as baryons. (In addition tothese phases, there is a color superconducting phase that has vastly different transport properties than the above, but with bulk properties, such as pressure and energy density, that are not greatlydifferent than that of Quarkyonic Matter.)
QCD sign problem for small chemical potential
Splittorff, K.; Verbaarschot, J. J. M.
2007-06-01
The expectation value of the complex phase factor of the fermion determinant is computed in the microscopic domain of QCD at nonzero chemical potential. We find that the average phase factor is nonvanishing below a critical value of the chemical potential equal to half the pion mass and vanishes exponentially in the volume for larger values of the chemical potential. This holds for QCD with dynamical quarks as well as for quenched and phase quenched QCD. The average phase factor has an essential singularity for zero chemical potential and cannot be obtained by analytic continuation from imaginary chemical potential or by means of a Taylor expansion. The leading order correction in the p-expansion of the chiral Lagrangian is calculated as well.
Phase diagram of chirally imbalanced QCD matter
Chernodub, M. N.; Nedelin, A. S.
2011-05-15
We compute the QCD phase diagram in the plane of the chiral chemical potential and temperature using the linear sigma model coupled to quarks and to the Polyakov loop. The chiral chemical potential accounts for effects of imbalanced chirality due to QCD sphaleron transitions which may emerge in heavy-ion collisions. We found three effects caused by the chiral chemical potential: the imbalanced chirality (i) tightens the link between deconfinement and chiral phase transitions; (ii) lowers the common critical temperature; (iii) strengthens the order of the phase transition by converting the crossover into the strong first order phase transition passing via the second order end point. Since the fermionic determinant with the chiral chemical potential has no sign problem, the chirally imbalanced QCD matter can be studied in numerical lattice simulations.
Light-front holographic QCD and emerging confinement
Brodsky, Stanley J.; de Téramond, Guy F.; Dosch, Hans Günter; Erlich, Joshua
2015-05-21
In this study we explore the remarkable connections between light-front dynamics, its holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and conformal quantum mechanics. This approach provides new insights into the origin of a fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essential features of hadron spectra in terms of a single scale. The light-front holographic methods described here give a precise interpretation of holographic variables and quantities in AdS space in terms of light-front variables and quantum numbers. This leads to a relation between the AdS wave functions and the boost-invariant light-front wave functions describing the internal structure of hadronic bound-states in physical spacetime. The pion is massless in the chiral limit and the excitation spectra of relativistic light-quark meson and baryon bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. In the light-front holographic approach described here currents are expressed as an infinite sum of poles, and form factors as a product of poles. At large q^{2} the form factor incorporates the correct power-law fall-off for hard scattering independent of the specific dynamics and is dictated by the twist. At low q^{2} the form factor leads to vector dominance. The approach is also extended to include small quark masses. We briefly review in this report other holographic approaches to QCD, in particular top-down and bottom-up models based on chiral symmetry breaking. We also include a discussion of open problems and future applications.
String breaking in four dimensional lattice QCD
Duncan, A.; Eichten, E.; Thacker, H.
2001-06-01
Virtual quark pair screening leads to breaking of the string between fundamental representation quarks in QCD. For unquenched four dimensional lattice QCD, this (so far elusive) phenomenon is studied using the recently developed truncated determinant algorithm (TDA). The dynamical configurations were generated on a 650 MHz PC. Quark eigenmodes up to 420 MeV are included exactly in these TDA studies performed at low quark mass on large coarse [but O(a{sup 2}) improved] lattices. A study of Wilson line correlators in Coulomb gauge extracted from an ensemble of 1000 two-flavor dynamical configurations reveals evidence for flattening of the string tension at distances R{approx}>1 fm.
Experimental Study of Nucleon Structure and QCD
Jian-Ping Chen
2012-03-01
Overview of Experimental Study of Nucleon Structure and QCD, with focus on the spin structure. Nucleon (spin) Structure provides valuable information on QCD dynamics. A decade of experiments from JLab yields these exciting results: (1) valence spin structure, duality; (2) spin sum rules and polarizabilities; (3) precision measurements of g{sub 2} - high-twist; and (4) first neutron transverse spin results - Collins/Sivers/A{sub LT}. There is a bright future as the 12 GeV Upgrade will greatly enhance our capability: (1) Precision determination of the valence quark spin structure flavor separation; and (2) Precision extraction of transversity/tensor charge/TMDs.
Hadron scattering and resonances in QCD
Dudek, Jozef J.
2016-05-01
I describe how hadron-hadron scattering amplitudes are related to the eigenstates of QCD in a finite cubic volume. The discrete spectrum of such eigenstates can be determined from correlation functions computed using lattice QCD, and the corresponding scattering amplitudes extracted. I review results from the Hadron Spectrum Collaboration who have used these finite volume methods to study pi pi elastic scattering, including the rho resonance, as well as coupled-channel pi K, eta K scattering. Ongoing calculations are advertised and the outlook for finite volume approaches is presented.
Reece, Matthew
2011-05-23
In this talk I give a brief assessment of the 'AdS/QCD correspondence', its successes, and its failures. I begin with a review of the AdS/CFT correspondence, with an emphasis on why the large N, large 't Hooft coupling limit is necessary for a calculable theory. I then briefly discuss attempts to extrapolate this correspondence to QCD-like theories, stressing why the failure of the large 't Hooft coupling limit is more important than the breakdown of the large N expansion. I sketch how event shapes can manifest stringy physics, and close with some brief remarks on the prospects for future improvements.
Is Fractional Electric Charge Problematic for QCD?
NASA Astrophysics Data System (ADS)
Slansky, R.
1982-11-01
A model of broken QCD is described here; SU3c is broken to SO3g (``g'' for ``glow'') such that color triplets become glow triplets. With this breaking pattern, there should exist low-mass, fractionally-charged diquark states that are not strongly bound to nuclei, but are rarely produced at present accelerator facilities. The breaking of QCD can be done with a 27c, in which case, this strong interaction theory is easily embedded in unified models such as those based on SU5, SO10, or E6. This work was done in collaboration with Terry Goldman of Los Alamos and Gordon Shaw of U.C., Irvine.
Geometric approach to condensates in holographic QCD
Hirn, Johannes; Rius, Nuria; Sanz, Veronica
2006-04-15
An SU(N{sub f})xSU(N{sub f}) Yang-Mills theory on an extra-dimensional interval is considered, with appropriate symmetry-breaking boundary conditions on the IR brane. UV-brane to UV-brane correlators at high energies are compared with the OPE of two-point functions of QCD quark currents. Condensates correspond to departure from the AdS metric of the (different) metrics felt by vector and axial combinations, away from the UV brane. Their effect on hadronic observables is studied: the extracted condensates agree with the signs and orders of magnitude expected from QCD.
Hadron scattering and resonances in QCD
NASA Astrophysics Data System (ADS)
Dudek, Jozef J.
2016-05-01
I describe how hadron-hadron scattering amplitudes are related to the eigenstates of QCD in a finite cubic volume. The discrete spectrum of such eigenstates can be determined from correlation functions computed using lattice QCD, and the corresponding scattering amplitudes extracted. I review results from the Hadron Spectrum Collaboration who have used these finite volume methods to study ππ elastic scattering, including the ρ resonance, as well as coupled-channel π >K, ηK scattering. Ongoing calculations are advertised and the outlook for finite volume approaches is presented.
Recent QCD Results from the Tevatron
Vellidis, Costas
2015-10-10
Four years after the shutdown of the Tevatron proton-antiproton collider, the two Tevatron experiments, CDF and DZero, continue producing important results that test the theory of the strong interaction, Quantum Chromodynamics (QCD). The experiments exploit the advantages of the data sample acquired during the Tevatron Run II, stemming from the unique pp initial state, the clean environment at the relatively low Tevatron instantaneous luminosities, and the good understanding of the data sample after many years of calibrations and optimizations. A summary of results using the full integrated luminosity is presented, focusing on measurements of prompt photon production, weak boson production associated with jets, and non-perturbative QCD processes.
Novel Aspects of Hard Diffraction in QCD
Brodsky, Stanley J.; /SLAC
2005-12-14
Initial- and final-state interactions from gluon-exchange, normally neglected in the parton model have a profound effect in QCD hard-scattering reactions, leading to leading-twist single-spin asymmetries, diffractive deep inelastic scattering, diffractive hard hadronic reactions, and nuclear shadowing and antishadowing--leading-twist physics not incorporated in the light-front wavefunctions of the target computed in isolation. I also discuss the use of diffraction to materialize the Fock states of a hadronic projectile and test QCD color transparency.
γ v NN^{*} Electrocouplings in Dyson-Schwinger Equations
NASA Astrophysics Data System (ADS)
Segovia, Jorge
2016-11-01
A symmetry preserving framework for the study of continuum Quantum Chromodynamics (QCD) is obtained from a truncated solution of the QCD equations of motion or QCD's Dyson-Schwinger equations (DSEs). A nonperturbative solution of the DSEs enables the study of, e.g., hadrons as composites of dressed-quarks and dressed-gluons, the phenomena of confinement and dynamical chiral symmetry breaking (DCSB), and therefrom an articulation of any connection between them. It is within this context that we present a unified study of Nucleon, Delta and Roper elastic and transition electromagnetic form factors, and compare predictions made using a framework built upon a Faddeev equation kernel and interaction vertices that possess QCD-like momentum dependence with results obtained using a symmetry-preserving treatment of a vector ⊗ vector contact-interaction. The comparison emphasises that experiment is sensitive to the momentum dependence of the running coupling and masses in QCD and highlights that the key to describing hadron properties is a veracious expression of DCSB in the bound-state problem.
A Study of the H-dibaryon in Holographic QCD
NASA Astrophysics Data System (ADS)
Matsumoto, Kohei; Nakagawa, Yuya; Suganuma, Hideo
We study the H-dibaryon (uuddss) in holographic QCD for the first time. Holographic QCD is derived from a QCD-equivalent D-brane system (S1-compactified D4/D8/overline{D8}) in the superstring theory via the gauge/gravity correspondence. In holographic QCD, all baryons appear as topological chiral solitons of Nambu-Goldstone bosons and (axial) vector mesons. In this framework, the H-dibaryon can be described as an SO(3)-type hedgehog state. We present the formalism of the H-dibaryon in holographic QCD, and perform the calculation to investigate its properties in the chiral limit.
Chiral logarithms in quenched QCD
Y. Chen; S. J. Dong; T. Draper; I. Horvath; F. X. Lee; K. F. Liu; N. Mathur; and J. B. Zhang
2004-08-01
The quenched chiral logarithms are examined on a 163x28 lattice with Iwasaki gauge action and overlap fermions. The pion decay constant fpi is used to set the lattice spacing, a = 0.200(3) fm. With pion mass as low as {approx}180 MeV, we see the quenched chiral logarithms clearly in mpi2/m and fP, the pseudoscalar decay constant. The authors analyze the data to determine how low the pion mass needs to be in order for the quenched one-loop chiral perturbation theory (chiPT) to apply. With the constrained curve-fitting method, they are able to extract the quenched chiral logarithmic parameter delta together with other low-energy parameters. Only for mpi<=300 MeV do we obtain a consistent and stable fit with a constant delta which they determine to be 0.24(3)(4) (at the chiral scale Lambdachi = 0.8 GeV). By comparing to the 123x28 lattice, they estimate the finite volume effect to be about 2.7% for the smallest pion mass. They also fitted the pion mass to the form for the re-summed cactus diagrams and found that its applicable region is extended farther than the range for the one-loop formula, perhaps up to mpi {approx}500-600 MeV. The scale independent delta is determined to be 0.20(3) in this case. The authors study the quenched non-analytic terms in the nucleon mass and find that the coefficient C1/2 in the nucleon mass is consistent with the prediction of one-loop chiPT. They also obtain the low energy constant L5 from fpi. They conclude from this study that it is imperative to cover only the range of data with the pion mass less than {approx}300 MeV in order to examine the chiral behavior of the hadron masses and decay constants in quenched QCD and match them with quenched one-loop chiPT.
NASA Astrophysics Data System (ADS)
Ablyazimov, T.; Abuhoza, A.; Adak, R. P.; Adamczyk, M.; Agarwal, K.; Aggarwal, M. M.; Ahammed, Z.; Ahmad, F.; Ahmad, N.; Ahmad, S.; Akindinov, A.; Akishin, P.; Akishina, E.; Akishina, T.; Akishina, V.; Akram, A.; Al-Turany, M.; Alekseev, I.; Alexandrov, E.; Alexandrov, I.; Amar-Youcef, S.; Anđelić, M.; Andreeva, O.; Andrei, C.; Andronic, A.; Anisimov, Yu.; Appelshäuser, H.; Argintaru, D.; Atkin, E.; Avdeev, S.; Averbeck, R.; Azmi, M. D.; Baban, V.; Bach, M.; Badura, E.; Bähr, S.; Balog, T.; Balzer, M.; Bao, E.; Baranova, N.; Barczyk, T.; Bartoş, D.; Bashir, S.; Baszczyk, M.; Batenkov, O.; Baublis, V.; Baznat, M.; Becker, J.; Becker, K.-H.; Belogurov, S.; Belyakov, D.; Bendarouach, J.; Berceanu, I.; Bercuci, A.; Berdnikov, A.; Berdnikov, Y.; Berendes, R.; Berezin, G.; Bergmann, C.; Bertini, D.; Bertini, O.; Beşliu, C.; Bezshyyko, O.; Bhaduri, P. P.; Bhasin, A.; Bhati, A. K.; Bhattacharjee, B.; Bhattacharyya, A.; Bhattacharyya, T. K.; Biswas, S.; Blank, T.; Blau, D.; Blinov, V.; Blume, C.; Bocharov, Yu.; Book, J.; Breitner, T.; Brüning, U.; Brzychczyk, J.; Bubak, A.; Büsching, H.; Bus, T.; Butuzov, V.; Bychkov, A.; Byszuk, A.; Cai, Xu; Cãlin, M.; Cao, Ping; Caragheorgheopol, G.; Carević, I.; Cătănescu, V.; Chakrabarti, A.; Chattopadhyay, S.; Chaus, A.; Chen, Hongfang; Chen, LuYao; Cheng, Jianping; Chepurnov, V.; Cherif, H.; Chernogorov, A.; Ciobanu, M. I.; Claus, G.; Constantin, F.; Csanád, M.; D'Ascenzo, N.; Das, Supriya; Das, Susovan; de Cuveland, J.; Debnath, B.; Dementiev, D.; Deng, Wendi; Deng, Zhi; Deppe, H.; Deppner, I.; Derenovskaya, O.; Deveaux, C. A.; Deveaux, M.; Dey, K.; Dey, M.; Dillenseger, P.; Dobyrn, V.; Doering, D.; Dong, Sheng; Dorokhov, A.; Dreschmann, M.; Drozd, A.; Dubey, A. K.; Dubnichka, S.; Dubnichkova, Z.; Dürr, M.; Dutka, L.; Dželalija, M.; Elsha, V. V.; Emschermann, D.; Engel, H.; Eremin, V.; Eşanu, T.; Eschke, J.; Eschweiler, D.; Fan, Huanhuan; Fan, Xingming; Farooq, M.; Fateev, O.; Feng, Shengqin; Figuli, S. P. D.; Filozova, I.; Finogeev, D.; Fischer, P.; Flemming, H.; Förtsch, J.; Frankenfeld, U.; Friese, V.; Friske, E.; Fröhlich, I.; Frühauf, J.; Gajda, J.; Galatyuk, T.; Gangopadhyay, G.; García Chávez, C.; Gebelein, J.; Ghosh, P.; Ghosh, S. K.; Gläßel, S.; Goffe, M.; Golinka-Bezshyyko, L.; Golovatyuk, V.; Golovnya, S.; Golovtsov, V.; Golubeva, M.; Golubkov, D.; Gómez Ramírez, A.; Gorbunov, S.; Gorokhov, S.; Gottschalk, D.; Gryboś, P.; Grzeszczuk, A.; Guber, F.; Gudima, K.; Gumiński, M.; Gupta, A.; Gusakov, Yu.; Han, Dong; Hartmann, H.; He, Shue; Hehner, J.; Heine, N.; Herghelegiu, A.; Herrmann, N.; Heß, B.; Heuser, J. M.; Himmi, A.; Höhne, C.; Holzmann, R.; Hu, Dongdong; Huang, Guangming; Huang, Xinjie; Hutter, D.; Ierusalimov, A.; Ilgenfritz, E.-M.; Irfan, M.; Ivanischev, D.; Ivanov, M.; Ivanov, P.; Ivanov, Valery; Ivanov, Victor; Ivanov, Vladimir; Ivashkin, A.; Jaaskelainen, K.; Jahan, H.; Jain, V.; Jakovlev, V.; Janson, T.; Jiang, Di; Jipa, A.; Kadenko, I.; Kähler, P.; Kämpfer, B.; Kalinin, V.; Kallunkathariyil, J.; Kampert, K.-H.; Kaptur, E.; Karabowicz, R.; Karavichev, O.; Karavicheva, T.; Karmanov, D.; Karnaukhov, V.; Karpechev, E.; Kasiński, K.; Kasprowicz, G.; Kaur, M.; Kazantsev, A.; Kebschull, U.; Kekelidze, G.; Khan, M. M.; Khan, S. A.; Khanzadeev, A.; Khasanov, F.; Khvorostukhin, A.; Kirakosyan, V.; Kirejczyk, M.; Kiryakov, A.; Kiš, M.; Kisel, I.; Kisel, P.; Kiselev, S.; Kiss, T.; Klaus, P.; Kłeczek, R.; Klein-Bösing, Ch.; Kleipa, V.; Klochkov, V.; Kmon, P.; Koch, K.; Kochenda, L.; Koczoń, P.; Koenig, W.; Kohn, M.; Kolb, B. W.; Kolosova, A.; Komkov, B.; Korolev, M.; Korolko, I.; Kotte, R.; Kovalchuk, A.; Kowalski, S.; Koziel, M.; Kozlov, G.; Kozlov, V.; Kramarenko, V.; Kravtsov, P.; Krebs, E.; Kreidl, C.; Kres, I.; Kresan, D.; Kretschmar, G.; Krieger, M.; Kryanev, A. V.; Kryshen, E.; Kuc, M.; Kucewicz, W.; Kucher, V.; Kudin, L.; Kugler, A.; Kumar, Ajit; Kumar, Ashwini; Kumar, L.; Kunkel, J.; Kurepin, A.; Kurepin, N.; Kurilkin, A.; Kurilkin, P.; Kushpil, V.; Kuznetsov, S.; Kyva, V.; Ladygin, V.; Lara, C.; Larionov, P.; Laso García, A.; Lavrik, E.; Lazanu, I.; Lebedev, A.; Lebedev, S.; Lebedeva, E.; Lehnert, J.; Lehrbach, J.; Leifels, Y.; Lemke, F.; Li, Cheng; Li, Qiyan; Li, Xin; Li, Yuanjing; Lindenstruth, V.; Linnik, B.; Liu, Feng; Lobanov, I.; Lobanova, E.; Löchner, S.; Loizeau, P.-A.; Lone, S. A.; Lucio Martínez, J. A.; Luo, Xiaofeng; Lymanets, A.; Lyu, Pengfei; Maevskaya, A.; Mahajan, S.; Mahapatra, D. P.; Mahmoud, T.; Maj, P.; Majka, Z.; Malakhov, A.; Malankin, E.; Malkevich, D.; Malyatina, O.; Malygina, H.; Mandal, M. M.; Mandal, S.; Manko, V.; Manz, S.; Marin Garcia, A. M.; Markert, J.; Masciocchi, S.; Matulewicz, T.; Meder, L.; Merkin, M.; Mialkovski, V.; Michel, J.; Miftakhov, N.; Mik, L.; Mikhailov, K.; Mikhaylov, V.; Milanović, B.; Militsija, V.; Miskowiec, D.; Momot, I.; Morhardt, T.; Morozov, S.; Müller, W. F. J.; Müntz, C.; Mukherjee, S.; Muñoz Castillo, C. E.; Murin, Yu.; Najman, R.; Nandi, C.; Nandy, E.; Naumann, L.; Nayak, T.; Nedosekin, A.; Negi, V. S.; Niebur, W.; Nikulin, V.; Normanov, D.; Oancea, A.; Oh, Kunsu; Onishchuk, Yu.; Ososkov, G.; Otfinowski, P.; Ovcharenko, E.; Pal, S.; Panasenko, I.; Panda, N. R.; Parzhitskiy, S.; Patel, V.; Pauly, C.; Penschuck, M.; Peshekhonov, D.; Peshekhonov, V.; Petráček, V.; Petri, M.; Petriş, M.; Petrovici, A.; Petrovici, M.; Petrovskiy, A.; Petukhov, O.; Pfeifer, D.; Piasecki, K.; Pieper, J.; Pietraszko, J.; Płaneta, R.; Plotnikov, V.; Plujko, V.; Pluta, J.; Pop, A.; Pospisil, V.; Poźniak, K.; Prakash, A.; Prasad, S. K.; Prokudin, M.; Pshenichnov, I.; Pugach, M.; Pugatch, V.; Querchfeld, S.; Rabtsun, S.; Radulescu, L.; Raha, S.; Rami, F.; Raniwala, R.; Raniwala, S.; Raportirenko, A.; Rautenberg, J.; Rauza, J.; Ray, R.; Razin, S.; Reichelt, P.; Reinecke, S.; Reinefeld, A.; Reshetin, A.; Ristea, C.; Ristea, O.; Rodriguez Rodriguez, A.; Roether, F.; Romaniuk, R.; Rost, A.; Rostchin, E.; Rostovtseva, I.; Roy, Amitava; Roy, Ankhi; Rożynek, J.; Ryabov, Yu.; Sadovsky, A.; Sahoo, R.; Sahu, P. K.; Sahu, S. K.; Saini, J.; Samanta, S.; Sambyal, S. S.; Samsonov, V.; Sánchez Rosado, J.; Sander, O.; Sarangi, S.; Satława, T.; Sau, S.; Saveliev, V.; Schatral, S.; Schiaua, C.; Schintke, F.; Schmidt, C. J.; Schmidt, H. R.; Schmidt, K.; Scholten, J.; Schweda, K.; Seck, F.; Seddiki, S.; Selyuzhenkov, I.; Semennikov, A.; Senger, A.; Senger, P.; Shabanov, A.; Shabunov, A.; Shao, Ming; Sheremetiev, A. D.; Shi, Shusu; Shumeiko, N.; Shumikhin, V.; Sibiryak, I.; Sikora, B.; Simakov, A.; Simon, C.; Simons, C.; Singaraju, R. N.; Singh, A. K.; Singh, B. K.; Singh, C. P.; Singhal, V.; Singla, M.; Sitzmann, P.; Siwek-Wilczyńska, K.; Škoda, L.; Skwira-Chalot, I.; Som, I.; Song, Guofeng; Song, Jihye; Sosin, Z.; Soyk, D.; Staszel, P.; Strikhanov, M.; Strohauer, S.; Stroth, J.; Sturm, C.; Sultanov, R.; Sun, Yongjie; Svirida, D.; Svoboda, O.; Szabó, A.; Szczygieł, R.; Talukdar, R.; Tang, Zebo; Tanha, M.; Tarasiuk, J.; Tarassenkova, O.; Târzilă, M.-G.; Teklishyn, M.; Tischler, T.; Tlustý, P.; Tölyhi, T.; Toia, A.; Topil'skaya, N.; Träger, M.; Tripathy, S.; Tsakov, I.; Tsyupa, Yu.; Turowiecki, A.; Tuturas, N. G.; Uhlig, F.; Usenko, E.; Valin, I.; Varga, D.; Vassiliev, I.; Vasylyev, O.; Verbitskaya, E.; Verhoeven, W.; Veshikov, A.; Visinka, R.; Viyogi, Y. P.; Volkov, S.; Volochniuk, A.; Vorobiev, A.; Voronin, Aleksey; Voronin, Alexander; Vovchenko, V.; Vznuzdaev, M.; Wang, Dong; Wang, Xi-Wei; Wang, Yaping; Wang, Yi; Weber, M.; Wendisch, C.; Wessels, J. P.; Wiebusch, M.; Wiechula, J.; Wielanek, D.; Wieloch, A.; Wilms, A.; Winckler, N.; Winter, M.; Wiśniewski, K.; Wolf, Gy.; Won, Sanguk; Wu, Ke-Jun; Wüstenfeld, J.; Xiang, Changzhou; Xu, Nu; Yang, Junfeng; Yang, Rongxing; Yin, Zhongbao; Yoo, In-Kwon; Yuldashev, B.; Yushmanov, I.; Zabołotny, W.; Zaitsev, Yu.; Zamiatin, N. I.; Zanevsky, Yu.; Zhalov, M.; Zhang, Yifei; Zhang, Yu; Zhao, Lei; Zheng, Jiajun; Zheng, Sheng; Zhou, Daicui; Zhou, Jing; Zhu, Xianglei; Zinchenko, A.; Zipper, W.; Żoładź, M.; Zrelov, P.; Zryuev, V.; Zumbruch, P.; Zyzak, M.
2017-03-01
Substantial experimental and theoretical efforts worldwide are devoted to explore the phase diagram of strongly interacting matter. At LHC and top RHIC energies, QCD matter is studied at very high temperatures and nearly vanishing net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was created at experiments at RHIC and LHC. The transition from the QGP back to the hadron gas is found to be a smooth cross over. For larger net-baryon densities and lower temperatures, it is expected that the QCD phase diagram exhibits a rich structure, such as a first-order phase transition between hadronic and partonic matter which terminates in a critical point, or exotic phases like quarkyonic matter. The discovery of these landmarks would be a breakthrough in our understanding of the strong interaction and is therefore in the focus of various high-energy heavy-ion research programs. The Compressed Baryonic Matter (CBM) experiment at FAIR will play a unique role in the exploration of the QCD phase diagram in the region of high net-baryon densities, because it is designed to run at unprecedented interaction rates. High-rate operation is the key prerequisite for high-precision measurements of multi-differential observables and of rare diagnostic probes which are sensitive to the dense phase of the nuclear fireball. The goal of the CBM experiment at SIS100 (√{s_{NN}}= 2.7-4.9 GeV) is to discover fundamental properties of QCD matter: the phase structure at large baryon-chemical potentials ( μ_B > 500 MeV), effects of chiral symmetry, and the equation of state at high density as it is expected to occur in the core of neutron stars. In this article, we review the motivation for and the physics programme of CBM, including activities before the start of data taking in 2024, in the context of the worldwide efforts to explore high-density QCD matter.
AdS/QCD, Light-Front Holography, and Sublimated Gluons
Brodsky, Stanley J.; de Teramond, Guy F.; /Costa Rica U.
2012-02-16
The gauge/gravity duality leads to a simple analytical and phenomenologically compelling nonperturbative approximation to the full light-front QCD Hamiltonian - 'Light-Front Holography', which provides a Lorentz-invariant first-approximation to QCD, and successfully describes the spectroscopy of light-quark meson and baryons, their elastic and transition form factors, and other hadronic properties. The bound-state Schroedinger and Dirac equations of the soft-wall AdS/QCD model predict linear Regge trajectories which have the same slope in orbital angular momentum L and radial quantum number n for both mesons and baryons. Light-front holography connects the fifth-dimensional coordinate of AdS space z to an invariant impact separation variable {zeta} in 3+1 space at fixed light-front time. A key feature is the determination of the frame-independent light-front wavefunctions of hadrons - the relativistic analogs of the Schroedinger wavefunctions of atomic physics which allow one to compute form factors, transversity distributions, spin properties of the valence quarks, jet hadronization, and other hadronic observables. One thus obtains a one-parameter color-confining model for hadron physics at the amplitude level. AdS/QCD also predicts the form of the non-perturbative effective coupling {alpha}{sub s}{sup AdS} (Q) and its {beta}-function with an infrared fixed point which agrees with the effective coupling a{sub g1} (Q{sup 2}) extracted from measurements of the Bjorken sum rule below Q{sup 2} < 1 GeV{sup 2}. This is consistent with a flux-tube interpretation of QCD where soft gluons with virtualities Q{sup 2} < 1 GeV{sup 2} are sublimated into a color-confining potential for quarks. We discuss a number of phenomenological hadronic properties which support this picture.
Spin chains in {N} = {2} superconformal theories from the {{Z}_2} quiver to superconformal QCD
NASA Astrophysics Data System (ADS)
Gadde, Abhijit; Pomoni, Elli; Rastelli, Leonardo
2012-06-01
In this paper we find preliminary evidence that {N} = {2} superconformal QCD, the SU( N c ) SYM theory with N f = 2 N c fundamental hypermultiplets, might be integrable in the large N Veneziano limit. We evaluate the one-loop dilation operator in the scalar sector of the {N} = {2} superconformal quiver with SU( N c ) × SU( N č ) gauge group, for N c ≡ N č . Both gauge couplings g and ǧ are exactly marginal. This theory interpolates between the {{Z}_2} orbifold of {N} = {4} SYM, which corresponds to ǧ = g, and {N} = {2} superconformal QCD, which is obtained for ǧ → 0. The planar one-loop dilation operator takes the form of a nearest-neighbor spin-chain Hamiltonian. For superconformal QCD the spin chain is of novel form: besides the color-adjoint fields φ_b^a, which occupy individual sites of the chain, there are "dimers" Q_i^aoverline Q_b^i of flavor-contracted fundamental fields, which occupy two neighboring sites. We solve the two-body scattering problem of magnon excitations and study the spectrum of bound states, for general ǧ/g. The dimeric excitations of superconformal QCD are seen to arise smoothly for ǧ → 0 as the limit of bound wavefunctions of the interpolating theory. Finally we check the Yang-Baxter equation for the two-magnon S-matrix. It holds as expected at the orbifold point ǧ = g. While violated for general ǧ ≠ g, it holds again in the limit ǧ → 0, hinting at one-loop integrability of planar {N} = {2} superconformal QCD.
NASA Astrophysics Data System (ADS)
Wu, Lian-Ao
1994-12-01
It is shown that the cyclic evolution posed by Aharonov and Anandan [Phys. Rev. Lett. 58, 1593 (1987)] universally exists in any quantum system: cyclic evolution occurs for special initial wave functions, whatever the concrete form of the Hamiltonian. The above results are illustrated and some specific geometric phases are given.
The CKM Matrix from Lattice QCD
Mackenzie, Paul B.; /Fermilab
2009-07-01
Lattice QCD plays an essential role in testing and determining the parameters of the CKM theory of flavor mixing and CP violation. Very high precisions are required for lattice calculations analyzing CKM data; I discuss the prospects for achieving them. Lattice calculations will also play a role in investigating flavor mixing and CP violation beyond the Standard Model.
The Chroma Software System for Lattice QCD
Robert Edwards; Balint Joo
2004-06-01
We describe aspects of the Chroma software system for lattice QCD calculations. Chroma is an open source C++ based software system developed using the software infrastructure of the US SciDAC initiative. Chroma interfaces with output from the BAGEL assembly generator for optimized lattice fermion kernels on some architectures. It can be run on workstations, clusters and the QCDOC supercomputer.
Exact adler function in supersymmetric QCD.
Shifman, M; Stepanyantz, K
2015-02-06
The Adler function D is found exactly in supersymmetric QCD. Our exact formula relates D(Q(2)) to the anomalous dimension of the matter superfields γ(α(s)(Q(2))). En route we prove another theorem: the absence of the so-called singlet contribution to D. While such singlet contributions are present in individual supergraphs, they cancel in the sum.
Exploring Hyperons and Hypernuclei with Lattice QCD
S.R. Beane; P.F. Bedaque; A. Parreno; M.J. Savage
2005-01-01
In this work we outline a program for lattice QCD that would provide a first step toward understanding the strong and weak interactions of strange baryons. The study of hypernuclear physics has provided a significant amount of information regarding the structure and weak decays of light nuclei containing one or two Lambda's, and Sigma's. From a theoretical standpoint, little is known about the hyperon-nucleon interaction, which is required input for systematic calculations of hypernuclear structure. Furthermore, the long-standing discrepancies in the P-wave amplitudes for nonleptonic hyperon decays remain to be understood, and their resolution is central to a better understanding of the weak decays of hypernuclei. We present a framework that utilizes Luscher's finite-volume techniques in lattice QCD to extract the scattering length and effective range for Lambda-N scattering in both QCD and partially-quenched QCD. The effective theory describing the nonleptonic decays of hyperons using isospin symmetry alone, appropriate for lattice calculations, is constructed.
On-Shell Methods in Perturbative QCD
Bern, Zvi; Dixon, Lance J.; Kosower, David A.
2007-04-25
We review on-shell methods for computing multi-parton scattering amplitudes in perturbative QCD, utilizing their unitarity and factorization properties. We focus on aspects which are useful for the construction of one-loop amplitudes needed for phenomenological studies at the Large Hadron Collider.
Bottom-up holographic approach to QCD
Afonin, S. S.
2016-01-22
One of the most known result of the string theory consists in the idea that some strongly coupled gauge theories may have a dual description in terms of a higher dimensional weakly coupled gravitational theory — the so-called AdS/CFT correspondence or gauge/gravity correspondence. The attempts to apply this idea to the real QCD are often referred to as “holographic QCD” or “AdS/QCD approach”. One of directions in this field is to start from the real QCD and guess a tentative dual higher dimensional weakly coupled field model following the principles of gauge/gravity correspondence. The ensuing phenomenology can be then developed and compared with experimental data and with various theoretical results. Such a bottom-up holographic approach turned out to be unexpectedly successful in many cases. In the given short review, the technical aspects of the bottom-up holographic approach to QCD are explained placing the main emphasis on the soft wall model.
Pluto collaboration
1981-02-01
Results obtained with the PLUTO detector at PETRA are presented. Multihadron final states have been analysed with respect to clustering, energy-energy correlations and transverse momenta in jets. QCD predictions for hard gluon emission and soft gluon-quark cascades are discussed. Results on ..cap alpha../sub s/ and the gluon spin are given.
QCD parton model at collider energies
Ellis, R.K.
1984-09-01
Using the example of vector boson production, the application of the QCD improved parton model at collider energies is reviewed. The reliability of the extrapolation to SSC energies is assessed. Predictions at ..sqrt..S = 0.54 TeV are compared with data. 21 references.
Local topological and chiral properties of QCD.
de Forcrand, Ph.
1998-10-30
To elucidate the role played by instantons in chiral symmetry breaking, the authors explore their properties, in full QCD, around the critical temperature. They study in particular, spatial correlations between low-lying Dirac eigenmodes and instantons. Their measurements are compared with the predictions of instanton-based models.
QCD PHASE TRANSITIONS-VOLUME 15.
SCHAFER,T.
1998-11-04
The title of the workshop, ''The QCD Phase Transitions'', in fact happened to be too narrow for its real contents. It would be more accurate to say that it was devoted to different phases of QCD and QCD-related gauge theories, with strong emphasis on discussion of the underlying non-perturbative mechanisms which manifest themselves as all those phases. Before we go to specifics, let us emphasize one important aspect of the present status of non-perturbative Quantum Field Theory in general. It remains true that its studies do not get attention proportional to the intellectual challenge they deserve, and that the theorists working on it remain very fragmented. The efforts to create Theory of Everything including Quantum Gravity have attracted the lion share of attention and young talent. Nevertheless, in the last few years there was also a tremendous progress and even some shift of attention toward emphasis on the unity of non-perturbative phenomena. For example, we have seen some. efforts to connect the lessons from recent progress in Supersymmetric theories with that in QCD, as derived from phenomenology and lattice. Another example is Maldacena conjecture and related development, which connect three things together, string theory, super-gravity and the (N=4) supersymmetric gauge theory. Although the progress mentioned is remarkable by itself, if we would listen to each other more we may have chance to strengthen the field and reach better understanding of the spectacular non-perturbative physics.
Marking up lattice QCD configurations and ensembles
P.Coddington; B.Joo; C.M.Maynard; D.Pleiter; T.Yoshie
2007-10-01
QCDml is an XML-based markup language designed for sharing QCD configurations and ensembles world-wide via the International Lattice Data Grid (ILDG). Based on the latest release, we present key ingredients of the QCDml in order to provide some starting points for colleagues in this community to markup valuable configurations and submit them to the ILDG.
QCD subgroup on diffractive and forward physics
Albrow, M.G.; Baker, W.; Bhatti, A.
1996-10-01
The goal is to understand the pomeron, and hence the behavior of total cross sections, elastic scattering and diffractive excitation, in terms of the underlying theory, QCD. A description of the basic ideas and phenomenology is followed by a discussion of hadron-hadron and electron-proton experiments. An appendix lists recommended diffractive-physics terms and definitions. 44 refs., 6 figs.
Nonperturbative QCD corrections to electroweak observables
Dru B Renner, Xu Feng, Karl Jansen, Marcus Petschlies
2011-12-01
Nonperturbative QCD corrections are important to many low-energy electroweak observables, for example the muon magnetic moment. However, hadronic corrections also play a significant role at much higher energies due to their impact on the running of standard model parameters, such as the electromagnetic coupling. Currently, these hadronic contributions are accounted for by a combination of experimental measurements and phenomenological modeling but ideally should be calculated from first principles. Recent developments indicate that many of the most important hadronic corrections may be feasibly calculated using lattice QCD methods. To illustrate this, we will examine the lattice computation of the leading-order QCD corrections to the muon magnetic moment, paying particular attention to a recently developed method but also reviewing the results from other calculations. We will then continue with several examples that demonstrate the potential impact of the new approach: the leading-order corrections to the electron and tau magnetic moments, the running of the electromagnetic coupling, and a class of the next-to-leading-order corrections for the muon magnetic moment. Along the way, we will mention applications to the Adler function, the determination of the strong coupling constant and QCD corrections to muonic-hydrogen.
Varelas, N.; D0 Collaboration
1997-10-01
We present recent results on jet production, dijet angular distributions, W+ Jets, and color coherence from p{anti p} collisions at {radical}s = 1.8 TeV at the Fermilab Tevatron Collider using the D0 detector. The data are compared to perturbative QCD calculations or to predictions of parton shower based Monte Carlo models.
QCD in hadron-hadron collisions
Albrow, M.
1997-03-01
Quantum Chromodynamics provides a good description of many aspects of high energy hadron-hadron collisions, and this will be described, along with some aspects that are not yet understood in QCD. Topics include high E{sub T} jet production, direct photon, W, Z and heavy flavor production, rapidity gaps and hard diffraction.
The Top Quark, QCD, And New Physics.
DOE R&D Accomplishments Database
Dawson, S.
2002-06-01
The role of the top quark in completing the Standard Model quark sector is reviewed, along with a discussion of production, decay, and theoretical restrictions on the top quark properties. Particular attention is paid to the top quark as a laboratory for perturbative QCD. As examples of the relevance of QCD corrections in the top quark sector, the calculation of e{sup+}e{sup -}+ t{bar t} at next-to-leading-order QCD using the phase space slicing algorithm and the implications of a precision measurement of the top quark mass are discussed in detail. The associated production of a t{bar t} pair and a Higgs boson in either e{sup+}e{sup -} or hadronic collisions is presented at next-to-leading-order QCD and its importance for a measurement of the top quark Yulrawa coupling emphasized. Implications of the heavy top quark mass for model builders are briefly examined, with the minimal supersymmetric Standard Model and topcolor discussed as specific examples.
Visualization Tools for Lattice QCD - Final Report
Massimo Di Pierro
2012-03-15
Our research project is about the development of visualization tools for Lattice QCD. We developed various tools by extending existing libraries, adding new algorithms, exposing new APIs, and creating web interfaces (including the new NERSC gauge connection web site). Our tools cover the full stack of operations from automating download of data, to generating VTK files (topological charge, plaquette, Polyakov lines, quark and meson propagators, currents), to turning the VTK files into images, movies, and web pages. Some of the tools have their own web interfaces. Some Lattice QCD visualization have been created in the past but, to our knowledge, our tools are the only ones of their kind since they are general purpose, customizable, and relatively easy to use. We believe they will be valuable to physicists working in the field. They can be used to better teach Lattice QCD concepts to new graduate students; they can be used to observe the changes in topological charge density and detect possible sources of bias in computations; they can be used to observe the convergence of the algorithms at a local level and determine possible problems; they can be used to probe heavy-light mesons with currents and determine their spatial distribution; they can be used to detect corrupted gauge configurations. There are some indirect results of this grant that will benefit a broader audience than Lattice QCD physicists.
Importance of proper renormalization scale-setting for QCD testing at colliders
NASA Astrophysics Data System (ADS)
Wu, Xing-Gang; Wang, Sheng-Quan; Brodsky, Stanley J.
2016-02-01
A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived from the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant α s to eliminate all non-conformal { β i } terms in the pQCD series. The { β i } terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the N C → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the "increasing-decreasing" behavior observed by the D0 collaboration for increasing t overline t invariant mass. At
Importance of proper renormalization scale-setting for QCD testing at colliders
Wu, Xing -Gang; Wang, Sheng -Quan; Brodsky, Stanley J.
2015-12-22
A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived from the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant αs to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the N_{C} → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the “increasing-decreasing” behavior observed by the D0 collaboration for increasing tt¯ invariant mass. At lower
Importance of proper renormalization scale-setting for QCD testing at colliders
Wu, Xing -Gang; Wang, Sheng -Quan; Brodsky, Stanley J.
2015-12-22
A primary problem affecting perturbative quantum chromodynamic (pQCD) analyses is the lack of a method for setting the QCD running-coupling renormalization scale such that maximally precise fixed-order predictions for physical observables are obtained. The Principle of Maximum Conformality (PMC) eliminates the ambiguities associated with the conventional renormalization scale-setting procedure, yielding predictions that are independent of the choice of renormalization scheme. The QCD coupling scales and the effective number of quark flavors are set order-by-order in the pQCD series. The PMC has a solid theoretical foundation, satisfying the standard renormalization group invariance condition and all of the self-consistency conditions derived frommore » the renormalization group. The PMC scales at each order are obtained by shifting the arguments of the strong force coupling constant αs to eliminate all non-conformal {βi} terms in the pQCD series. The {βi} terms are determined from renormalization group equations without ambiguity. The correct behavior of the running coupling at each order and at each phase-space point can then be obtained. The PMC reduces in the NC → 0 Abelian limit to the Gell-Mann-Low method. In this brief report, we summarize the results of our recent application of the PMC to a number of collider processes, emphasizing the generality and applicability of this approach. A discussion of hadronic Z decays shows that, by applying the PMC, one can achieve accurate predictions for the total and separate decay widths at each order without scale ambiguities. We also show that, if one employs the PMC to determine the top-quark pair forward-backward asymmetry at the next-to-next-to-leading order level, one obtains a comprehensive, self-consistent pQCD explanation for the Tevatron measurements of the asymmetry. This accounts for the “increasing-decreasing” behavior observed by the D0 collaboration for increasing tt¯ invariant mass. At lower
Topological Charge Evolution in the Markov-Chain of QCD
Derek Leinweber; Anthony Williams; Jian-bo Zhang; Frank Lee
2004-04-01
The topological charge is studied on lattices of large physical volume and fine lattice spacing. We illustrate how a parity transformation on the SU(3) link-variables of lattice gauge configurations reverses the sign of the topological charge and leaves the action invariant. Random applications of the parity transformation are proposed to traverse from one topological charge sign to the other. The transformation provides an improved unbiased estimator of the ensemble average and is essential in improving the ergodicity of the Markov chain process.
Methods in QCD and non-perturbative physics
NASA Astrophysics Data System (ADS)
Lee, Dean Junyuel
1998-11-01
This thesis explores several new and different methods in the study of QCD and non-perturbative field theory. In Chapter 1 we introduce a sum-rule for large-Nc QCD which relates the density of heavy quarkonium states, the state-averaged square of the wavefunction at the origin, and the heavy quark current-current correlator. Focusing on the region of energy just above perturbative threshold, we calculate the correlator by incorporating arbitrarily high orders in the QCD coupling αs. We use the sum-rule to determine the bottomonium potential using experimentally measured s- wave leptonic widths and compare the result with the potential obtained by direct calculation from the measured s-wave spectrum. We discuss the utility of the sum-rule method for accurate determination of the confining potential. In Chapter 2 we study the singular Landau surfaces of planar diagrams contributing to scattering of a massless quark and antiquark in 3 + 1 dimensions. In particular, we look at singularities which remain after integration with respect to the various angular degrees of freedom. We derive a general relation between these singularities and the singularities of quark-antiquark scattering in 1 + 1 dimensions. We then classify all Landau surfaces of the 1 + 1 dimensional system. Combining these results, we deduce that the singular surfaces of the angle-integrated 3 + 1 dimensional amplitude must satisfy at least one of three conditions, which we call the planar light-cone conditions. We discuss the extension of our results to non-perturbative processes by means of the non- perturbative operator product expansion. Our findings offer new insights into the connection between the 't Hooft model and large-Nc mesons in 3 + 1 dimensions and may prove useful in studies of confinement in relativistic meson systems. In Chapter 3 we introduce a new technique called spherical field theory. Spherical field theory is a non-perturbative method for studying quantum field theories. It uses
Spectral densities for hot QCD plasmas in a leading-log approximation
Hong, Juhee; Teaney, Derek
2010-10-15
We compute the spectral densities of T{sup {mu}{nu}}and J{sup {mu}}in high-temperature QCD plasmas at small frequency and momentum, {omega},k{approx}g{sup 4}T. The leading log Boltzmann equation is reformulated as a Fokker-Planck equation with nontrivial boundary conditions, and the resulting partial differential equation is solved numerically in momentum space. The spectral densities of the current, shear, sound, and bulk channels exhibit a smooth transition from free-streaming quasiparticles to ideal hydrodynamics. This transition is analyzed with conformal and nonconformal second-order hydrodynamics and a second-order diffusion equation. We determine all of the second-order transport coefficients that characterize the linear response in the hydrodynamic regime.
AdS/QCD, LIight-Front Holography, and the Non-perturbative Running Coupling
Brodsky, Stanley J.; de Teramond, Guy; Deur, Alexandre; /Jefferson Lab
2010-04-29
The combination of Anti-de Sitter space (AdS) methods with light-front (LF) holography provides a remarkably accurate first approximation for the spectra and wavefunctions of meson and baryon light-quark bound states. The resulting bound-state Hamiltonian equation of motion in QCD leads to relativistic light-front wave equations in terms of an invariant impact variable {zeta} which measures the separation of the quark and gluonic constituents within the hadron at equal light-front time. These equations of motion in physical space-time are equivalent to the equations of motion which describe the propagation of spin-J modes in anti-de Sitter (AdS) space. The eigenvalues give the hadronic spectrum, and the eigenmodes represent the probability distributions of the hadronic constituents at a given scale. A positive-sign confining dilaton background modifying AdS space gives a very good account of meson and baryon spectroscopy and form factors. The light-front holographic mapping of this model also leads to a non-perturbative effective coupling {alpha}{sub s}{sup Ads} (Q{sup 2}) which agrees with the effective charge defined by the Bjorken sum rule and lattice simulations. It displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale {approx} 1 GeV. The resulting {beta}-function appears to capture the essential characteristics of the full {beta}-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD.
Electrical conductivity of hot QCD matter.
Cassing, W; Linnyk, O; Steinert, T; Ozvenchuk, V
2013-05-03
We study the electric conductivity of hot QCD matter at various temperatures T within the off-shell parton-hadron-string dynamics transport approach for interacting partonic, hadronic or mixed systems in a finite box with periodic boundary conditions. The response of the strongly interacting system in equilibrium to an external electric field defines the electric conductivity σ(0). We find a sizable temperature dependence of the ratio σ(0)/T well in line with calculations in a relaxation time approach for T(c)
Exploring Three Nucleon Forces in Lattice QCD
Doi, Takumi
2011-10-21
We study the three nucleon force in N{sub f} = 2 dynamical clover fermion lattice QCD, utilizing the Nambu-Bethe-Salpeter wave function of the three nucleon system. Since parity-odd two nucleon potentials are not available in lattice QCD at this moment, we develop a new formulation to extract the genuine three nucleon force which requires only the information of parity-even two nucleon potentials. In order to handle the extremely expensive calculation cost, we consider a specific three-dimensional coordinate configuration for the three nucleons. We find that the linear setup is advantageous, where nucleons are aligned linearly with equal spacings. The lattice calculation is performed with 16{sup 3}x32 configurations at {beta} = 1.95, m{sub {pi}} = 1.13 GeV generated by CP-PACS Collaboration, and the result of the three nucleon force in triton channel is presented.
Hadronization of QCD and effective interactions
Frank, M.R.
1994-07-01
An introductory treatment of hadronization through functional integral calculus and bifocal Bose fields is given. Emphasis is placed on the utility of this approach for providing a connection between QCD and effective hadronic field theories. The hadronic interactions obtained by this method are nonlocal due to the QCD substructure, yet, in the presence of an electromagnetic field, maintain the electromagnetic gauge invariance manifest at the quark level. A local chiral model which is structurally consistent with chiral perturbation theory is obtained through a derivative expansion of the nonlocalities with determined, finite coefficients. Tree-level calculations of the pion form factor and {pi} {minus} {pi} scattering, which illustrate the dual constituent-quark-chiral-model nature of this approach, are presented.
Electrical Conductivity of Hot QCD Matter
NASA Astrophysics Data System (ADS)
Cassing, W.; Linnyk, O.; Steinert, T.; Ozvenchuk, V.
2013-05-01
We study the electric conductivity of hot QCD matter at various temperatures T within the off-shell parton-hadron-string dynamics transport approach for interacting partonic, hadronic or mixed systems in a finite box with periodic boundary conditions. The response of the strongly interacting system in equilibrium to an external electric field defines the electric conductivity σ0. We find a sizable temperature dependence of the ratio σ0/T well in line with calculations in a relaxation time approach for Tc
An Analytic Approach to Perturbative QCD
NASA Astrophysics Data System (ADS)
Magradze, B. A.
The two-loop invariant (running) coupling of QCD is written in terms of the Lambert W function. The analyticity structure of the coupling in the complex Q2-plane is established. The corresponding analytic coupling is reconstructed via a dispersion relation. We also consider some other approximations to the QCD β-function, when the corresponding couplings are solved in terms of the Lambert function. The Landau gauge gluon propagator has been considered in the renormalization group invariant analytic approach (IAA). It is shown that there is a nonperturbative ambiguity in determination of the anomalous dimension function of the gluon field. Several analytic solutions for the propagator at the one-loop order are constructed. Properties of the obtained analytical solutions are discussed.
The {Lambda}(1405) in Full QCD
Menadue, Benjamin J.; Kamleh, Waseem; Leinweber, Derek B.; Mahbub, M. Selim
2011-12-14
At 1405.1 MeV, the lowest-lying negative-parity state of the {Lambda} baryon lies surprising low. Indeed, this is lower than the lowest negative-parity state of the nucleon, even though the {Lambda}(1405) possesses a valence strange quark. However, previous Lattice QCD studies have been unable to identify such a low-lying state. Using the PACS-CS (2+1)-flavour full-QCD ensembles, available through the ILDG, we utilise a variational analysis with source and sink smearing to isolate this elusive state. We find three low-lying odd-parity states, and for the first time reproduce the correct level ordering with respect to the nearby scattering thresholds.
η and η' mesons from lattice QCD.
Christ, N H; Dawson, C; Izubuchi, T; Jung, C; Liu, Q; Mawhinney, R D; Sachrajda, C T; Soni, A; Zhou, R
2010-12-10
The large mass of the ninth pseudoscalar meson, the η', is believed to arise from the combined effects of the axial anomaly and the gauge field topology present in QCD. We report a realistic, 2+1-flavor, lattice QCD calculation of the η and η' masses and mixing which confirms this picture. The physical eigenstates show small octet-singlet mixing with a mixing angle of θ=-14.1(2.8)°. Extrapolation to the physical light quark mass gives, with statistical errors only, mη=573(6) MeV and mη'=947(142) MeV, consistent with the experimental values of 548 and 958 MeV.
Compositeness and QCD at the SSC
Barnes, V.; Blumenfeld, B.; Cahn, R.; Chivukula, S.; Ellis, S.; Freeman, J.; Heusch, C.; Huston, J.; Kondo, K.; Morfin, J.
1987-10-12
Compositeness may be signaled by an increase in the production of high transverse momentum hadronic jet pairs or lepton pairs. The hadronic jet signal competes with the QCD production of jets, a subject of interest in its own right. Tests of perturbative QCD at the SSC will be of special interest because the calculations are expected to be quite reliable. Studies show that compositeness up to a scale of 20 to 35 TeV would be detected in hadronic jets at the SSC. Leptonic evidence would be discovered for scales up to 10 to 20 TeV. The charge asymmetry for leptons would provide information on the nature of the compositeness interaction. Calorimetry will play a crucial role in the detection of compositeness in the hadronic jet signal. Deviations from an e/h response of 1 could mask the effect. The backgrounds for lepton pair production seem manageable. 30 refs., 19 figs., 10 tabs.
Nucleon Structure from Dynamical Lattice QCD
Huey-Wen Lin
2007-06-01
We present lattice QCD numerical calculations of hadronic structure functions and form factors from full-QCD lattices, with a chirally symmetric fermion action, domain-wall fermions, for the sea and valence quarks. The lattice spacing is about 0.12 fm with physical volume approximately (2 fm)3 for RBC 2-flavor ensembles and (3 fm)3 for RBC/UKQCD 2+1-flavor dynamical ones. The lightest sea quark mass is about 1/2 the strange quark mass for the former ensembles and 1/4 for the latter ones. Our calculations include: isovector vector- and axial-charge form factors and the first few moments of the polarized and unpolarized structure functions of the nucleon. Nonperturbative renormalization in RI/MOM scheme is applied.
Nucleon Structure from Dynamical Lattice QCD
Lin, H.-W.
2007-06-13
We present lattice QCD numerical calculations of hadronic structure functions and form factors from full-QCD lattices, with a chirally symmetric fermion action, domain-wall fermions, for the sea and valence quarks. The lattice spacing is about 0.12 fm with physical volume approximately (2 fm)3 for RBC 2-flavor ensembles and (3 fm)3 for RBC/UKQCD 2+1-flavor dynamical ones. The lightest sea quark mass is about 1/2 the strange quark mass for the former ensembles and 1/4 for the latter ones. Our calculations include: isovector vector- and axial-charge form factors and the first few moments of the polarized and unpolarized structure functions of the nucleon. Nonperturbative renormalization in RI/MOM scheme is applied.
Proton spin structure from lattice QCD
Fukugita, M.; Kuramashi, Y.; Okawa, M.; Ukawa, A. ||
1995-09-11
A lattice QCD calculation of the proton matrix element of the flavor singlet axial-vector current is reported. Both the connected and disconnected contributions are calculated, for the latter employing the variant method of wall source without gauge fixing. From simulations in quenched QCD with the Wilson quark action on a 16{sup 3}{times}20 lattice at {beta}=5.7 (the lattice spacing {ital a}{approx}0.14 fm), we find {Delta}{Sigma}={Delta}{ital u}+{Delta}{ital d}+{Delta}{ital s}=+0.638(54){minus}0.347(46){minus}0.109(30)=+0.18(10) with the disconnected contribution to {Delta}{ital u} and {Delta}{ital d} equal to {minus}0.119(44), which is reasonably consistent with the experiment.
Phase transitions in QCD and string theory
NASA Astrophysics Data System (ADS)
Campell, Bruce A.; Ellis, John; Kalara, S.; Nanopoulos, D. V.; Olive, Keith A.
1991-02-01
We develop a unified effective field theory approach to the high-temperature phase transitions in QCD and string theory, incorporating winding modes (time-like Polyakov loops, vortices) as well as low-mass states (pseudoscalar mesons and glueballs, matter and dilaton supermultiplets). Anomalous scale invariance and the Z3 structure of the centre of SU(3) decree a first-order phase transition with simultaneous deconfinement and Polyakov loop condensation in QCD, whereas string vortex condensation is a second-order phase transition breaking a Z2 symmetry. We argue that vortex condensation is accompanied by a dilaton phase transition to a strong coupling regime, and comment on the possible role of soliton degrees of freedom in the high-temperature string phase. On leave of absence from the School of Physics & Astronomy, University of Minnesota, Minneapolis, Minnesota, USA.
Spectral Models Based on Boussinesq Equations
2006-10-03
equations assume periodic solutions apriori. This, however, also forces the question of which extended Boussinesq model to use. Various one- equation ... equations of Nwogu (1993), without the traditional reduction to a one- equation model. Optimal numerical techniques to solve this system of equations are...A. and Madsen, P. A. (2004). "Boussinesq evolution equations : numerical efficiency, breaking and amplitude dispersion," Coastal Engineering, 51, 1117
BB Potentials in Quenched Lattice QCD
William Detmold; Kostas Orginos; Martin J. Savage
2007-12-01
The potentials between two B-mesons are computed in the heavy-quark limit using quenched lattice QCD at $m_\\pi\\sim 400~{\\rm MeV}$. Non-zero central potentials are clearly evident in all four spin-isospin channels, (I,s_l) = (0,0) , (0,1) , (1,0) , (1,1), where s_l is the total spin of the light degrees of freedom. At short distance, we find repulsion in the $I\
Advances in QCD sum-rule calculations
Melikhov, Dmitri
2016-01-22
We review the recent progress in the applications of QCD sum rules to hadron properties with the emphasis on the following selected problems: (i) development of new algorithms for the extraction of ground-state parameters from two-point correlators; (ii) form factors at large momentum transfers from three-point vacuum correlation functions: (iii) properties of exotic tetraquark hadrons from correlation functions of four-quark currents.
Bootstrapping One-Loop QCD Amplitudes
Berger, Carola F.; /SLAC
2006-09-08
We review the recently developed bootstrap method for the computation of high-multiplicity QCD amplitudes at one loop. We illustrate the general algorithm step by step with a six-point example. The method combines (generalized) unitarity with on-shell recursion relations to determine the not cut-constructible, rational terms of these amplitudes. Our bootstrap approach works for arbitrary configurations of gluon helicities and arbitrary numbers of external legs.
Hadron physics as Seiberg dual of QCD
Kitano, Ryuichiro
2012-07-27
We try to identify the light hadron world as the magnetic picture of QCD. We take both phenomenological and theoretical approaches to this hypothesis, and find that the interpretation seems to show interesting consistencies. In particular, one can identify the {rho} and {omega} mesons as the magnetic gauge bosons, and the Higgs mechanism for them provides a dual picture of the color confinement{sup 1}.
Lattice QCD calculations of weak matrix elements
NASA Astrophysics Data System (ADS)
Detar, Carleton
2017-01-01
Lattice QCD has become the method of choice for calculating the hadronic environment of the electroweak interactions of quarks. So it is now an essential tool in the search for new physics beyond the Standard Model. Advances in computing power and algorithms have resulted in increasingly precise predictions and increasingly stringent tests of the Standard Model. I review results of recent calculations of weak matrix elements and discuss their implications for new physics. Supported by US NSF grant PHY10-034278.
Theoretical overview: Hot and dense QCD in equilibrium
Hatsuda, Tetsuo
1991-11-01
Static and dynamical properties of QCD at finite temperature and density are reviewed. Non-perturbative aspects of the QCD plasma and modification of the hadron properties associated with the chiral transition are discussed on the basis of lattice data, effective theories and QCD sum rules. Special emphasis is laid on the importance of the finite baryon density to see the effects of the restoration of chiral symmetry in experiment.
Quarkyonic Matter and the Phase Diagram of QCD
McLerran,L.
2008-05-15
Quarkyonic matter is a new phase of QCD at finite temperature and density which is distinct from the confined and de-confined phases. Its existence is unambiguously argued in the large numbers of colors limit, N{sub c} {yields} {infinity}, of QCD. Hints of its existence for QCD, N{sub c} = 3, are shown in lattice Monte-Carlo data and in heavy ion experiments.
Structure and dynamical nature of hot and dense QCD matter
Hatsuda, Tetsuo.
1991-07-01
Static and dynamical properties of QCD at finite temperature and density are reviewed. Non-perturbative aspects of the QCD plasma and the modification of the hadron properties associated with the chiral transition are discussed on the basis of lattice data, effective theories and QCD sum rules. Special emphasis is laid on the importance of the finite baryon density to see the effects of the restoration of chiral symmetry in experiment.
Simple Derivation of the Lindblad Equation
ERIC Educational Resources Information Center
Pearle, Philip
2012-01-01
The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is…
Astrophysical Implications of the QCD Phase Transition
Schaffner-Bielich, J.; Sagert, I.; Hempel, M.; Pagliara, G.; Fischer, T.; Mezzacappa, Anthony; Thielemann, Friedrich-Karl W.; Liebendoerfer, Matthias
2009-01-01
The possible role of a first order QCD phase transition at nonvanishing quark chemical potential and temperature for cold neutron stars and for supernovae is delineated. For cold neutron stars, we use the NJL model with a nonvanishing color superconducting pairing gap, which describes the phase transition to the 2SC and the CFL quark matter phases at high baryon densities. We demonstrate that these two phase transitions can both be present in the core of neutron stars and that they lead to the appearance of a third family of solution for compact stars. In particular, a core of CFL quark matter can be present in stable compact star configurations when slightly adjusting the vacuum pressure to the onset of the chiral phase transition from the hadronic model to the NJL model. We show that a strong first order phase transition can have a strong impact on the dynamics of core collapse supernovae. If the QCD phase transition sets in shortly after the first bounce, a second outgoing shock wave can be generated which leads to an explosion. The presence of the QCD phase transition can be read off from the neutrino and antineutrino signal of the supernova.
QCD with Chiral Imbalance: models vs. lattice
NASA Astrophysics Data System (ADS)
Andrianov, Alexander; Andrianov, Vladimir; Espriu, Domenec
2017-03-01
In heavy ion collisions (HIC) at high energies there may appear new phases of matter which must be described by QCD. These phases may have different color and flavour symmetries associated with the constituents involved in collisions as well as various space-time symmetries of hadron matter. Properties of the QCD medium in such a matter can be approximately described, in particular, by a number of right-handed (RH) and left-handed (LH) light quarks. The chiral imbalance (ChI) is characterized by the difference between the numbers of RH and LH quarks and supposedly occurs in the fireball after HIC. Accordingly we have to introduce a quark chiral (axial) chemical potential which simulates a ChI emerging in such a phase. In this report we discuss the possibility of a phase with Local spatial Parity Breaking (LPB) in such an environment and outline conceivable signatures for the registration of LPB as well as the appearance of new states in the spectra of scalar, pseudoscalar and vector particles as a consequence of local ChI. The comparison of the results obtained in the effective QCD- motivated models with lattice data is also performed.
QCD in heavy quark production and decay
Wiss, J.
1997-06-01
The author discusses how QCD is used to understand the physics of heavy quark production and decay dynamics. His discussion of production dynamics primarily concentrates on charm photoproduction data which are compared to perturbative QCD calculations which incorporate fragmentation effects. He begins his discussion of heavy quark decay by reviewing data on charm and beauty lifetimes. Present data on fully leptonic and semileptonic charm decay are then reviewed. Measurements of the hadronic weak current form factors are compared to the nonperturbative QCD-based predictions of Lattice Gauge Theories. He next discusses polarization phenomena present in charmed baryon decay. Heavy Quark Effective Theory predicts that the daughter baryon will recoil from the charmed parent with nearly 100% left-handed polarization, which is in excellent agreement with present data. He concludes by discussing nonleptonic charm decay which is traditionally analyzed in a factorization framework applicable to two-body and quasi-two-body nonleptonic decays. This discussion emphasizes the important role of final state interactions in influencing both the observed decay width of various two-body final states as well as modifying the interference between interfering resonance channels which contribute to specific multibody decays. 50 refs., 77 figs.
Full CKM matrix with lattice QCD
Okamoto, Masataka; /Fermilab
2004-12-01
The authors show that it is now possible to fully determine the CKM matrix, for the first time, using lattice QCD. |V{sub cd}|, |V{sub cs}|, |V{sub ub}|, |V{sub cb}| and |V{sub us}| are, respectively, directly determined with the lattice results for form factors of semileptonic D {yields} {pi}lv, D {yields} Klv, B {yields} {pi}lv, B {yields} Dlv and K {yields} {pi}lv decays. The error from the quenched approximation is removed by using the MILC unquenced lattice gauge configurations, where the effect of u, d and s quarks is included. The error from the ''chiral'' extrapolation (m{sub l} {yields} m{sub ud}) is greatly reduced by using improved staggered quarks. The accuracy is comparable to that of the Particle Data Group averages. In addition, |V{sub ud}|, |V{sub ts}|, |V{sub ts}| and |V{sub td}| are determined by using unitarity of the CKM matrix and the experimental result for sin (2{beta}). In this way, they obtain all 9 CKM matrix elements, where the only theoretical input is lattice QCD. They also obtain all the Wolfenstein parameters, for the first time, using lattice QCD.
QCD, Tevatron results and LHC prospects
Elvira, V.Daniel; /Fermilab
2008-08-01
We present a summary of the most recent measurements relevant to Quantum Chromodynamics (QCD) delivered by the D0 and CDF Tevatron experiments by May 2008. CDF and D0 are moving toward precision measurements of QCD based on data samples in excess of 1 fb-1. The inclusive jet cross sections have been extended to forward rapidity regions and measured with unprecedented precision following improvements in the jet energy calibration. Results on dijet mass distributions, bbbar dijet production using tracker based triggers, underlying event in dijet and Drell-Yan samples, inclusive photon and diphoton cross sections complete the list of measurements included in this paper. Good agreement with pQCD within errors is observed for jet production measurements. An improved and consistent theoretical description is needed for photon+jets processes. Collisions at the LHC are scheduled for early fall 2008, opening an era of discoveries at the new energy frontier, 5-7 times higher than that of the Tevatron.
Lattice analysis for the energy scale of QCD phenomena.
Yamamoto, Arata; Suganuma, Hideo
2008-12-12
We formulate a new framework in lattice QCD to study the relevant energy scale of QCD phenomena. By considering the Fourier transformation of link variable, we can investigate the intrinsic energy scale of a physical quantity nonperturbatively. This framework is broadly available for all lattice QCD calculations. We apply this framework for the quark-antiquark potential and meson masses in quenched lattice QCD. The gluonic energy scale relevant for the confinement is found to be less than 1 GeV in the Landau or Coulomb gauge.
Pion transition form factor through Dyson-Schwinger equations
NASA Astrophysics Data System (ADS)
Raya, Khépani
2016-10-01
In the framework of Dyson-Schwinger equations (DSE), we compute the γ*γ→π0 transition form factor, G(Q2). For the first time, in a continuum approach to quantun chromodynamics (QCD), it was possible to compute G(Q2) on the whole domain of space-like momenta. Our result agrees with CELLO, CLEO and Belle collaborations and, with the well- known asymptotic QCD limit, 2ƒπ. Our analysis unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA) and elastic electromagnetic form factor.
Charmonium-nucleon interaction from lattice QCD with 2+1 flavors of dynamical quarks
NASA Astrophysics Data System (ADS)
Kawanai, Taichi; Sasaki, Shoichi
2011-10-01
We report results for charmonium-nucleon potential Vcc¯N(r) from lattice QCD, which is calculated from the equal-time Bethe-Salpeter amplitude through the effective Schrödinger equation. Detailed information of the low-energy interaction between the charmonia (ηc and J/ψ) and the nucleon is indispensable for exploring the formation of charmonium bound to nuclei. Our simulations are carried out at a lattice cutoff of 1/a≈2 GeV in a spatial volume of (3fm)3 with the non-perturbatively O(a)-improved Wilson fermions for the light quarks and a relativistic heavy quark action for the charm quark. Although our main results are calculated in quenched lattice calculations, we also present preliminary full QCD results by using 2+1 flavor QCD configurations generated by the PACS-CS Collaboration. We have found that the charmonium-nucleon potential is weakly attractive at short distances and exponentially screened at large distances.
Light-front holographic QCD and emerging confinement
Brodsky, Stanley J.; de Téramond, Guy F.; Dosch, Hans Günter; ...
2015-05-21
In this study we explore the remarkable connections between light-front dynamics, its holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and conformal quantum mechanics. This approach provides new insights into the origin of a fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essential features of hadron spectra in terms of a single scale. Themore » light-front holographic methods described here give a precise interpretation of holographic variables and quantities in AdS space in terms of light-front variables and quantum numbers. This leads to a relation between the AdS wave functions and the boost-invariant light-front wave functions describing the internal structure of hadronic bound-states in physical spacetime. The pion is massless in the chiral limit and the excitation spectra of relativistic light-quark meson and baryon bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. In the light-front holographic approach described here currents are expressed as an infinite sum of poles, and form factors as a product of poles. At large q2 the form factor incorporates the correct power-law fall-off for hard scattering independent of the specific dynamics and is dictated by the twist. At low q2 the form factor leads to vector dominance. The approach is also extended to include small quark masses. We briefly review in this report other holographic approaches to QCD, in particular top-down and bottom-up models based on chiral symmetry breaking. We also include a discussion of open problems and future applications.« less