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Sample records for multi-parton scattering amplitudes

  1. Bootstrapping Multi-Parton Loop Amplitudes in QCD

    SciTech Connect

    Bern, Zvi; Dixon, Lance J.; Kosower, David A.; /Saclay, SPhT

    2005-07-06

    The authors present a new method for computing complete one-loop amplitudes, including their rational parts, in non-supersymmetric gauge theory. This method merges the unitarity method with on-shell recursion relations. It systematizes a unitarity-factorization bootstrap approach previously applied by the authors to the one-loop amplitudes required for next-to-leading order QCD corrections to the processes e{sup +}e{sup -} {yields} Z, {gamma}* {yields} 4 jets and pp {yields} W + 2 jets. We illustrate the method by reproducing the one-loop color-ordered five-gluon helicity amplitudes in QCD that interfere with the tree amplitude, namely A{sub 5;1}(1{sup -}, 2{sup -}, 3{sup +}, 4{sup +}, 5{sup +}) and A{sub 5;1}(1{sup -}, 2{sup +}, 3{sup -}, 4{sup +}, 5{sup +}). Then we describe the construction of the six- and seven-gluon amplitudes with two adjacent negative-helicity gluons, A{sub 6;1}(1{sup -}, 2{sup -}, 3{sup +}, 4{sup +}, 5{sup +}, 6{sup +}) and A{sub 7;1}(1{sup -}, 2{sup -}, 3{sup +}, 4{sup +}, 5{sup +}, 6{sup +}, 7{sup +}), which uses the previously-computed logarithmic parts of the amplitudes as input. They present a compact expression for the six-gluon amplitude. No loop integrals are required to obtain the rational parts.

  2. Calculating scattering amplitudes efficiently

    SciTech Connect

    Dixon, L.

    1996-01-01

    We review techniques for more efficient computation of perturbative scattering amplitudes in gauge theory, in particular tree and one- loop multi-parton amplitudes in QCD. We emphasize the advantages of (1) using color and helicity information to decompose amplitudes into smaller gauge-invariant pieces, and (2) exploiting the analytic properties of these pieces, namely their cuts and poles. Other useful tools include recursion relations, special gauges and supersymmetric rearrangements. 46 refs., 11 figs.

  3. Multi-parton loop amplitudes and next-to-leading order jet cross-sections

    SciTech Connect

    Bern, Z.; Dixon, L.; Kosower, D.A.; Signer, A.

    1998-02-01

    The authors review recent developments in the calculation of QCD loop amplitudes with several external legs, and their application to next-to-leading order jet production cross-sections. When a number of calculational tools are combined together--helicity, color and supersymmetry decompositions, plus unitarity and factorization properties--it becomes possible to compute multi-parton one-loop QCD amplitudes without ever evaluating analytically standard one-loop Feynman diagrams. One-loop helicity amplitudes are now available for processes with five external partons (ggggg, q{anti q}ggg and q{anti q}q {anti q}{prime} g), and for an intermediate vector boson V {equivalent_to} {gamma}{sup *}, Z, W plus four external partons (V q{anti q} and V q{anti q}q{prime}{anti q}{prime}). Using these amplitudes, numerical programs have been constructed for the next-to-leading order corrections to the processes p{anti p} {yields} 3 jets (ignoring quark contributions so far) and e{sup +}e{sup -} {yields} 4 jets.

  4. One-Loop Multi-Parton Amplitudes with a Vector Boson for the LHC

    SciTech Connect

    Berger, C.F.; Bern, Z.; Dixon, L.J.; Cordero, F.Febres; Forde, D.; Ita, H.; Kosower, D.A.; Maitre, D.; /SLAC

    2008-08-11

    In this talk, we present the first, numerically stable, results for the one-loop amplitudes needed for computing W; Z + 3 jet cross sections at the LHC to next-to-leading order in the QCD coupling. We implemented these processes in BlackHat, an automated program based on on-shell methods. These methods scale very well with increasing numbers of external partons, and are applicable to a wide variety of problems of phenomenological interest at the LHC.

  5. Topics in Scattering Amplitudes

    NASA Astrophysics Data System (ADS)

    Dennen, Tristan Lucas

    In Part 1, we combine on-shell methods with the six-dimensional helicity formalism of Cheung and O'Connell to construct tree-level and multiloop scattering amplitudes. As a nontrivial multiloop example, we confirm that the recently constructed four-loop four-point amplitude of N=4 super-Yang-Mills theory, including nonplanar contributions, is valid for dimensions less than or equal to six. We demonstrate that the tree-level amplitudes of maximal super-Yang-Mills theory in six dimensions, when stripped of their overall momentum and supermomentum delta functions, are covariant with respect to the six-dimensional dual conformal group. We demonstrate that this property is also present for loop amplitudes. In Part 2, we explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged to satisfy Jacobi-like identities in one-to-one correspondence to the associated color factors. The related squaring relations express gravity amplitudes in terms of gauge-theory ingredients. We then present a Yang-Mills Lagrangian whose diagrams through five points manifestly satisfy the duality between color and kinematics. Finally, we compute the coefficient of the potential three-loop divergence in pure N=4 supergravity and show that it vanishes, contrary to expectations from symmetry arguments.

  6. Effective string theory and QCD scattering amplitudes

    SciTech Connect

    Makeenko, Yuri

    2011-01-15

    QCD string is formed at distances larger than the confinement scale and can be described by the Polchinski-Strominger effective string theory with a nonpolynomial action, which has nevertheless a well-defined semiclassical expansion around a long-string ground state. We utilize modern ideas about the Wilson-loop/scattering-amplitude duality to calculate scattering amplitudes and show that the expansion parameter in the effective string theory is small in the Regge kinematical regime. For the amplitudes we obtain the Regge behavior with a linear trajectory of the intercept (d-2)/24 in d dimensions, which is computed semiclassically as a momentum-space Luescher term, and discuss an application to meson scattering amplitudes in QCD.

  7. Deep Inelastic Scattering at the Amplitude Level

    SciTech Connect

    Brodsky, Stanley J.; /SLAC

    2005-08-04

    The deep inelastic lepton scattering and deeply virtual Compton scattering cross sections can be interpreted in terms of the fundamental wavefunctions defined by the light-front Fock expansion, thus allowing tests of QCD at the amplitude level. The AdS/CFT correspondence between gauge theory and string theory provides remarkable new insights into QCD, including a model for hadronic wavefunctions which display conformal scaling at short distances and color confinement at large distances.

  8. CAMORRA: A C++ library for recursive computation of particle scattering amplitudes

    NASA Astrophysics Data System (ADS)

    Kleiss, R.; van den Oord, G.

    2011-02-01

    We present a new Monte Carlo tool that computes full tree-level matrix elements in high-energy physics. The program accepts user-defined models and has no restrictions on the process multiplicity. To achieve acceptable performance, CAMORRA evaluates the matrix elements in a recursive way by combining off-shell currents. Furthermore, CAMORRA can be used to compute amplitudes involving continuous color and helicity final states. Program summaryProgram title: CAMORRA Catalogue identifier: AEHN_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHN_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL version 2 No. of lines in distributed program, including test data, etc.: 252 572 No. of bytes in distributed program, including test data, etc.: 1 711 469 Distribution format: tar.gz Programming language: C++ Computer: All Operating system: Tested on Linux and Mac OS, but should work on any system Classification: 4.4 Nature of problem: Current recursive matrix element computation programs are confined to standard model amplitudes, whereas many new physics signatures and backgrounds at hadron colliders are associated with multi-parton final states. Solution method: The library applies the Berends-Giele/Caravaglios-Moretti recursive algorithm in a generic way applicable to a wide range of quantum field theories. It allows the user to define a new physics model and consequently compute its predicted scattering amplitudes with exponential growth of the computing time with process multiplicity rather than factorial growth. Restrictions: There are no built-in restrictions on process complexity. Unusual features: CAMORRA can cope with Majorana fermions. Running time: A ten-gluon amplitude typically takes 9 ms per event.

  9. Amplitude for N-Gluon Superstring Scattering

    SciTech Connect

    Stieberger, Stephan; Taylor, Tomasz R.

    2006-11-24

    We consider scattering processes involving N gluonic massless states of open superstrings with a certain Regge slope {alpha}{sup '}. At the semiclassical level, the string world-sheet sweeps a disk and N gluons are created or annihilated at the boundary. We present exact expressions for the corresponding amplitudes, valid to all orders in {alpha}{sup '}, for the so-called maximally helicity violating configurations, with N=4, 5 and N=6. We also obtain the leading O({alpha}{sup '2}) string corrections to the zero-slope N-gluon Yang-Mills amplitudes.

  10. Scattering amplitudes with off-shell quarks

    NASA Astrophysics Data System (ADS)

    van Hameren, A.; Kutak, K.; Salwa, T.

    2013-11-01

    We present a prescription to calculate manifestly gauge invariant tree-level scattering amplitudes for arbitrary scattering processes with off-shell initial-state quarks within the kinematics of high-energy scattering. Consider the embedding of the process, in which the off-shell u-quark is replaced by an auxiliary quark qA, and an auxiliary photon γA is added in final state. The momentum flow is as if qA carries momentum k1 and the momentum of γA is identical to 0. γA only interacts via Eq. (3), and qA further only interacts with gluons via normal quark-gluon vertices. qA-line propagators are interpreted as iℓ̸1/(2ℓ1ṡp), and are diagonal in color space. Sum the squared amplitude over helicities of the auxiliary photon. For one helicity, simultaneously assign to the external qA-quark and to γA the spinor and polarization vector |ℓ1], {<ℓ1|γμ|ℓ2]}/{√{2}[ℓ1|ℓ2]}, and for the other helicity assign |ℓ1>, {<ℓ2|γμ|ℓ1]}/{√{2}<ℓ2|ℓ1>}. Multiply the amplitude with √{-x1k12/2}. For the rest, normal Feynman rules apply.Some remarks are at order. Regarding the momentum flow, we stress, as in [20], that momentum components proportional to k1 do not contribute in the eikonal propagators, and there is a freedom in the choice of the momenta flowing through qA-lines.Regarding the sum over helicities, one might argue that only one of them leads to a non-zero result for given helicity of the final-state quark, but there may, for example, be several identical such quarks in the final state with different helicities.In case of more than one quark in the final state with the same flavor as the off-shell quark, the rules as such admit graphs with γA-propagators. These must be omitted. They do not survive the limit Λ→∞ in the derivation, since the γA-propagators are suppressed by 1/Λ.The rules regarding the qA-line could be elaborated further like in [20], leading to simplified vertices for gluons attached to this line and reducing the

  11. Direct Calculation of the Scattering Amplitude Without Partial Wave Analysis

    NASA Technical Reports Server (NTRS)

    Shertzer, J.; Temkin, A.; Fisher, Richard R. (Technical Monitor)

    2001-01-01

    Two new developments in scattering theory are reported. We show, in a practical way, how one can calculate the full scattering amplitude without invoking a partial wave expansion. First, the integral expression for the scattering amplitude f(theta) is simplified by an analytic integration over the azimuthal angle. Second, the full scattering wavefunction which appears in the integral expression for f(theta) is obtained by solving the Schrodinger equation with the finite element method (FEM). As an example, we calculate electron scattering from the Hartree potential. With minimal computational effort, we obtain accurate and stable results for the scattering amplitude.

  12. Recurrence relations of Kummer functions and Regge string scattering amplitudes

    NASA Astrophysics Data System (ADS)

    Lee, Jen-Chi; Mitsuka, Yoshihiro

    2013-04-01

    We discover an infinite number of recurrence relations among Regge string scattering amplitudes [11, 30] of different string states at arbitrary mass levels in the open bosonic string theory. As a result, all Regge string scattering amplitudes can be algebraically solved up to multiplicative factors. Instead of decoupling zero-norm states in the fixed angle regime, the calculation is based on recurrence relations and addition theorem of Kummer functions of the second kind. These recurrence relations among Regge string scattering amplitudes are dual to linear relations or symmetries among high-energy fixed angle string scattering amplitudes discovered previously.

  13. Scattering amplitudes in gauge theories: progress and outlook Scattering amplitudes in gauge theories: progress and outlook

    NASA Astrophysics Data System (ADS)

    Roiban, Radu; Spradlin, Marcus; Volovich, Anastasia

    2011-11-01

    This issue aims to serve as an introduction to our current understanding of the structure of scattering amplitudes in gauge theory, an area which has seen particularly rapid advances in recent years following decades of steady progress. The articles contained herein provide a snapshot of the latest developments which we hope will serve as a valuable resource for graduate students and other scientists wishing to learn about the current state of the field, even if our continually evolving understanding of the subject might soon render this compilation incomplete. Why the fascination with scattering amplitudes, which have attracted the imagination and dedicated effort of so many physicists? Part of it stems from the belief, supported now by numerous examples, that unexpected simplifications of otherwise apparently complicated calculations do not happen by accident. Instead they provide a strong motivation to seek out an underlying explanation. The insight thereby gained can subsequently be used to make the next class of seemingly impossible calculations not only possible, but in some cases even trivial. This two-pronged strategy of exploring and exploiting the structure of gauge theory amplitudes appeals to a wide audience from formal theorists interested in mathematical structure for the sake of its own beauty to more phenomenologically-minded physicists eager to speed up the next generation of analysis software. Understandably it is the maximally supersymmetric 𝒩 = 4 Yang-Mills theory (SYM) which has the simplest structure and has correspondingly received the most attention. Rarely in theoretical physics are we fortunate enough to encounter a toy model which is simple enough to be solved completely yet rich enough to possess interesting non-trivial structure while simultaneously, and most importantly, being applicable (even if only as a good approximation) to a wide range of 'real' systems. The canonical example in quantum mechanics is of course the harmonic

  14. Calculation of the Scattering Amplitude Without Partial Wave Expansion

    NASA Technical Reports Server (NTRS)

    Shertzer, J.; Temkin, Aaron; Fisher, Richard R. (Technical Monitor)

    2001-01-01

    Two developments in the direct calculation of the angular differential scattering amplitude have been implemented: (a) The integral expansion of the scattering amplitude is simplified by analytically integration over the azimuthal angle. (b) The resulting integral as a function of scattering angle is calculated by using the numerically generated wave function from a finite element method calculation. Results for electron-hydrogen scattering in the static approximation will be shown to be as accurate as a partial wave expansion with as many l's as is necessary for convergence at the incident energy being calculated.

  15. Multiple parton scattering in nuclei: Beyond helicity amplitude approximation

    SciTech Connect

    Zhang, Ben-Wei; Wang, Xin-Nian

    2003-01-21

    Multiple parton scattering and induced parton energy loss in deeply inelastic scattering (DIS) off heavy nuclei is studied within the framework of generalized factorization in perturbative QCD with a complete calculation beyond the helicity amplitude (or soft bremsstrahlung) approximation. Such a calculation gives rise to new corrections to the modified quark fragmentation functions. The effective parton energy loss is found to be reduced by a factor of 5/6 from the result of helicity amplitude approximation.

  16. Scattering Amplitudes: The Most Perfect Microscopic Structures in the Universe

    SciTech Connect

    Dixon, Lance J.; /CERN /SLAC

    2011-11-04

    This article gives an overview of many of the recent developments in understanding the structure of relativistic scattering amplitudes in gauge theories ranging from QCD to N = 4 super-Yang-Mills theory, as well as (super)gravity. I also provide a pedagogical introduction to some of the basic tools used to organize and illuminate the color and kinematic structure of amplitudes. This article is an invited review introducing a special issue of Journal of Physics A devoted to 'Scattering Amplitudes in Gauge Theories'.

  17. Compact Multigluonic Scattering Amplitudes with Heavy Scalars and Fermions

    SciTech Connect

    Ferrario, Paola; Rodrigo, German; Talavera, Pere

    2006-05-12

    Combining the Berends-Giele and on-shell recursion relations we obtain an extremely compact expression for the scattering amplitude of a complex massive scalar-antiscalar pair and an arbitrary number of positive helicity gluons. This is one of the basic building blocks for constructing other helicity configurations from recursion relations. We also show explicitly that the scattering amplitude of massive fermions to gluons, all with positive helicity, is proportional to the scalar one, confirming in this way the recently advocated SUSY-like Ward identities relating both amplitudes.

  18. Loop Integrands for Scattering Amplitudes from the Riemann Sphere.

    PubMed

    Geyer, Yvonne; Mason, Lionel; Monteiro, Ricardo; Tourkine, Piotr

    2015-09-18

    The scattering equations on the Riemann sphere give rise to remarkable formulas for tree-level gauge theory and gravity amplitudes. Adamo, Casali, and Skinner conjectured a one-loop formula for supergravity amplitudes based on scattering equations on a torus. We use a residue theorem to transform this into a formula on the Riemann sphere. What emerges is a framework for loop integrands on the Riemann sphere that promises to have a wide application, based on off-shell scattering equations that depend on the loop momentum. We present new formulas, checked explicitly at low points, for supergravity and super-Yang-Mills amplitudes and for n-gon integrands at one loop. Finally, we show that the off-shell scattering equations naturally extend to arbitrary loop order, and we give a proposal for the all-loop integrands for supergravity and planar super-Yang-Mills theory. PMID:26430983

  19. Loop Integrands for Scattering Amplitudes from the Riemann Sphere

    NASA Astrophysics Data System (ADS)

    Geyer, Yvonne; Mason, Lionel; Monteiro, Ricardo; Tourkine, Piotr

    2015-09-01

    The scattering equations on the Riemann sphere give rise to remarkable formulas for tree-level gauge theory and gravity amplitudes. Adamo, Casali, and Skinner conjectured a one-loop formula for supergravity amplitudes based on scattering equations on a torus. We use a residue theorem to transform this into a formula on the Riemann sphere. What emerges is a framework for loop integrands on the Riemann sphere that promises to have a wide application, based on off-shell scattering equations that depend on the loop momentum. We present new formulas, checked explicitly at low points, for supergravity and super-Yang-Mills amplitudes and for n -gon integrands at one loop. Finally, we show that the off-shell scattering equations naturally extend to arbitrary loop order, and we give a proposal for the all-loop integrands for supergravity and planar super-Yang-Mills theory.

  20. Wilson loops and QCD/string scattering amplitudes

    SciTech Connect

    Makeenko, Yuri; Olesen, Poul

    2009-07-15

    We generalize modern ideas about the duality between Wilson loops and scattering amplitudes in N=4 super Yang-Mills theory to large N QCD by deriving a general relation between QCD meson scattering amplitudes and Wilson loops. We then investigate properties of the open-string disk amplitude integrated over reparametrizations. When the Wilson-loop is approximated by the area behavior, we find that the QCD scattering amplitude is a convolution of the standard Koba-Nielsen integrand and a kernel. As usual poles originate from the first factor, whereas no (momentum-dependent) poles can arise from the kernel. We show that the kernel becomes a constant when the number of external particles becomes large. The usual Veneziano amplitude then emerges in the kinematical regime, where the Wilson loop can be reliably approximated by the area behavior. In this case, we obtain a direct duality between Wilson loops and scattering amplitudes when spatial variables and momenta are interchanged, in analogy with the N=4 super Yang-Mills theory case.

  1. Collinear limit of scattering amplitudes at strong coupling.

    PubMed

    Basso, Benjamin; Sever, Amit; Vieira, Pedro

    2014-12-31

    In this Letter, we consider the collinear limit of gluon scattering amplitudes in planar N=4 super-Yang-Mills theory at strong coupling. We argue that in this limit scattering amplitudes map into correlators of twist fields in the two dimensional nonlinear O(6) sigma model, similar to those appearing in recent studies of entanglement entropy. We provide evidence for this assertion by combining the intuition springing from the string world-sheet picture and the predictions coming from the operator product expansion series. One of the main implications of these considerations is that scattering amplitudes receive equally important contributions at strong coupling from both the minimal string area and its fluctuations in the sphere. PMID:25615305

  2. Effective Field Theories from Soft Limits of Scattering Amplitudes

    NASA Astrophysics Data System (ADS)

    Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav

    2015-06-01

    We derive scalar effective field theories—Lagrangians, symmetries, and all—from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.

  3. Effective Field Theories from Soft Limits of Scattering Amplitudes.

    PubMed

    Cheung, Clifford; Kampf, Karol; Novotny, Jiri; Trnka, Jaroslav

    2015-06-01

    We derive scalar effective field theories-Lagrangians, symmetries, and all-from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist. PMID:26196613

  4. Light focusing through strongly scattering media by binary amplitude modulation

    NASA Astrophysics Data System (ADS)

    Huang, Hui-ling; Sun, Cun-zhi; Chen, Zi-yang; Pu, Ji-xiong

    2015-07-01

    Based on the angular spectrum method and the circular Gaussian distribution (CGD) model of scattering media, we numerically simulate light focusing through strongly scattering media. A high contrast focus in the target area is produced by using feedback optimization algorithm with binary amplitude modulation. It is possible to form the focusing with one focus or multiple foci at arbitrary areas. The influence of the number of square segments of spatial light modulation on the enhancement factor of intensity is discussed. Simulation results are found to be in good agreement with theoretical analysis for light refocusing.

  5. Analytical {pi}{pi} scattering amplitude and the light scalars

    SciTech Connect

    Achasov, N. N.; Kiselev, A. V.

    2011-03-01

    In this work we construct the {pi}{pi} scattering amplitude T{sub 0}{sup 0} with regular analytical properties in the s complex plane, which describes simultaneously the data on the {pi}{pi} scattering, {phi}{yields}{pi}{sup 0}{pi}0{gamma} decay, and {pi}{pi}{yields}KK reaction. The chiral shielding of the {sigma}(600) meson and its mixing with the f{sub 0}(980) meson are also taken into account. The data agrees with the four-quark nature of the {sigma}(600) and f{sub 0}(980) mesons. The amplitude in the range -5m{sub {pi}}{sup 2}

  6. Infrared singularities of scattering amplitudes in perturbative QCD

    SciTech Connect

    Becher, Thomas; Neubert, Matthias

    2013-11-01

    An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficients of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.

  7. [ital I]=2 pion scattering amplitude with Wilson fermions

    SciTech Connect

    Gupta, R. ); Patel, A. ); Sharpe, S.R. )

    1993-07-01

    We present an exploratory calculation of the [ital I]=2 [pi][pi] scattering amplitude at threshold using Wilson fermions in the quenched approximation, including all the required contractions. We find good agreement with the predictions of chiral perturbation theory even for pions of mass 560--700 MeV. Within 10% error, we do not see the onset of the bad chiral behavior expected for Wilson fermions. We also derive rigorous inequalities that apply to two-particle correlators and as a consequence show that the interaction in the antisymmetric state of two pions has to be attractive.

  8. Scattering amplitude of a single fracture under uniaxial stress

    NASA Astrophysics Data System (ADS)

    Blum, T. E.; van Wijk, K.; Snieder, R.

    2014-05-01

    Remotely sensing the properties of fractures has applications ranging from exploration geophysics to hazard monitoring. Newly developed capabilities to measure the in-plane component of dense laser-based ultrasound wave fields allow us to test the applicability of a linear slip model to describe fracture properties. In particular, we estimate the diameter, and the normal and tangential compliance of a fracture from the measured scattering amplitudes of P and S waves in the laboratory. Finally, we show that the normal compliance decreases linearly with increasing uniaxial static stress in the plane of the fracture, but that our measurements of the SV scattered field do not show significant changes in the tangential compliance.

  9. The Stoyanovsky-Ribault Map and String Scattering Amplitudes

    NASA Astrophysics Data System (ADS)

    Giribet, Gaston; Nakayama, Yu

    Recently, Ribault and Teschner pointed out the existence of a one-to-one correspondence between N-point correlation functions for the SL(2,ℂ)k/SU(2) WZNW model on the sphere and certain set of 2N-2-point correlation functions in Liouville field theory. This result is based on a seminal work by Stoyanovsky. Here, we discuss the implications of this correspondence focusing on its application to string theory on curved backgrounds. For instance, we analyze how the divergences corresponding to worldsheet instantons in AdS3 can be understood as arising from the insertion of the dual screening operator in the Liouville theory side. We also study the pole structure of N-point functions in the 2D Euclidean black hole and its holographic meaning in terms of the Little String Theory. This enables us to interpret the correspondence between CFT's as encoding a LSZ-type reduction procedure. Furthermore, we discuss the scattering amplitudes violating the winding number conservation in those backgrounds and provide a formula connecting such amplitudes with observables in Liouville field theory. Finally, we study the WZNW correlation functions in the limit k → 0 and show that, at the point k = 0, the Stoyanovsky-Ribault-Teschner dictionary turns out to be in agreement with the FZZ conjecture at a particular point of the space of parameters where the Liouville central charge becomes cL = -2. This result makes contact with recent studies on the dynamical tachyon condensation in closed string theory.

  10. Strong-field cyclotron scattering. I - Scattering amplitudes and natural line width

    NASA Astrophysics Data System (ADS)

    Graziani, Carlo

    1993-07-01

    The introduction of resonance line width into the QED cyclotron scattering amplitudes is considered. It is shown that the width arises from loop corrections to the electron propagator, which also bring about shifts in the Landau energy levels. A formalism is developed that allows the dressed electron propagator to be derived. It is shown that the states of Herold et al. (1982) and of Sokolov and Ternov (1968), which diagonalize the component of the magnetic moment operator parallel to the external magnetic field, are appropriate for calculation of the scattering amplitudes, whereas the states of Johnson and Lippmann (1949) are not. In addition, it is shown that the Breit-Wigner broadening approximation E tends to E - i(Gamma)/2 is consistent with the perturbation-theoretic order of the calculation, if the former basis states are chosen, but not the latter.

  11. Relating multichannel scattering and production amplitudes in a microscopic OZI-based model

    SciTech Connect

    Beveren, Eef van Rupp, George

    2008-05-15

    Relations between scattering and production amplitudes are studied in a microscopic multichannel model for meson-meson scattering, with coupling to confined quark-antiquark channels. Overlapping resonances and a proper threshold behaviour are treated exactly in the model. Under the spectator assumption, it is found that the two-particle production amplitude shares a common denominator with the elastic scattering amplitude, besides a numerator consisting of a linear combination of all elastic and some inelastic matrix elements. The coefficients in these linear combinations are shown to be generally complex. Finally, the standard operator expressions relating production and scattering amplitudes, viz. A=T/VandIm(A)=T*A, are fulfilled, while in the small-coupling limit the usual isobar model is recovered.

  12. Calculation of the Full Scattering Amplitude without Partial Wave Decomposition. 2; Inclusion of Exchange

    NASA Technical Reports Server (NTRS)

    Shertzer, Janine; Temkin, Aaron

    2004-01-01

    The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.

  13. Topics in Nonsupersymmetric Scattering Amplitudes in Gauge and Gravity Theories

    NASA Astrophysics Data System (ADS)

    Nohle, Joshua David

    In Chapters 1 and 2, we introduce and review the duality between color and kinematics in Yang-Mills theory uncovered by Bern, Carrasco and Johansson (BCJ). In Chapter 3, we provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions. In Chapter 4, we extend the four-point one-loop nonsupersymmetric pure Yang-Mills discussion of Chapter 3 to include fermions and scalars circulating in the loop with all external gluons. This gives another nontrivial loop-level example showing that the duality between color and kinematics holds in nonsupersymmetric gauge theory. The construction is valid in any spacetime dimension and written in terms of formal polarization vectors. We also convert these expressions into a four-dimensional form with explicit external helicity states. Using this, we compare our results to one-loop duality-satisfying amplitudes that are already present in literature. In Chapter 5, we switch from the topic of color-kinematics duality to discuss the recently renewed interest in the soft behavior of gravitons and gluons. Specifically, we discuss the subleading low-energy behavior. Cachazo and Strominger recently proposed an extension of the soft-graviton theorem found by Weinberg. In addition, they proved the validity of their extension at

  14. Implementation of the Duality between Wilson Loops and Scattering Amplitudes in QCD

    SciTech Connect

    Makeenko, Yuri; Olesen, Poul

    2009-02-20

    We generalize modern ideas about the duality between Wilson loops and scattering amplitudes in N=4 super Yang-Mills theory to large-N (or quenched) QCD. We show that the area-law behavior of asymptotically large Wilson loops is dual to the Regge-Veneziano behavior of scattering amplitudes at high energies and fixed momentum transfer, when the quark mass is small and/or the number of particles is large. We elaborate on this duality for string theory in flat space, identifying the asymptotes of the disk amplitude and the Wilson loop of large-N QCD.

  15. Scattering amplitudes to all orders in meson exchange

    SciTech Connect

    Silbar, R.R.; Mattis, M.P.

    1990-01-01

    As the number of colors in QCD, N{sub C}, becomes large, it is possible to sum up all meson-exchange contributions, however arbitrarily complicated, to meson-baryon and baryon-baryon scattering. A semi-classical structure for the two-flavor theory emerges, in close correspondence to vector-meson-augmented Skyrme models. In this limit, baryons act as extended static sources for the classical meson fields. This leads to non-linear differential equations for the classical meson fields which can be solved numerically for static radial (hedgehog-like) solutions. The non-linear terms in the equations of motion for the quantized meson fields can then be simplified, to leading order in 1/N{sub C}, by replacing all factors of the meson field but one by the previously-found classical field. This results in linear, Schroedinger-like equations, which are easily solved. For the meson-baryon case the solution can be subsequently analyzed to obtain the phase shifts for the scattering and, from these, the baryon resonance spectrum of the model. As the warm-up, we have carried out this calculation for the simple case of {sigma} mesons only, finding sensible results. 8 refs., 3 figs.

  16. Amplitude description of elastic pp scattering at 800 MeV

    NASA Astrophysics Data System (ADS)

    Moravcsik, Michael J.; Arash, Firooz; Goldstein, Gary R.

    1985-04-01

    Recent polarization data on proton-proton elastic scattering at 800 MeV taken at LAMPF are used for an amplitude analysis using the optimal formalism. The direct analysis of data is done in the transversity frame, which is best suited to parity-conserving reactions. From the results, amplitudes are also obtained in the helicity frame and the ``magic'' frame. Agreement with previous amplitudes obtained from an energy-dependent phase-shift analysis is good. The comparison of the helicity amplitudes c and e strengthens previous suggestions for a possible triplet-state dibaryon resonance. The comparison of the amplitudes am and cm in the magic frame indicates a possible domination of the process near 90° scattering angle by one-particle-exchange mechanism involving exchanged particles with natural parity.

  17. Quark born diagrams: Meson-meson scattering amplitudes from the nonrelativistic quark potential model

    SciTech Connect

    Barnes, T. |

    1992-12-31

    In this talk I summarize recent calculations of meson-meson scattering amplitudes in the nonrelativistic quark potential model, which assume that the scattering mechanism is one-gluon-exchange followed by constituent exchange (OGE+CEX). We refer to the scattering diagrams as ``quark Born diagrams``. For the cases chosen to isolate this mechanism, I=2 {pi}{pi} and I=3/2 K{pi}, the theoretical results are in remarkably good agreement with experimental S- and P-wave phase shifts and PCAC scattering lengths, given standard potential-model parameters.

  18. Quark born diagrams: Meson-meson scattering amplitudes from the nonrelativistic quark potential model

    SciTech Connect

    Barnes, T. Tennessee Univ., Knoxville, TN . Dept. of Physics)

    1992-01-01

    In this talk I summarize recent calculations of meson-meson scattering amplitudes in the nonrelativistic quark potential model, which assume that the scattering mechanism is one-gluon-exchange followed by constituent exchange (OGE+CEX). We refer to the scattering diagrams as quark Born diagrams''. For the cases chosen to isolate this mechanism, I=2 [pi][pi] and I=3/2 K[pi], the theoretical results are in remarkably good agreement with experimental S- and P-wave phase shifts and PCAC scattering lengths, given standard potential-model parameters.

  19. Non-Perturbative, Unitary Quantum-Particle Scattering Amplitudes from Three-Particle Equations

    SciTech Connect

    Lindesay, James V

    2002-03-19

    We here use our non-perturbative, cluster decomposable relativistic scattering formalism to calculate photon-spinor scattering, including the related particle-antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antiparticles for particles. We extract from it unitary two-particle amplitude for quantum-particle scattering. We verify that we have done this correctly by showing that our calculated photon-spinor amplitude reduces in the weak coupling limit to the usual lowest order, manifestly covariant (QED) result with the correct normalization. That we are able to successfully do this directly demonstrates that renormalizability need not be a fundamental requirement for all physically viable models.

  20. Scattering amplitude of ultracold atoms near the p-wave magnetic Feshbach resonance

    SciTech Connect

    Zhang Peng; Naidon, Pascal; Ueda, Masahito

    2010-12-15

    Most of the current theories on the p-wave superfluid in cold atomic gases are based on the effective-range theory for the two-body scattering, where the low-energy p-wave scattering amplitude f{sub 1}(k) is given by f{sub 1}(k)=-1/[ik+1/(Vk{sup 2})+1/R]. Here k is the incident momentum, V and R are the k-independent scattering volume and effective range, respectively. However, due to the long-range nature of the van der Waals interaction between two colliding ultracold atoms, the p-wave scattering amplitude of the two atoms is not described by the effective-range theory [J. Math. Phys. 4, 54 (1963); Phys. Rev. A 58, 4222 (1998)]. In this paper we provide an explicit calculation for the p-wave scattering of two ultracold atoms near the p-wave magnetic Feshbach resonance. We show that in this case the low-energy p-wave scattering amplitude f{sub 1}(k)=-1/[ik+1/(V{sup eff}k{sup 2})+1/(S{sup eff}k)+1/R{sup eff}] where V{sup eff}, S{sup eff}, and R{sup eff} are k-dependent parameters. Based on this result, we identify sufficient conditions for the effective-range theory to be a good approximation of the exact scattering amplitude. Using these conditions we show that the effective-range theory is a good approximation for the p-wave scattering in the ultracold gases of {sup 6}Li and {sup 40}K when the scattering volume is enhanced by the resonance.

  1. Direct Calculation of the Scattering Amplitude Without Partial Wave Decomposition. III; Inclusion of Correlation Effects

    NASA Technical Reports Server (NTRS)

    Shertzer, Janine; Temkin, Aaron

    2007-01-01

    In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.

  2. Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II

    NASA Technical Reports Server (NTRS)

    Shertzer, J.; Temkin, A.

    2003-01-01

    As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.

  3. Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

    NASA Technical Reports Server (NTRS)

    Shertzer, Janine; Temkin, A.

    2003-01-01

    As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.

  4. Non-relativistic scattering amplitude for a new multi-parameter exponential-type potential

    NASA Astrophysics Data System (ADS)

    Yazarloo, B. H.; Mehraban, H.; Hassanabadi, H.

    2016-08-01

    In this paper, we study the scattering properties of s-wave Schrödinger equation for the multi-parameter potential, which can be reduced into four special cases for different values of potential parameters, i.e., Hulthén, Manning–Rosen, and Eckart potentials. We also obtain and investigate the scattering amplitudes of these special cases. Some numerical results are also obtained and reported.

  5. Observations on open and closed string scattering amplitudes at high energies

    NASA Astrophysics Data System (ADS)

    Caputa, Pawel; Hirano, Shinji

    2012-02-01

    We study massless open and closed string scattering amplitudes in flat space at high energies. Similarly to the case of AdS space, we demonstrate that, under the T-duality map, the open string amplitudes are given by the exponential of minus minimal surface areas whose boundaries are cusped closed loops formed by lightlike momentum vectors. We show further that the closed string amplitudes are obtained by gluing two copies of minimal surfaces along their cusped lightlike boundaries. This can be thought of as a manifestation of the Kawai-Lewellen-Tye (KLT) relation at high energies. We also discuss the KLT relation in AdS/CFT and its possible connection to amplitudes in mathcal{N} = {8} supergravity as well as the correlator/amplitude duality.

  6. Chiral representation of the πN scattering amplitude and the pion-nucleon sigma term

    NASA Astrophysics Data System (ADS)

    Alarcón, J. M.; Camalich, J. Martin; Oller, J. A.

    2012-03-01

    We present a novel analysis of the πN scattering amplitude in Lorentz covariant baryon chiral perturbation theory renormalized in the extended-on-mass-shell scheme. This amplitude, valid up to O(p3) in the chiral expansion, systematically includes the effects of the Δ(1232) in the δ-counting, has the right analytic properties, and is renormalization-scale independent. This approach overcomes the limitations that previous chiral analyses of the πN scattering amplitude had, providing an accurate description of the partial wave phase shifts of the Karlsruhe-Helsinki and George-Washington groups up to energies just below the resonance region. We also study the solution of the Matsinos group which focuses on the parameterization of the data at low energies. Once the values of the low-energy constants are determined by adjusting the center-of-mass energy dependence of the amplitude to the scattering data, we obtain predictions on different observables. In particular, we extract an accurate value for the pion-nucleon sigma term, σπN. This allows us to avoid the usual method of extrapolation to the unphysical region of the amplitude. Our study indicates that the inclusion of modern meson-factory and pionic-atom data favors relatively large values of the sigma term. We report the value σπN=59(7)MeV and comment on implications that this result may have.

  7. Construction of Non-Perturbative, Unitary Particle-Antiparticle Amplitudes for Finite Particle Number Scattering Formalisms

    SciTech Connect

    Lindesay, James V

    2002-03-12

    Starting from a unitary, Lorentz invariant two-particle scattering amplitude, we show how to use an identification and replacement process to construct a unique, unitary particle-antiparticle amplitude. This process differs from conventional on-shell Mandelstam s,t,u crossing in that the input and constructed amplitudes can be off-diagonal and off-energy shell. Further, amplitudes are constructed using the invariant parameters which are appropriate to use as driving terms in the multi-particle, multichannel nonperturbative, cluster decomposable, relativistic scattering equations of the Faddeev-type integral equations recently presented by Alfred, Kwizera, Lindesay and Noyes. It is therefore anticipated that when so employed, the resulting multi-channel solutions will also be unitary. The process preserves the usual particle-antiparticle symmetries. To illustrate this process, we construct a J=0 scattering length model chosen for simplicity. We also exhibit a class of physical models which contain a finite quantum mass parameter and are Lorentz invariant. These are constructed to reduce in the appropriate limits, and with the proper choice of value and sign of the interaction parameter, to the asymptotic solution of the nonrelativistic Coulomb problem, including the forward scattering singularity , the essential singularity in the phase, and the Bohr bound-state spectrum.

  8. Double-logarithmic asymptotics of quark scattering amplitudes with flavor exchange

    SciTech Connect

    Kirschner, R.; Lipatov, L.N.

    1982-09-01

    We propose simple equations in terms of the definite-signature partial waves of the quark scattering and annihilation amplitudes with quark-quark and quark-antiquark states in the exchange channel. We discuss the singularities in the complex angular momentum plane generated by the double-logarithmic contributions and point out their relation to the particle Regge trajectories.

  9. Extracting hadron-neutron scattering amplitudes from hadron-proton and hadron-deuteron measurements

    NASA Technical Reports Server (NTRS)

    Franco, V.

    1977-01-01

    A method is presented for extracting hadron-neutron scattering amplitudes from hadron-proton and hadron-deuteron measurements within the framework of the Glauber approximation. This method, which involves the solution of a linear integral equation, is applied to pn collisions between 15 and 275 GeV/c. Effects arising from inelastic intermediate states are estimated.

  10. Relativistic electron scattering by magnetosonic waves: Effects of discrete wave emission and high wave amplitudes

    SciTech Connect

    Artemyev, A. V.; Mourenas, D.; Krasnoselskikh, V. V.

    2015-06-15

    In this paper, we study relativistic electron scattering by fast magnetosonic waves. We compare results of test particle simulations and the quasi-linear theory for different spectra of waves to investigate how a fine structure of the wave emission can influence electron resonant scattering. We show that for a realistically wide distribution of wave normal angles θ (i.e., when the dispersion δθ≥0.5{sup °}), relativistic electron scattering is similar for a wide wave spectrum and for a spectrum consisting in well-separated ion cyclotron harmonics. Comparisons of test particle simulations with quasi-linear theory show that for δθ>0.5{sup °}, the quasi-linear approximation describes resonant scattering correctly for a large enough plasma frequency. For a very narrow θ distribution (when δθ∼0.05{sup °}), however, the effect of a fine structure in the wave spectrum becomes important. In this case, quasi-linear theory clearly fails in describing accurately electron scattering by fast magnetosonic waves. We also study the effect of high wave amplitudes on relativistic electron scattering. For typical conditions in the earth's radiation belts, the quasi-linear approximation cannot accurately describe electron scattering for waves with averaged amplitudes >300 pT. We discuss various applications of the obtained results for modeling electron dynamics in the radiation belts and in the Earth's magnetotail.

  11. The string BCJ relations revisited and extended recurrence relations of nonrelativistic string scattering amplitudes

    NASA Astrophysics Data System (ADS)

    Lai, Sheng-Hong; Lee, Jen-Chi; Yang, Yi

    2016-05-01

    We review and extend high energy four point string BCJ relations in both the fixed angle and Regge regimes. We then give an explicit proof of four point string BCJ relations for all energy. This calculation provides an alternative proof of the one based on monodromy of integration in string amplitude calculation. In addition, we calculate both s- t and t- u channel nonrelativistic low energy string scattering amplitudes of three tachyons and one higher spin string state at arbitrary mass levels. We discover that the mass and spin dependent nonrelativistic string BCJ relations can be expressed in terms of Gauss hypergeometry functions. As an application, for each fixed mass level N, we derive extended recurrence relations among nonrelativistic low energy string scattering amplitudes of string states with different spins and different channels.

  12. Correlations among angular wave component amplitudes in elastic multiple-scattering random media.

    PubMed

    Hoover, Brian G; Deslauriers, Louis; Grannell, Shawn M; Ahmed, Rizwan E; Dilworth, David S; Athey, Brian D; Leith, Emmett N

    2002-02-01

    The propagation of scalar waves through random media that provide multiple elastic scattering is considered by derivation of an expression for the angular correlation of the scattered wave amplitudes. Coherent wave transmission is shown to occur through a mechanism similar to that responsible for coherent backscattering. While the properties of the scattered wave are generally consistent with radiative-transfer theory for sufficiently small incident and scattering angles, coherent transmission provides corrections to radiative-transfer results at larger angles. The theoretical angular correlation curves are fit, by specifying the probability densities of two random variables that correspond to material parameters, to measured data of laser light scattering from various polymer microsphere suspensions. PMID:11863685

  13. Statistical density model for composite system scattering: Modified ensemble densities and bounded amplitudes

    NASA Astrophysics Data System (ADS)

    Hahn, Y. K.

    2016-09-01

    A statistical density model for composite system scattering is formulated, by incorporating the ensemble density functional approach in describing the correlation dynamics during the collision. The principal difficulty of non-integrable propagating waves is first resolved by treating the open and closed channels separately; only the closed channel part does allow a density description. The unique open/closed channel separation adopted here allows not only the closed channel Hamiltonian MQ to support integrable densities, but also to establish the important bounds on the scattering amplitude. A modified ensemble energy functional for the MQ is constructed, and the statistical densities ρmtQ for the closed channels are generated. The scattering amplitude is then formulated in terms of the ρmtQ and the coefficients of variation that connect the closed channels to the asymptotic source. Evaluation of the amplitude integrals requires the determinantal functions deduced from the ρmtQ, which also leads to a coupled channel approach. The bound property of the amplitude allows variational optimization of the coefficients. Approximate procedures for securing the orthogonality of the MQ and for evaluation of the source term itself are discussed, including a judicious choice of configurations with zero and one inner-shell holes. Validity of the several critical modifications introduced is assessed.

  14. Modulating the amplitude of dark soliton by scattering-length management in Bose-Einstein condensates

    NASA Astrophysics Data System (ADS)

    Zhang, W. X.; Wang, D. L.; He, Z. M.; Wang, F. J.; Ding, J. W.

    2008-06-01

    We present a family of soliton solutions of the quasi-one-dimensional Bose-Einstein condensates with time-dependent scattering length, by developing multiple-scale method combined with truncated Painlevé expansion. Then, by numerical calculating the solutions, it is shown that there exhibit two types of dark solitons-black soliton (the zero minimum amplitude at its center) and gray soliton (the minimum density does not drop to zero) in a repulsive condensate. Furthermore, we propose experimental protocols to realize the exchange between black and gray solitons by varying the scattering length via the Feshbach resonance in currently experimental conditions.

  15. Generalized polarizabilities and the spin-averaged amplitude in virtual Compton scattering off the nucleon

    SciTech Connect

    Drechsel, D.; Knoechlein, G.; Metz, A.; Scherer, S.

    1997-01-01

    We discuss the low-energy behavior of the spin-averaged amplitude of virtual Compton scattering off a nucleon. Based on gauge invariance, Lorentz invariance, and the discrete symmetries, it is shown that to first order in the frequency of the final real photon only two generalized polarizabilities appear. Different low-energy expansion schemes are discussed and put into perspective. {copyright} {ital 1997} {ital The American Physical Society}

  16. Time-dependent treatment of scattering - Integral equation approaches using the time-dependent amplitude density

    NASA Technical Reports Server (NTRS)

    Hoffman, David K.; Sharafeddin, Omar; Judson, Richard S.; Kouri, Donald J.

    1990-01-01

    The time-dependent form of the Lippmann-Schwinger integral equation is used as the basis of several new wave packet propagation schemes. These can be formulated in terms of either the time-dependent wave function or a time-dependent amplitude density. The latter is nonzero only in the region of configuratiaon space for which the potential is nonzero, thereby in principle obviating the necessity of large grids or the use of complex absorbing potentials when resonances cause long collision times (leading, consequently, to long propagation times). Transition amplitudes are obtained in terms of Fourier transforms of the amplitude density from the time to the energy domain. The approach is illustrated by an application to a standard potential scattering model problem where, as in previous studies, the action of the kinetic energy operator is evaluated by fast Fourier transform (FFT) techniques.

  17. J. J. Sakurai Prize: Scattering Amplitudes - the Story of Loops and Legs

    NASA Astrophysics Data System (ADS)

    Dixon, Lance

    2014-03-01

    Scattering amplitudes are at the interface between quantum field theory and particle experiment. Precise predictions for reactions at energy frontier machines such as the Large Hadron Collider (LHC) rely on quantum corrections to scattering amplitudes involving multiple quarks and gluons, as well as other particles. For decades, theorists used Feynman diagrams for this job. However, Feynman diagrams are just too slow, even on fast computers, to allow adequate precision for complicated events with many jets of hadrons in the final state. Such events are produced copiously at the LHC, and constitute formidable backgrounds to many searches for new physics. Over the past two decades, alternative methods to Feynman diagrams have come to fruition. The new ``on-shell'' methods are based on the old principle of unitarity. They can be much more efficient because they exploit the underlying simplicity of scattering amplitudes, and recycle lower-loop information. The same methods have also enabled new insight into the structure of gauge theory and gravity at the quantum level, especially in highly supersymmetric theories where they maintain all of the symmetries. I'll give a brief motivation for and introduction to the new methods, which will be followed by descriptions of their phenomenological and formal applications by David Kosower and Zvi Bern.

  18. Integrand reduction for two-loop scattering amplitudes through multivariate polynomial division

    NASA Astrophysics Data System (ADS)

    Mastrolia, Pierpaolo; Mirabella, Edoardo; Ossola, Giovanni; Peraro, Tiziano

    2013-04-01

    We describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented. This technique yields the complete integrand decomposition for arbitrary amplitudes, regardless of the number of loops. It allows for the determination of the residue at any multiparticle cut, whose knowledge is a mandatory prerequisite for applying the integrand-reduction procedure. By using the division modulo Gröbner basis, we can derive a simple integrand recurrence relation that generates the multiparticle pole decomposition for integrands of arbitrary multiloop amplitudes. We apply the new reduction algorithm to the two-loop planar and nonplanar diagrams contributing to the five-point scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity in four dimensions, whose numerator functions contain up to rank-two terms in the integration momenta. We determine all polynomial residues parametrizing the cuts of the corresponding topologies and subtopologies. We obtain the integral basis for the decomposition of each diagram from the polynomial form of the residues. Our approach is well suited for a seminumerical implementation, and its general mathematical properties provide an effective algorithm for the generalization of the integrand-reduction method to all orders in perturbation theory.

  19. Yangian symmetry of scattering amplitudes in Script N = 4 super Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Drummond, James; Henn, Johannes; Plefka, Jan

    2009-05-01

    Tree-level scattering amplitudes in Script N = 4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a `dual' superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,2|4) of the theory. In this paper we derive the action of the dual superconformal generators in on-shell superspace and extend the dual generators suitably to leave scattering amplitudes invariant. We then study the algebra of standard and dual symmetry generators and show that the inclusion of the dual superconformal generators lifts the psu(2,2|4) symmetry algebra to a Yangian. The non-local Yangian generators acting on amplitudes turn out to be cyclically invariant due to special properties of psu(2,2|4). The representation of the Yangian generators takes the same form as in the case of local operators, suggesting that the Yangian symmetry is an intrinsic property of planar Script N = 4 super Yang-Mills, at least at tree level.

  20. Pion-nucleus forward scattering amplitudes from total cross section measurements

    NASA Astrophysics Data System (ADS)

    Jeppesen, R. H.; Jakobson, M. J.; Cooper, M. D.; Hagerman, D. C.; Johnson, M. B.; Redwine, R. P.; Burleson, G. R.; Johnson, K. F.; Marrs, R. E.; Meyer, H. O.; Halpern, I.; Knutson, L. D.

    1983-02-01

    Measurements have been made of the attenuation cross sections for both π+ and π- mesons on Al, 40Ca, Cu, Sn, Ho, and Pb nuclei. The measurements were made at several energies between 114 and 215 MeV. A new method of data analysis has been used to extract both the real and the imaginary parts of a Coulomb-distorted forward scattering amplitude fN(0). Insight into the nature of fN(0) is obtained by the comparison of experimental data with theoretical values calculated from a simple absorption model. This comparison demonstrates that much of the observed rotation of the forward amplitude, when plotted on an Argand diagram, can be attributed to the Coulomb phase contained in fN(0). Comparison is also made with results of similar experiments. Although the present results are in general agreement with previously published ones, some differences are noted for the heavier elements. NUCLEAR REACTIONS Measured pion forward scattering amplitudes; Al, 40Ca, Cu, Sn, Ho, and Pb; E=114-215 MeV; strong absorption model.

  1. Rapid computation of the amplitude and phase of tightly focused optical fields distorted by scattering particles.

    PubMed

    Ranasinghesagara, Janaka C; Hayakawa, Carole K; Davis, Mitchell A; Dunn, Andrew K; Potma, Eric O; Venugopalan, Vasan

    2014-07-01

    We develop an efficient method for accurately calculating the electric field of tightly focused laser beams in the presence of specific configurations of microscopic scatterers. This Huygens-Fresnel wave-based electric field superposition (HF-WEFS) method computes the amplitude and phase of the scattered electric field in excellent agreement with finite difference time-domain (FDTD) solutions of Maxwell's equations. Our HF-WEFS implementation is 2-4 orders of magnitude faster than the FDTD method and enables systematic investigations of the effects of scatterer size and configuration on the focal field. We demonstrate the power of the new HF-WEFS approach by mapping several metrics of focal field distortion as a function of scatterer position. This analysis shows that the maximum focal field distortion occurs for single scatterers placed below the focal plane with an offset from the optical axis. The HF-WEFS method represents an important first step toward the development of a computational model of laser-scanning microscopy of thick cellular/tissue specimens. PMID:25121440

  2. Rapid computation of the amplitude and phase of tightly focused optical fields distorted by scattering particles

    PubMed Central

    Ranasinghesagara, Janaka C.; Hayakawa, Carole K.; Davis, Mitchell A.; Dunn, Andrew K.; Potma, Eric O.; Venugopalan, Vasan

    2014-01-01

    We develop an efficient method for accurately calculating the electric field of tightly focused laser beams in the presence of specific configurations of microscopic scatterers. This Huygens–Fresnel wave-based electric field superposition (HF-WEFS) method computes the amplitude and phase of the scattered electric field in excellent agreement with finite difference time-domain (FDTD) solutions of Maxwell’s equations. Our HF-WEFS implementation is 2–4 orders of magnitude faster than the FDTD method and enables systematic investigations of the effects of scatterer size and configuration on the focal field. We demonstrate the power of the new HF-WEFS approach by mapping several metrics of focal field distortion as a function of scatterer position. This analysis shows that the maximum focal field distortion occurs for single scatterers placed below the focal plane with an offset from the optical axis. The HF-WEFS method represents an important first step toward the development of a computational model of laser-scanning microscopy of thick cellular/tissue specimens. PMID:25121440

  3. Role of Möbius constants and scattering functions in Cachazo-He-Yuan scalar amplitudes

    NASA Astrophysics Data System (ADS)

    Lam, C. S.; Yao, York-Peng

    2016-05-01

    The integration over the Möbius variables leading to the Cachazo-He-Yuan double-color n -point massless scalar amplitude are carried out one integral at a time. Möbius invariance dictates the final amplitude to be independent of the three Möbius constants σr,σs,σt, but their choice affects integrations and the intermediate results. The effect of the Möbius constants, which will be held finite but otherwise arbitrary, the two sets of colors, and the scattering functions on each integration is investigated. A general systematic way to carry out the n -3 integrations is explained, each exposing one of the n -3 propagators of a single Feynman diagram. Two detailed examples are shown to illustrate the procedure, one a five-point amplitude, and the other a nine-point amplitude. Our procedure does not generate intermediate spurious poles, in contrast to what is common by choosing Möbius constants at 0, 1, and ∞ .

  4. Pion-nucleon scattering in the Skyrme model and the P-wave Born amplitudes

    NASA Astrophysics Data System (ADS)

    Hayashi, A.; Saito, S.; Uehara, M.

    1991-03-01

    We treat fluctuating pion fields around a rotating Skyrmion by means of Dirac's quantization method. The rotational collective motion of the Skyrmion is described by collective coordinates, and conventional gauge-fixing conditions are imposed. Taking into account all the relevant terms at the tree level appearing in the Hamiltonian, we show that pion-nucleon scattering amplitudes exhibit the P-wave Born amplitudes attributed to the Yukawa coupling of order √Nc , which is consistent with the prediction of chiral symmetry such as the Adler-Weisberger relation. This resolves the difficulty that the Skyrme model predicts a wrong Nc dependence for the coupling of order N-3/2c.

  5. Broadband flat-amplitude multiwavelength Brillouin-Raman fiber laser with spectral reshaping by Rayleigh scattering.

    PubMed

    Wang, Zinan; Wu, Han; Fan, Mengqiu; Li, Yi; Gong, Yuan; Rao, Yunjiang

    2013-12-01

    In this letter, we propose a novel configuration for generating multiwavelength Brillouin-Raman fiber laser (MBRFL). The spectral reshaping effect introduced by Rayleigh scattering in a 50 km single mode fiber unifies the generated Brillouin comb in terms of both power level and linewidth. As a consequence, we are able to obtain a 40 nm flat-amplitude MBRFL with wide bandwidth from 1557 nm to 1597 nm covering >500 Stokes lines. This is, to the best of our knowledge, the widest flat-amplitude bandwidth of MBRFL with uniform Stokes combs using just a single Raman pump laser. The channel-spacing is 0.08 nm and the measured OSNR is higher than 12.5 dB. We also demonstrate that the output spectrum of the MBRFL is nearly unaffected over 14 dB range of Brillouin pumping power. PMID:24514489

  6. Scattering Amplitudes, the AdS/CFT Correspondence, Minimal Surfaces, and Integrability

    DOE PAGESBeta

    Alday, Luis F.

    2010-01-01

    We focus on the computation of scattering amplitudes of planar maximally supersymmetric Yang-Mill in four dimensions at strong coupling by means of the AdS/CFT correspondence and explain how the problem boils down to the computation of minimal surfaces in AdS in the first part of this paper. In the second part of this review we explain how integrability allows to give a solution to the problem in terms of a set of integral equations. The intention of the review is to give a pedagogical, rather than very detailed, exposition.

  7. Calculation of Scattering Amplitude Without Partial Analysis. II; Inclusion of Exchange

    NASA Technical Reports Server (NTRS)

    Temkin, Aaron; Shertzer, J.; Fisher, Richard R. (Technical Monitor)

    2002-01-01

    There was a method for calculating the whole scattering amplitude, f(Omega(sub k)), directly. The idea was to calculate the complete wave function Psi numerically, and use it in an integral expression for f, which can be reduced to a 2 dimensional quadrature. The original application was for e-H scattering without exchange. There the Schrodinger reduces a 2-d partial differential equation (pde), which was solved using the finite element method (FEM). Here we extend the method to the exchange approximation. The S.E. can be reduced to a pair of coupled pde's, which are again solved by the FEM. The formal expression for f(Omega(sub k)) consists two integrals, f+/- = f(sub d) +/- f(sub e); f(sub d) is formally the same integral as the no-exchange f. We have also succeeded in reducing f(sub e) to a 2-d integral. Results will be presented at the meeting.

  8. Proton-Nucleus Elastic Cross Sections Using Two-Body In-Medium Scattering Amplitudes

    NASA Technical Reports Server (NTRS)

    Tripathi, R. K.; Wilson, John W.; Cucinotta, Francis A.

    2001-01-01

    Recently, a method was developed of extracting nucleon-nucleon (NN) cross sections in the medium directly from experiment. The in-medium NN cross sections form the basic ingredients of several heavy-ion scattering approaches including the coupled-channel approach developed at the Langley Research Center. The ratio of the real to the imaginary part of the two-body scattering amplitude in the medium was investigated. These ratios are used in combination with the in-medium NN cross sections to calculate elastic proton-nucleus cross sections. The agreement is excellent with the available experimental data. These cross sections are needed for the radiation risk assessment of space missions.

  9. Bipartite field theories: from D-brane probes to scattering amplitudes

    NASA Astrophysics Data System (ADS)

    Franco, Sebastián

    2012-11-01

    We introduce and initiate the investigation of a general class of 4d, {N}=1 quiver gauge theories whose Lagrangian is defined by a bipartite graph on a Riemann surface, with or without boundaries. We refer to such class of theories as Bipartite Field Theories (BFTs). BFTs underlie a wide spectrum of interesting physical systems, including: D3-branes probing toric Calabi-Yau 3-folds, their mirror configurations of D6-branes, cluster integrable systems in (0 + 1) dimensions and leading singularities in scattering amplitudes for {N}=4 SYM. While our discussion is fully general, we focus on models that are relevant for scattering amplitudes. We investigate the BFT perspective on graph modifications, the emergence of Calabi-Yau manifolds (which arise as the master and moduli spaces of BFTs), the translation between square moves in the graph and Seiberg duality and the identification of dual theories by means of the underlying Calabi-Yaus, the phenomenon of loop reduction and the interpretation of the boundary operator for cells in the positive Grassmannian as higgsing in the BFT. We develop a technique based on generalized Kasteleyn matrices that permits an efficient determination of the Calabi-Yau geometries associated to arbitrary graphs. Our techniques allow us to go beyond the planar limit by both increasing the number of boundaries of the graphs and the genus of the underlying Riemann surface. Our investigation suggests a central role for Calabi-Yau manifolds in the context of leading singularities, whose full scope is yet to be uncovered.

  10. Decomposition of the scattering amplitude into shadow and surface components with inclusion of spin-orbit coupling

    SciTech Connect

    Melo, German; David, Jorge; Restrepo, Albeiro

    2008-09-15

    We propose a decomposition of the scattering amplitude into shadow and surface components for proton scattering against calcium isotopes as targets at 21 MeV. We account for spin-orbit coupling effects for the optical potential in the nonrelativistic limit. Our calculations show very good agreement with experimental trends.

  11. Improved Persistent Scatterer analysis using Amplitude Dispersion Index optimization of dual polarimetry data

    NASA Astrophysics Data System (ADS)

    Esmaeili, Mostafa; Motagh, Mahdi

    2016-07-01

    Time-series analysis of Synthetic Aperture Radar (SAR) data using the two techniques of Small BAseline Subset (SBAS) and Persistent Scatterer Interferometric SAR (PSInSAR) extends the capability of conventional interferometry technique for deformation monitoring and mitigating many of its limitations. Using dual/quad polarized data provides us with an additional source of information to improve further the capability of InSAR time-series analysis. In this paper we use dual-polarized data and combine the Amplitude Dispersion Index (ADI) optimization of pixels with phase stability criterion for PSInSAR analysis. ADI optimization is performed by using Simulated Annealing algorithm to increase the number of Persistent Scatterer Candidate (PSC). The phase stability of PSCs is then measured using their temporal coherence to select the final sets of pixels for deformation analysis. We evaluate the method for a dataset comprising of 17 dual polarization SAR data (HH/VV) acquired by TerraSAR-X data from July 2013 to January 2014 over a subsidence area in Iran and compare the effectiveness of the method for both agricultural and urban regions. The results reveal that using optimum scattering mechanism decreases the ADI values in urban and non-urban regions. As compared to single-pol data the use of optimized polarization increases initially the number of PSCs by about three times and improves the final PS density by about 50%, in particular in regions with high rate of deformation which suffer from losing phase stability over the time. The classification of PS pixels based on their optimum scattering mechanism revealed that the dominant scattering mechanism of the PS pixels in the urban area is double-bounce while for the non-urban regions (ground surfaces and farmlands) it is mostly single-bounce mechanism.

  12. Medium modified two-body scattering amplitude from proton-nucleus total cross-sections

    NASA Technical Reports Server (NTRS)

    Tripathi, R. K.; Wilson, J. W.; Cucinotta, F. A.

    2001-01-01

    Recently (R.K. Tripathi, J.W. Wilson, F.A. Cucinotta, Nucl. Instr. and Meth. B 145 (1998) 277; R.K. Tripathi, F.A. Cucinotta, J.W. Wilson, NASA-TP-1998-208438), we have extracted nucleon-nucleon (N-N) cross-sections in the medium directly from experiment. The in-medium N-N cross-sections form the basic ingredients of several heavy-ion scattering approaches including the coupled-channel approach developed at the NASA Langley Research Center. Here, we investigate the ratio of real to imaginary part of the two-body scattering amplitude in the medium. These ratios are used in combination with the in-medium N-N cross-sections to calculate total proton-nucleus cross-sections. The agreement is excellent with the available experimental data. These cross-sections are needed for the radiation risk assessment of space missions. c2001 Elsevier Science B.V. All rights reserved.

  13. Single Spin Asymmetries in Inclusive Dis and Multi-Parton Correlations in the Nucleon

    NASA Astrophysics Data System (ADS)

    Metz, Andreas; Pitonyak, Daniel; Schäfer, Andreas; Schlegel, Marc; Vogelsang, Werner; Zhou, Jian

    Transverse single spin asymmetries in inclusive deep-inelastic lepton-nucleon scattering can be generated through multi-photon exchange between the leptonic and the hadronic part of the process. Here we consider two-photon exchange, and mainly focus on the transverse target spin asymmetry. In particular, we investigate the case where two photons couple to different quarks. Such a contribution involves a quark-photon-quark correlator in the nucleon, which has a (model-dependent) relation to the Efremov-Teryaev-Qiu-Sterman quark-gluon-quark correlator TF. Using different parameterizations for TF we compute the transverse target spin asymmetry for both a proton and a neutron target, and compare the results to recent experimental data. Potential implications on our general understanding of single spin asymmetries in hard scattering processes are discussed as well.

  14. Thomson-Scattering Measurements of Ion-Acoustic Wave Amplitudes Driven by the Two-Plasmon-Decay Instability

    NASA Astrophysics Data System (ADS)

    Follett, R. K.; Michel, D. T.; Myatt, J. F.; Hu, S. X.; Yaakobi, B.; Froula, D. H.

    2012-10-01

    Thomson scattering was used to measure enhanced ion-acoustic waves (IAW's) driven by the two-plasmon-decay (TPD) instability. The IAW amplitude scales with the 3/2φ emission (a TPD signature). Up to 20 beams with 860-μm-diam laser spots generated by 2-ns-long pulses of 3φ (0.351-μm) light with overlapped intensities up to 4 x 10^14 W/cm^2 were used to produce ˜300-μm density-scale lengths. The IAW amplitudes were measured using 4φ Thomson scattering near 3φ quarter-critical densities. Time-resolved 3/2φ spectroscopy was used to compare the amplitude of 3/2φ emission to the IAW amplitude. QZAKfootnotetext K. Y. Sanbonmatsu et al., Phys. Rev. Lett. 82, 932 (1999).^,footnotetext K. Y. Sanbonmatsu et al., Phys. Plasmas 7, 2824 (2000). modeling shows a similar onset threshold and wave amplitude as the experiments. The model suggests that the source of the IAW growth is from the beating of electron-plasma waves, which drive density perturbations through the ponderomotive force. This conclusion is supported by the experimental geometry. This process is shown to be a saturation mechanism for TPD from simulations.footnotetext R. Yan et al., Phys. Rev. Lett. 103, 175002 (2009). This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52-08NA28302.

  15. Strong-field cyclotron scattering. I - Scattering amplitudes and natural line width. [in spectra of accretion-powered X-ray pulsars

    NASA Technical Reports Server (NTRS)

    Graziani, Carlo

    1993-01-01

    The introduction of resonance line width into the QED cyclotron scattering amplitudes is considered. It is shown that the width arises from loop corrections to the electron propagator, which also bring about shifts in the Landau energy levels. A formalism is developed that allows the dressed electron propagator to be derived. It is shown that the states of Herold et al. (1982) and of Sokolov and Ternov (1968), which diagonalize the component of the magnetic moment operator parallel to the external magnetic field, are appropriate for calculation of the scattering amplitudes, whereas the states of Johnson and Lippmann (1949) are not. In addition, it is shown that the Breit-Wigner broadening approximation E tends to E - i(Gamma)/2 is consistent with the perturbation-theoretic order of the calculation, if the former basis states are chosen, but not the latter.

  16. Detecting the Amplitude Mode of Strongly Interacting Lattice Bosons by Bragg Scattering

    SciTech Connect

    Bissbort, Ulf; Hofstetter, Walter; Li Yongqiang

    2011-05-20

    We report the first detection of the Higgs-type amplitude mode using Bragg spectroscopy in a strongly interacting condensate of ultracold atoms in an optical lattice. By the comparison of our experimental data with a spatially resolved, time-dependent bosonic Gutzwiller calculation, we obtain good quantitative agreement. This allows for a clear identification of the amplitude mode, showing that it can be detected with full momentum resolution by going beyond the linear response regime. A systematic shift of the sound and amplitude modes' resonance frequencies due to the finite Bragg beam intensity is observed.

  17. The Analytic Structure of Scattering Amplitudes in N = 4 Super-Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Litsey, Sean Christopher

    We begin the dissertation in Chapter 1 with a discussion of tree-level amplitudes in Yang-. Mills theories. The DDM and BCJ decompositions of the amplitudes are described and. related to one another by the introduction of a transformation matrix. This is related to the. Kleiss-Kuijf and BCJ amplitude identities, and we conjecture a connection to the existence. of a BCJ representation via a condition on the generalized inverse of that matrix. Under. two widely-believed assumptions, this relationship is proved. Switching gears somewhat, we introduce the RSVW formulation of the amplitude, and the extension of BCJ-like features to residues of the RSVW integrand is proposed. Using the previously proven connection of BCJ representations to the generalized inverse condition, this extension is validated, including a version of gravitational double copy. The remainder of the dissertation involves an analysis of the analytic properties of loop. amplitudes in N = 4 super-Yang-Mills theory. Chapter 2 contains a review of the planar case, including an exposition of dual variables and momentum twistors, dual conformal symmetry, and their implications for the amplitude. After defining the integrand and on-shell diagrams, we explain the crucial properties that the amplitude has no poles at infinite momentum and that its leading singularities are dual-conformally-invariant cross ratios, and can therefore be normalized to unity. We define the concept of a dlog form, and show that it is a feature of the planar integrand as well. This leads to the definition of a pure integrand basis. The proceeding setup is connected to the amplituhedron formulation, and we put forward the hypothesis that the amplitude is determined by zero conditions. Chapter 3 contains the primary computations of the dissertation. This chapter treats. amplitudes in fully nonplanar N = 4 super-Yang-Mills, analyzing the conjecture that they. follow the pattern of having no poles at infinity, can be written in dlog

  18. Near-Forward Rescattering Photoelectron Holography in Strong-Field Ionization: Extraction of the Phase of the Scattering Amplitude.

    PubMed

    Zhou, Yueming; Tolstikhin, Oleg I; Morishita, Toru

    2016-04-29

    We revisit the concept of near-forward rescattering strong-field photoelectron holography introduced by Y. Huismans et al. [Science 331, 61 (2011)]. The recently developed adiabatic theory is used to show how the phase of the scattering amplitude for near-forward rescattering of an ionized electron by the parent ion is encoded in and can be read out from the corresponding interference pattern in photoelectron momentum distributions (PEMDs) produced in the ionization of atoms and molecules by intense laser pulses. A procedure to extract the phase is proposed. Its application to PEMDs obtained by solving the time-dependent Schrödinger equation for a model atom yields results in good agreement with scattering calculations. This establishes a novel general approach to extracting structural information from strong-field observables capable of providing time-resolved imaging of ultrafast processes. PMID:27176518

  19. Argand-diagram representation of transition amplitudes for resonant reactive scattering: e+HCl and e+H2

    NASA Astrophysics Data System (ADS)

    Lutrus, C. K.; Suck Salk, S. H.

    1989-01-01

    Resonances for rearrangement collisions (reactive scattering) involving the two dissociative attachment processes, e+HCl-->H+Cl- and e+H2-->H+H-, are examined. It is shown from the Argand-diagram representation of transition amplitudes that strong resonance is present in the former but not in the latter. That is, the strong resonance is evidenced by the clear exhibition of a phase change by π in a counterclockwise direction in the Argand diagram as the collision energy increases. Such a manifest phase change is absent in the dissociative attachment process of e+H2-->H+H-. This is attributed to the presence of equally strong, direct, and resonant scattering processes, and to the strong influence of mutually destructive interference.

  20. Near-Forward Rescattering Photoelectron Holography in Strong-Field Ionization: Extraction of the Phase of the Scattering Amplitude

    NASA Astrophysics Data System (ADS)

    Zhou, Yueming; Tolstikhin, Oleg I.; Morishita, Toru

    2016-04-01

    We revisit the concept of near-forward rescattering strong-field photoelectron holography introduced by Y. Huismans et al. [Science 331, 61 (2011)]. The recently developed adiabatic theory is used to show how the phase of the scattering amplitude for near-forward rescattering of an ionized electron by the parent ion is encoded in and can be read out from the corresponding interference pattern in photoelectron momentum distributions (PEMDs) produced in the ionization of atoms and molecules by intense laser pulses. A procedure to extract the phase is proposed. Its application to PEMDs obtained by solving the time-dependent Schrödinger equation for a model atom yields results in good agreement with scattering calculations. This establishes a novel general approach to extracting structural information from strong-field observables capable of providing time-resolved imaging of ultrafast processes.

  1. Elastic electron-atom scattering in amplitude-phase representation with application to electron diffraction and spectroscopy

    NASA Astrophysics Data System (ADS)

    Rundgren, J.

    2007-11-01

    The amplitude-phase representation (APR) [W. E. Milne, Phys. Rev. 35, 863 (1930)] is applied to the relativistic radial Schrödinger equation corresponding to the Dirac equations with central potential. The initial conditions, hitherto unspecified, for the nonlinear second-order amplitude equation at the finite radius of a muffin-tin (MT) sphere are established by a semiconvergent method. This opens the possibility of using APR for the calculation of electron scattering phase shifts with a finite MT radius as well as with a large atomic radius, whereby the first wave node is phase of reference equal to a multiple of π , adding nothing to the phase shifts. Furthermore, APR is used for benchmarking wave functions obtained by ordinary differential equation integration of the Dirac equations up to high energy and high orbital quantum number. The present APR procedure is discussed with reference to earlier numerical methods. To complete the physical picture, the paper ends with a discussion on exchange-correlation dependent scattering potential in MT spheres of optimized radii, a crystal potential model whose dependence on radii and energy dependent inner potential has recently been corroborated by low energy electron diffraction in oxides with many atoms per unit cell.

  2. Elastic electron-atom scattering in amplitude-phase representation with application to electron diffraction and spectroscopy

    SciTech Connect

    Rundgren, J.

    2007-11-15

    The amplitude-phase representation (APR) [W. E. Milne, Phys. Rev. 35, 863 (1930)] is applied to the relativistic radial Schroedinger equation corresponding to the Dirac equations with central potential. The initial conditions, hitherto unspecified, for the nonlinear second-order amplitude equation at the finite radius of a muffin-tin (MT) sphere are established by a semiconvergent method. This opens the possibility of using APR for the calculation of electron scattering phase shifts with a finite MT radius as well as with a large atomic radius, whereby the first wave node is phase of reference equal to a multiple of {pi}, adding nothing to the phase shifts. Furthermore, APR is used for benchmarking wave functions obtained by ordinary differential equation integration of the Dirac equations up to high energy and high orbital quantum number. The present APR procedure is discussed with reference to earlier numerical methods. To complete the physical picture, the paper ends with a discussion on exchange-correlation dependent scattering potential in MT spheres of optimized radii, a crystal potential model whose dependence on radii and energy dependent inner potential has recently been corroborated by low energy electron diffraction in oxides with many atoms per unit cell.

  3. Surface plasmon transmission through discontinuous conducting surfaces: Plasmon amplitude modulation by grazing scattered fields

    NASA Astrophysics Data System (ADS)

    Mayoral-Astorga, L. A.; Gaspar-Armenta, J. A.; Ramos-Mendieta, F.

    2016-04-01

    We have studied numerically the diffraction of a surface plasmon polariton (SPP) when it encounters a wide multi-wavelength slit in conducting films. As a jump process a SPP is excited beyond the slit by wave scattering at the second slit edge. The exciting radiation is produced when the incident SPP collapses at the first slit edge. We have found that the transmitted SPP supports inherent and unavoidable interference with grazing scattered radiation; the spatial modulation extends to the fields in the diffraction region where a series of low intensity spots arises. We demonstrate that the SPP generated on the second slab depends on the frequency but not on the wave vector of the collapsed SPP; a SPP is transmitted even when the two metals forming the slit are different. The numerical results were obtained using the Finite Difference Time Domain (FDTD) method with a grid size λ/100.

  4. Application of amplitude changes of monochromatic scattered light to investigation of dust grain composition

    NASA Astrophysics Data System (ADS)

    Kirkiewicz, Jozef; Chrzanowski, Janusz

    1999-07-01

    The light beam crossing the dust area meets with the loss of energy. We know by experience that the scattering indikatrix depends on the size of the dust particles. The measurement of the light energy scattered into given solid angle enables to identify and specification of the grain composition of the dust particles. Basis on the research a special head has been made to step change of the location of the photodetectors and in result to measure a specific or even desirable dust fraction for the sake of technology. In this paper the graphs of the grain dust distribution are presented with regard to the materials which are transported most frequently by Polish merchant marine.

  5. Integrand reduction of one-loop scattering amplitudes through Laurent series expansion

    NASA Astrophysics Data System (ADS)

    Mastrolia, Pierpaolo; Mirabella, Edoardo; Peraro, Tiziano

    2012-06-01

    We present a semi-analytic method for the integrand reduction of one-loop amplitudes, based on the systematic application of the Laurent expansions to the integrand-decomposition. In the asymptotic limit, the coefficients of the master integrals are the solutions of a diagonal system of equations, properly corrected by counterterms whose parametric form is known a priori. The Laurent expansion of the integrand is implemented through polynomial division. The extension of the integrand-reduction to the case of numerators with rank larger than the number of propagators is discussed as well.

  6. Geometric scaling behavior of the scattering amplitude for DIS with nuclei

    NASA Astrophysics Data System (ADS)

    Kormilitzin, Andrey; Levin, Eugene; Tapia, Sebastian

    2011-12-01

    The main question, that we answer in this paper, is whether the initial condition can influence on the geometric scaling behavior of the amplitude for DIS at high energy. We re-write the non-linear Balitsky-Kovchegov equation in the form which is useful for treating the interaction with nuclei. Using the simplified BFKL kernel, we find the analytical solution to this equation with the initial condition given by the McLerran-Venugopalan formula. This solution does not show the geometric scaling behavior of the amplitude deeply in the saturation region. On the other hand, the BFKL Pomeron calculus with the initial condition at x=1/mR given by the solution to Balitsky-Kovchegov equation, leads to the geometric scaling behavior. The McLerran-Venugopalan formula is the natural initial condition for the Color Glass Condensate (CGC) approach. Therefore, our result gives a possibility to check experimentally which approach: CGC or BFKL Pomeron calculus, is more satisfactory.

  7. Investigating Persistent and Distributed Scatterers to Better Resolve Low Amplitude Deformation with InSAR in Vegetated Terrains

    NASA Astrophysics Data System (ADS)

    Tong, X.; Schmidt, D. A.

    2014-12-01

    Multi-temporal InSAR methods are successful at revealing low amplitude surface deformation by reducing the noise from the atmosphere and the Digital Elevation Model (DEM). The Persistent Scatters (PS) InSAR and Small baseline (SBAS) methods are used widely by the InSAR community. However, it is still challenging to recover low deformation rates in highly vegetated mountainous areas. Our goal is to explore different approaches to identifying PS or stable Distributed Scatterers (DS) for multi-temporal InSAR processing. We are investigating the following methods: 1) amplitude dispersion (Ferretti et al., 2001); 2) average correlation; 3) spatial correlation of phase (Hooper et al., 2004); 4) comparison of phase against a known mathematical model (Shanker and Zebker, 2007); 5) statistical analysis of the coherence matrix (Ferretti et al., 2011); 6) polarimetric bounce characteristics. We first align the SAR images to form a stack of Single Look Complex (SLC) using "batch processing". We work with this 3-dimensional SLC stack to identify high-quality PS and DS using the aforementioned methods. Next we design a filter based on the characteristics of the scatterers to form interferograms. This comparative study on identifying and filtering PS and DS can be integrated with interferogram stacking or time-series approaches like PSInSAR, SBAS or wavelet-based methods. We are working with the ERS-1, ERS-2 and ALOS-1 SAR data to study landslides and volcano deformation over various terrains in the Cascade Range. From these observations we will be able to construct better physical models to explain various deformation processes.

  8. Pion-kaon scattering amplitude constrained with forward dispersion relations up to 1.6 GeV

    NASA Astrophysics Data System (ADS)

    Pelaez, J. R.; Rodas, A.

    2016-04-01

    In this work we provide simple and precise parametrizations of the existing π K scattering data from threshold up to 1.6 GeV, which are constrained to satisfy forward dispersion relations as well as three additional threshold sum rules. We also provide phenomenological values of the threshold parameters and of the resonance poles that appear in elastic scattering.

  9. Broad-band linear polarization in cool stars. II - Amplitude and wavelength dependence for magnetic and scattering regions

    NASA Technical Reports Server (NTRS)

    Saar, Steven H.; Huovelin, Juhani

    1993-01-01

    We have developed a model to estimate the amplitude and wavelength dependence of broad-band linear polarization (BLP) from magnetic regions on cool stars. The model includes corrections both for line blends and for the partial cancellation of polarization in the vector sum over the stellar disk. Our results agree with recent calculations of BLP in the red, but show larger amplitudes and a different wavelength dependence in the blue. We find that the detailed wavelength dependence of the polarization is complex and varies with effective temperature and gravity due to changes in line blanketing. The BLP amplitudes depend strongly on field strength, blanketing, and magnetic region filling factor and geometry. We make rough estimates of the maximum BLP for stars of various spectral types and demonstrate a method for deriving a lower limit to the filling factor from the maximum observed BLP. This lower limit is related to the fractional area covered by the spatially asymmetric component of magnetic regions.

  10. Measurement of the transverse beam spin asymmetry in elastic electron-proton scattering and the inelastic contribution to the imaginary part of the two-photon exchange amplitude.

    PubMed

    Maas, F E; Aulenbacher, K; Baunack, S; Capozza, L; Diefenbach, J; Gläser, B; Imai, Y; Hammel, T; von Harrach, D; Kabuss, E-M; Kothe, R; Lee, J H; Sanchez-Lorente, A; Schilling, E; Schwaab, D; Stephan, G; Weber, G; Weinrich, C; Altarev, I; Arvieux, J; Elyakoubi, M; Frascaria, R; Kunne, R; Morlet, M; Ong, S; Vandewiele, J; Kowalski, S; Suleiman, R; Taylor, S

    2005-03-01

    We report on a measurement of the asymmetry in the scattering of transversely polarized electrons off unpolarized protons, A( perpendicular), at two Q2 values of 0.106 and 0.230 (GeV/c)(2) and a scattering angle of 30 degrees amplitude. There is no obvious reason why this should be different for the real part of the two-photon amplitude, which enters into the radiative corrections for the Rosenbluth separation measurements of the electric form factor of the proton. PMID:15783877

  11. Remarks on the mixed Ramond-Ramond, open string scattering amplitudes of BPS, non-BPS and brane-anti-brane

    NASA Astrophysics Data System (ADS)

    Hatefi, Ehsan

    2015-11-01

    From the world-sheet point of view we compute three, four and five point BPS and non-BPS scattering amplitudes of type IIA and IIB superstring theory. All these mixed S-matrix elements including a Ramond-Ramond closed string (RR) in the bulk and a scalar/gauge or tachyons with all different pictures (including an RR in asymmetric and symmetric pictures) have been carried out. We have also shown that in asymmetric pictures various equations must be kept fixed. More importantly, by direct calculations on the upper half plane, it is realised that some of the equations (which must be true) for BPS branes cannot be necessarily applied to non-BPS amplitudes. We also derive the S-matrix elements of < V_C^{-2} V_{φ }0V _A0 V_T0 rangle and clarify the fact that in the presence of the scalar field and an RR, the terms carrying momentum of an RR in the transverse directions play an important role in the entire form of the S-matrix and their presence is needed in order to have gauge invariance for the entire S-matrix elements of type IIA (IIB) superstring theory.

  12. Mathematical Aspects of Scattering Amplitudes

    NASA Astrophysics Data System (ADS)

    Duhr, Claude

    In these lectures we discuss some of the mathematical structures that appear when computing multi-loop Feynman integrals. We focus on a specific class of special functions, the so-called multiple polylogarithms, and introduce their Hopf algebra structure. We show how these mathematical concepts are useful in physics by illustrating on several examples how these algebraic structures are useful to perform analytic computations of loop integrals, in particular to derive functional equations among polylogarithms.

  13. Off-shell extrapolation of Regge-model NN scattering amplitudes describing final state interactions in 2H(e,e'p)

    DOE PAGESBeta

    Ford, William Paul; van Orden, Wally

    2013-11-25

    In this work, an off-shell extrapolation is proposed for the Regge-model NN amplitudes presented in a paper by Ford and Van Orden [ Phys. Rev. C 87 014004 (2013)] and in an eprint by Ford (arXiv:1310.0871 [nucl-th]). The prescriptions for extrapolating these amplitudes for one nucleon off-shell in the initial state are presented. Application of these amplitudes to calculations of deuteron electrodisintegration are presented and compared to the limited available precision data in the kinematical region covered by the Regge model.

  14. Off-shell extrapolation of Regge-model NN scattering amplitudes describing final state interactions in 2H(e,e'p)

    SciTech Connect

    Ford, William Paul; van Orden, Wally

    2013-11-25

    In this work, an off-shell extrapolation is proposed for the Regge-model NN amplitudes presented in a paper by Ford and Van Orden [ Phys. Rev. C 87 014004 (2013)] and in an eprint by Ford (arXiv:1310.0871 [nucl-th]). The prescriptions for extrapolating these amplitudes for one nucleon off-shell in the initial state are presented. Application of these amplitudes to calculations of deuteron electrodisintegration are presented and compared to the limited available precision data in the kinematical region covered by the Regge model.

  15. {sup 12}C-{sup 12}C elastic scattering at 1.016, 1.449, and 2.4 GeV and the NN amplitude

    SciTech Connect

    Chauhan, Deeksha; Khan, Z. A.

    2007-05-15

    Working within the framework of the Coulomb modified Glauber model, we analyze the elastic angular distribution and reaction cross section for the {sup 12}C-{sup 12}C system at 1.016, 1.449, and 2.4 GeV. The elastic S matrix is evaluated using the effective profile function approach, and a correlation expansion for the Glauber amplitude is obtained. We emphasize the parametrization of the basic (input) NN amplitude, which may be used for a wide range of angles. Retaining the first two terms of the correlation expansion and using the realistic densities for the colliding nuclei, we find that (i) the consideration of higher momentum transfer components, and hence the nondiffractive behavior, of the NN amplitude provides a more satisfactory account of the data than does the conventional (one-term) Gaussian parametrization for the NN amplitude, (ii) the in-medium effects seem to reduce the (free) NN total cross section and influence the other parameters of the NN amplitude as well, (iii) the phase of the NN amplitude does not help in improving the theoretical situation, and (iv) the c.m. correlations play an important role at the energies considered. We also discuss the suitability of the effective profile function approach in the present context.

  16. Off-shell CHY amplitudes

    NASA Astrophysics Data System (ADS)

    Lam, C. S.; Yao, York-Peng

    2016-06-01

    The Cachazo-He-Yuan (CHY) formula for on-shell scattering amplitudes is extended off-shell. The off-shell amplitudes (amputated Green's functions) are Möbius invariant, and have the same momentum poles as the on-shell amplitudes. The working principles which drive the modifications to the scattering equations are mainly Möbius covariance and energy momentum conservation in off-shell kinematics. The same technique is also used to obtain off-shell massive scalars. A simple off-shell extension of the CHY gauge formula which is Möbius invariant is proposed, but its true nature awaits further study.

  17. CHY formula and MHV amplitudes

    NASA Astrophysics Data System (ADS)

    Du, Yi-Jian; Teng, Fei; Wu, Yong-Shi

    2016-05-01

    In this paper, we study the relation between the Cachazo-He-Yuan (CHY) formula and the maximal-helicity-violating (MHV) amplitudes of Yang-Mills and gravity in four dimensions. We prove that only one special rational solution of the scattering equations found by Weinzierl supports the MHV amplitudes. Namely, localized at this solution, the integrated CHY formula produces the Parke-Taylor formula for MHV Yang-Mills amplitudes as well as the Hodges formula for MHV gravitational amplitudes, with an arbitrary number of external gluons/gravitons. This is achieved by developing techniques, in a manifestly Möbius covariant formalism, to explicitly compute relevant reduced Pfaffians/determinants. We observe and prove two interesting properties (or identities), which facilitate the computations. We also check that all the other ( n - 3)! - 1 solutions to the scattering equations do not support the MHV amplitudes, and prove analytically that this is indeed true for the other special rational solution proposed by Weinzierl, that actually supports the anti-MHV amplitudes. Our results reveal a mysterious feature of the CHY formalism that in Yang-Mills and gravity theory, solutions of scattering equations, involving only external momenta, somehow know about the configuration of external polarizations of the scattering amplitudes.

  18. Toward complete pion nucleon amplitudes

    NASA Astrophysics Data System (ADS)

    Mathieu, V.; Danilkin, I. V.; Fernández-Ramírez, C.; Pennington, M. R.; Schott, D.; Szczepaniak, Adam P.; Fox, G.

    2015-10-01

    We compare the low-energy partial-wave analyses of π N scattering with high-energy data via finite-energy sum rules. We construct a new set of amplitudes by matching the imaginary part from the low-energy analysis with the high-energy, Regge parametrization and reconstruct the real parts using dispersion relations.

  19. Toward complete pion nucleon amplitudes

    DOE PAGESBeta

    Mathieu, Vincent; Danilkin, Igor V.; Fernández-Ramírez, Cesar; Pennington, Michael R.; Schott, Diane M.; Szczepaniak, Adam P.; Fox, G.

    2015-10-05

    We compare the low-energy partial wave analyses πN scattering with a high-energy data via finite energy sum rules. We also construct a new set of amplitudes by matching the imaginary part from the low-energy analysis with the high-energy, Regge parametrization and then reconstruct the real parts using dispersion relations.

  20. Positive amplitudes in the amplituhedron

    NASA Astrophysics Data System (ADS)

    Arkani-Hamed, Nima; Hodges, Andrew; Trnka, Jaroslav

    2015-08-01

    The all-loop integrand for scattering amplitudes in planar SYM is determined by an "amplitude form" with logarithmic singularities on the boundary of the amplituhedron. In this note we provide strong evidence for a new striking property of the superamplitude, which we conjecture to be true to all loop orders: the amplitude form is positive when evaluated inside the amplituhedron. The statement is sensibly formulated thanks to the natural "bosonization" of the superamplitude associated with the amplituhedron geometry. However this positivity is not manifest in any of the current approaches to scattering amplitudes, and in particular not in the cellulations of the amplituhedron related to on-shell diagrams and the positive grassmannian. The surprising positivity of the form suggests the existence of a "dual amplituhedron" formulation where this feature would be made obvious. We also suggest that the positivity is associated with an extended picture of amplituhedron geometry, with the amplituhedron sitting inside a co-dimension one surface separating "legal" and "illegal" local singularities of the amplitude. We illustrate this in several simple examples, obtaining new expressions for amplitudes not associated with any triangulations, but following in a more invariant manner from a global view of the positive geometry.

  1. On-Shell Methods in Perturbative QCD

    SciTech Connect

    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.

  2. Connecting physical resonant amplitudes and lattice QCD

    NASA Astrophysics Data System (ADS)

    Bolton, Daniel R.; Briceño, Raúl A.; Wilson, David J.

    2016-06-01

    We present a determination of the isovector, P-wave ππ scattering phase shift obtained by extrapolating recent lattice QCD results from the Hadron Spectrum Collaboration using mπ = 236 MeV. The finite volume spectra are described using extensions of Lüscher's method to determine the infinite volume Unitarized Chiral Perturbation Theory scattering amplitude. We exploit the pion mass dependence of this effective theory to obtain the scattering amplitude at mπ = 140 MeV. The scattering phase shift is found to agree with experiment up to center of mass energies of 1.2 GeV. The analytic continuation of the scattering amplitude to the complex plane yields a ρ-resonance pole at Eρ = [ 755 (2) (1) (20 02) -i/2 129 (3) (1) (7 1) ] MeV. The techniques presented illustrate a possible pathway towards connecting lattice QCD observables of few-body, strongly interacting systems to experimentally accessible quantities.

  3. Connecting physical resonant amplitudes and lattice QCD

    NASA Astrophysics Data System (ADS)

    Bolton, Daniel R.; Briceño, Raúl A.; Wilson, David J.

    2016-06-01

    We present a determination of the isovector, P-wave ππ scattering phase shift obtained by extrapolating recent lattice QCD results from the Hadron Spectrum Collaboration using mπ = 236 MeV. The finite volume spectra are described using extensions of Lüscher's method to determine the infinite volume Unitarized Chiral Perturbation Theory scattering amplitude. We exploit the pion mass dependence of this effective theory to obtain the scattering amplitude at mπ = 140 MeV. The scattering phase shift is found to agree with experiment up to center of mass energies of 1.2 GeV. The analytic continuation of the scattering amplitude to the complex plane yields a ρ-resonance pole at Eρ = [ 755 (2) (1) (20 -i/2 129 (3) (1) 7 1) ] MeV. The techniques presented illustrate a possible pathway towards connecting lattice QCD observables of few-body, strongly interacting systems to experimentally accessible quantities.

  4. OPE for all helicity amplitudes

    NASA Astrophysics Data System (ADS)

    Basso, Benjamin; Caetano, João; Córdova, Lucía; Sever, Amit; Vieira, Pedro

    2015-08-01

    We extend the Operator Product Expansion (OPE) for scattering amplitudes in planar SYM to account for all possible helicities of the external states. This is done by constructing a simple map between helicity configurations and so-called charged pentagon transitions. These OPE building blocks are generalizations of the bosonic pentagons entering MHV amplitudes and they can be bootstrapped at finite coupling from the integrable dynamics of the color flux tube. A byproduct of our map is a simple realization of parity in the super Wilson loop picture.

  5. Constraining higher derivative supergravity with scattering amplitudes

    SciTech Connect

    Wang, Yifan; Yin, Xi

    2015-08-31

    We study supersymmetry constraints on higher derivative deformations of type IIB supergravity by consideration of superamplitudes. Thus, combining constraints of on-shell supervertices and basic results from string perturbation theory, we give a simple argument for the non-renormalization theorem of Green and Sethi, and some of its generalizations.

  6. DVCS amplitude with kinematical twist-3 terms

    SciTech Connect

    Radyushkin, A.V.; Weiss, C.

    2000-08-01

    The authors compute the amplitude of deeply virtual Compton scattering (DVCS) using the calculus of QCD string operators in coordinate representation. To restore the electromagnetic gauge invariance (transversality) of the twist-2 amplitude they include the operators of twist-3 which appear as total derivatives of twist-2 operators. The results are equivalent to a Wandzura-Wilczek approximation for twist-3 skewed parton distributions. They find that this approximation gives a finite result for the amplitude of a longitudinally polarized virtual photon, while the amplitude for transverse polarization is divergent, i.e., factorization breaks down in this term.

  7. Scattering theory for arbitrary potentials

    SciTech Connect

    Kadyrov, A.S.; Bray, I.; Stelbovics, A.T.; Mukhamedzhanov, A.M.

    2005-09-15

    The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. Definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a Coulomb tail are presented. It is shown that for the Coulomb potential the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure.

  8. Phase variation of hadronic amplitudes

    SciTech Connect

    Dedonder, J.-P.; Gibbs, W. R.; Nuseirat, Mutazz

    2008-04-15

    The phase variation with angle of hadronic amplitudes is studied with a view to understanding the underlying physical quantities that control it and how well it can be determined in free space. We find that unitarity forces a moderately accurate determination of the phase in standard amplitude analyses but that the nucleon-nucleon analyses done to date do not give the phase variation needed to achieve a good representation of the data in multiple scattering calculations. Models are examined that suggest its behavior near forward angles is related to the radii of the real and absorptive parts of the interaction. The dependence of this phase on model parameters is such that if these radii are modified in the nuclear medium (in combination with the change due to the shift in energy of the effective amplitude in the medium) then the larger magnitudes of the phase needed to fit the data might be attainable but only for negative values of the phase variation parameter.

  9. Relations between closed string amplitudes at higher-order tree level and open string amplitudes

    NASA Astrophysics Data System (ADS)

    Chen, Yi-Xin; Du, Yi-Jian; Ma, Qian

    2010-01-01

    KLT relations almost factorize closed string amplitudes on S by two open string tree amplitudes which correspond to the left- and the right-moving sectors. In this paper, we investigate string amplitudes on D and RP. We find that KLT factorization relations do not hold in these two cases. The relations between closed and open string amplitudes have new forms. On D and RP, the left- and the right-moving sectors are connected into a single sector. Then an amplitude with closed strings on D or RP can be given by one open string tree amplitude except for a phase factor. The relations depends on the topologies of the world-sheets. Under T-duality, the relations on D and RP give the amplitudes between closed strings scattering from D-brane and O-plane respectively by open string partial amplitudes. In the low energy limits of these two cases, the factorization relations for graviton amplitudes do not hold. The amplitudes for gravitons must be given by the new relations instead.

  10. PULSE AMPLITUDE ANALYSERS

    DOEpatents

    Lewis, I.A.D.

    1956-05-15

    This patent pentains to an electrical pulse amplitude analyzer, capable of accepting input pulses having a separation between adjacent pulses in the order of one microsecond while providing a large number of channels of classification. In its broad aspect the described pulse amplitude analyzer utilizes a storage cathode ray tube und control circuitry whereby the amplitude of the analyzed pulses controls both the intensity and vertical defiection of the beam to charge particular spots in horizontal sectors of the tube face as the beam is moved horizontally across the tube face. As soon as the beam has swept the length of the tube the information stored therein is read out by scanning individually each horizontal sector corresponding to a certain range of pulse amplitudes and applying the output signal from each scan to separate indicating means.

  11. PULSE AMPLITUDE ANALYZER

    DOEpatents

    Greenblatt, M.H.

    1958-03-25

    This patent pertains to pulse amplitude analyzers for sorting and counting a serles of pulses, and specifically discloses an analyzer which ls simple in construction and presents the puise height distribution visually on an oscilloscope screen. According to the invention, the pulses are applied to the vertical deflection plates of an oscilloscope and trigger the horizontal sweep. Each pulse starts at the same point on the screen and has a maximum amplitude substantially along the same vertical line. A mask is placed over the screen except for a slot running along the line where the maximum amplitudes of the pulses appear. After the slot has been scanned by a photocell in combination with a slotted rotating disk, the photocell signal is displayed on an auxiliary oscilloscope as vertical deflection along a horizontal time base to portray the pulse amplitude distribution.

  12. Large-N QCD and the Veneziano amplitude

    NASA Astrophysics Data System (ADS)

    Armoni, Adi

    2016-05-01

    We consider four scalar mesons scattering in large-Nc QCD. Using the worldline formalism we show that the scattering amplitude can be written as a formal sum over Wilson loops. The AdS/CFT correspondence maps this sum into a sum over string worldsheets in a confining background. We then argue that for well separated mesons the sum is dominated by flat space configurations. Under additional assumptions about the dual string path integral we obtain the Veneziano amplitude.

  13. Amplitudes in N = 4 Super-Yang-Mills Theory

    NASA Astrophysics Data System (ADS)

    Spradlin, Marcus

    These lecture notes provide a lightning introduction to some aspects of scattering amplitudes in maximally supersymmetric theory, aimed at the audience of students attending the 2014 TASI summer school "Journeys Through the Precision Frontier: Amplitudes for Colliders". Emphasis is placed on explaining modern terminology so that students needing to delve further may more easily access the available literature.

  14. Amplitudes and Ultraviolet Behavior of N = 8 Supergravity

    SciTech Connect

    Bern, Zvi; Carrasco, John Joseph; Dixon, Lance J.; Johansson, Henrik; Roiban, Radu; /Penn State U.

    2011-05-20

    In this contribution we describe computational tools that permit the evaluation of multi-loop scattering amplitudes in N = 8 supergravity, in terms of amplitudes in N = 4 super-Yang-Mills theory. We also discuss the remarkable ultraviolet behavior of N = 8 supergravity, which follows from these amplitudes, and is as good as that of N = 4 super-Yang-Mills theory through at least four loops.

  15. Reinforcing Saccadic Amplitude Variability

    ERIC Educational Resources Information Center

    Paeye, Celine; Madelain, Laurent

    2011-01-01

    Saccadic endpoint variability is often viewed as the outcome of neural noise occurring during sensorimotor processing. However, part of this variability might result from operant learning. We tested this hypothesis by reinforcing dispersions of saccadic amplitude distributions, while maintaining constant their medians. In a first experiment we…

  16. Subleading soft factor for string disk amplitudes

    NASA Astrophysics Data System (ADS)

    Schwab, Burkhard U. W.

    2014-08-01

    We investigate the behavior of superstring disk scattering amplitudes in the presence of a soft external momentum at finite string tension. We prove that there are no α'-corrections to the field theory form of the subleading soft factor S (1). At the end of this work, we also comment on the possibility to find the corresponding subleading soft factors in closed string theory using our result and the KLT relations.

  17. Amplitude Modulator Chassis

    SciTech Connect

    Erbert, G

    2009-09-01

    The Amplitude Modulator Chassis (AMC) is the final component in the MOR system and connects directly to the PAM input through a 100-meter fiber. The 48 AMCs temporally shape the 48 outputs of the MOR using an arbitrary waveform generator coupled to an amplitude modulator. The amplitude modulation element is a two stage, Lithium Niobate waveguide device, where the intensity of the light passing through the device is a function of the electrical drive applied. The first stage of the modulator is connected to a programmable high performance Arbitrary Waveform Generator (AWG) consisting of 140 impulse generators space 250 ps apart. An arbitrary waveform is generated by independently varying the amplitude of each impulse generator and then summing the impulses together. In addition to the AWG a short pulse generator is also connected to the first stage of the modulator to provide a sub 100-ps pulse used for timing experiments. The second stage of the modulator is connect to a square pulse generator used to further attenuate any pre or post pulse light passing through the first stage of the modulator. The fast rise and fall time of the square pulse generator is also used to produce fast rise and fall times of the AWG by clipping the AWG pulse. For maximum extinction, a pulse bias voltage is applied to each stage of the modulator. A pulse voltage is applied as opposed to a DC voltage to prevent charge buildup on the modulator. Each bias voltage is adjustable to provide a minimum of 50-dB extinction. The AMC is controlled through ICCS to generate the desired temporal pulse shape. This process involves a closed-loop control algorithm, which compares the desired temporal waveform to the produced optical pulse, and iterates the programming of the AWG until the two waveforms agree within an allowable tolerance.

  18. China Amplitude Tomography

    NASA Astrophysics Data System (ADS)

    Hearn, T. M.

    2014-12-01

    Modern data from the China Bulletin and temporary network deployments has been used to update amplitude tomography using ML and MS seismic amplitudes. This work builds on the results of Hearn et al., 2008. ML attenuation estimates are much better resolved due to the inclusion of subnet data. We find that the trade-off between geometrical spreading and attenuation estimates are well constrained; however, both of these parameters have significant trade-off with the frequency dependence of attenuation. Maps of attenuation using the ML amplitudes are similar to those of Lg attenuation found by other authors suggesting that ML attenuation estimates form a suitable proxy for Lg attenuation estimates. We are now able to associate high attenuation directly with the Longmen Shan and the Qilian Shan mountains and also, where resolved, with the Kunlun Shan, Altyn Tag, and Tian Shan mountains. Grabens around the Ordos Platform also show high attenuation. Basins, however, do not in general show high attenuation. The main exception to this is the Bohai Basin. We conclude that the ML waveforms, like the Lg waveforms, interrogate the entire crustal column and are most sensitive to tectonically active structures and rapid changes in crustal structure. Data from MS data do not include subnet readings and do not have the resolution that was obtained with the ML data. Nonetheless, features are similar with the exception that basins appear more highly attenuative.

  19. PULSE AMPLITUDE ANALYZER

    DOEpatents

    Gray, G.W.; Jensen, A.S.

    1957-10-22

    A pulse-height analyzer system of improved design for sorting and counting a series of pulses, such as provided by a scintillation detector in nuclear radiation measurements, is described. The analyzer comprises a main transmission line, a cathode-ray tube for each section of the line with its deflection plates acting as the line capacitance; means to bias the respective cathode ray tubes so that the beam strikes a target only when a prearranged pulse amplitude is applied, with each tube progressively biased to respond to smaller amplitudes; pulse generating and counting means associated with each tube to respond when the beam is deflected; a control transmission line having the same time constant as the first line per section with pulse generating means for each tube for initiating a pulse on the second transmission line when a pulse triggers the tube of corresponding amplitude response, the former pulse acting to prevent successive tubes from responding to the pulse under test. This arrangement permits greater deflection sensitivity in the cathode ray tube and overcomes many of the disadvantages of prior art pulse-height analyzer circuits.

  20. Kaon-nucleus scattering

    NASA Technical Reports Server (NTRS)

    Hong, Byungsik; Maung, Khin Maung; Wilson, John W.; Buck, Warren W.

    1989-01-01

    The derivations of the Lippmann-Schwinger equation and Watson multiple scattering are given. A simple optical potential is found to be the first term of that series. The number density distribution models of the nucleus, harmonic well, and Woods-Saxon are used without t-matrix taken from the scattering experiments. The parameterized two-body inputs, which are kaon-nucleon total cross sections, elastic slope parameters, and the ratio of the real to the imaginary part of the forward elastic scattering amplitude, are presented. The eikonal approximation was chosen as our solution method to estimate the total and absorptive cross sections for the kaon-nucleus scattering.

  1. Remarks on the identities of gluon tree amplitudes

    NASA Astrophysics Data System (ADS)

    Tye, S.-H. Henry; Zhang, Yang

    2010-10-01

    Recently, Bjerrum-Bohr, Damgaard, Feng, and Sondergaard derived a set of new interesting quadratic identities of the Yang-Mills (YM) tree scattering amplitudes, besides Bern-Carrasco-Johansson (BCJ) identities. Here we comment that these quadratic identities of YM amplitudes actually follow directly from the KLT (Kawai-Lewellen-Tye) relation for graviton-dilaton-axion scattering amplitudes (in four-dimensional spacetime). This clarifies their physical origin and also provides a simpler version of the new identities. We also comment that the recently discovered BCJ identities of YM helicity amplitudes, at least for the maximal helicity-violating case, can be verified by using (repeatedly) the Schouten identity. We also point out additional quadratic identities that can be written down from the KLT relations.

  2. Particle Distribution Modification by Low Amplitude Modes

    SciTech Connect

    White, R. B.; Gorelenkov, N.; Heidbrink, W. W.; Van Zeeland, M. A.

    2009-08-28

    Modification of a high energy particle distribution by a spectrum of low amplitude modes is investigated using a guiding center code. Only through resonance are modes effective in modifying the distribution. Diagnostics are used to illustrate the mode-particle interaction and to find which effects are relevant in producing significant resonance, including kinetic Poincare plots and plots showing those orbits with time averaged mode-particle energy transfer. Effects of pitch angle scattering and drag are studied, as well as plasma rotation and time dependence of the equilibrium and mode frequencies. A specific example of changes observed in a DIII-D deuterium beam distribution in the presence of low amplitude experimentally validated Toroidal Alfven (TAE) eigenmodes and Reversed Shear Alfven (RSAE) eigenmodes is examined in detail. Comparison with experimental data shows that multiple low amplitude modes can account for significant modification of high energy beam particle distributions. It is found that there is a stochastic threshold for beam profile modification, and that the experimental amplitudes are only slightly above this threshold.

  3. Delbrück amplitudes: new calculations

    NASA Astrophysics Data System (ADS)

    Kahane, Sylvian

    1992-06-01

    Calculations of the first-order Delbrück scattering amplitudes were parallelized in a medium-grain mode assuring a very efficient, equal-load implementation, on systems with a moderate number of processors. New numerical values were calculated in the energy range 7.92-28 MeV and in the angular range 0.001°-120° with an estimated accuracy of as good as 1%. The old tables of Bar-Noy and Kahane are improved by these new calculations especially the values of Re A+- amplitudes. Good agreement is found with the calculations of Turrini, Maino and Ventura with a smoother behaviour of the present values. The calculations were performed on a system of eight transputers.

  4. An algebraic approach to the scattering equations

    NASA Astrophysics Data System (ADS)

    Huang, Rijun; Rao, Junjie; Feng, Bo; He, Yang-Hui

    2015-12-01

    We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.

  5. PULSE AMPLITUDE DISTRIBUTION RECORDER

    DOEpatents

    Cowper, G.

    1958-08-12

    A device is described for automatica1ly recording pulse annplitude distribution received from a counter. The novelty of the device consists of the over-all arrangement of conventional circuit elements to provide an easy to read permanent record of the pulse amplitude distribution during a certain time period. In the device a pulse analyzer separates the pulses according to annplitude into several channels. A scaler in each channel counts the pulses and operates a pen marker positioned over a drivable recorder sheet. Since the scalers in each channel have the sanne capacity, the control circuitry permits counting of the incoming pulses until one scaler reaches capacity, whereupon the input is removed and an internal oscillator supplies the necessary pulses to fill up the other scalers. Movement of the chart sheet is initiated wben the first scaler reaches capacity to thereby give a series of marks at spacings proportional to the time required to fill the remaining scalers, and accessory equipment marks calibration points on the recorder sheet to facilitate direct reading of the number of external pulses supplied to each scaler.

  6. Tree-level amplitudes in the nonlinear sigma model

    NASA Astrophysics Data System (ADS)

    Kampf, Karol; Novotný, Jirí; Trnka, Jaroslav

    2013-05-01

    We study in detail the general structure and further properties of the tree-level amplitudes in the SU( N) nonlinear sigma model. We construct the flavor-ordered Feynman rules for various parameterizations of the SU( N) fields U ( x), write down the Berends-Giele relations for the semi-on-shell currents and discuss their efficiency for the amplitude calculation in comparison with those of renormalizable theories. We also present an explicit form of the partial amplitudes up to ten external particles. It is well known that the standard BCFW recursive relations cannot be used for reconstruction of the the on-shell amplitudes of effective theories like the SU( N) nonlinear sigma model because of the inappropriate behavior of the deformed on-shell amplitudes at infinity. We discuss possible generalization of the BCFW approach introducing "BCFW formula with subtractions" and with help of Berends-Giele relations we prove particular scaling properties of the semi-on-shell amplitudes of the SU( N) nonlinear sigma model under specific shifts of the external momenta. These results allow us to define alternative deformation of the semi-on-shell amplitudes and derive BCFW-like recursion relations. These provide a systematic and effective tool for calculation of Goldstone bosons scattering amplitudes and it also shows the possible applicability of on-shell methods to effective field theories. We also use these BCFW-like relations for the investigation of the Adler zeroes and double soft limit of the semi-on-shell amplitudes.

  7. On the Period-Amplitude and Amplitude-Period Relationships

    NASA Technical Reports Server (NTRS)

    Wilson, Robert M.; Hathaway, David H.

    2008-01-01

    Examined are Period-Amplitude and Amplitude-Period relationships based on the cyclic behavior of the 12-month moving averages of monthly mean sunspot numbers for cycles 0.23, both in terms of Fisher's exact tests for 2x2 contingency tables and linear regression analyses. Concerning the Period-Amplitude relationship (same cycle), because cycle 23's maximum amplitude is known to be 120.8, the inferred regressions (90-percent prediction intervals) suggest that its period will be 131 +/- 24 months (using all cycles) or 131 +/- 18 months (ignoring cycles 2 and 4, which have the extremes of period, 108 and 164 months, respectively). Because cycle 23 has already persisted for 142 months (May 1996 through February 2008), based on the latter prediction, it should end before September 2008. Concerning the Amplitude-Period relationship (following cycle maximum amplitude versus preceding cycle period), because cycle 23's period is known to be at least 142 months, the inferred regressions (90-percent prediction intervals) suggest that cycle 24's maximum amplitude will be about less than or equal to 96.1 +/- 55.0 (using all cycle pairs) or less than or equal to 91.0 +/- 36.7 (ignoring statistical outlier cycle pairs). Hence, cycle 24's maximum amplitude is expected to be less than 151, perhaps even less than 128, unless cycle pair 23/24 proves to be a statistical outlier.

  8. Weak Deeply Virtual Compton Scattering

    SciTech Connect

    Ales Psaker; Wolodymyr Melnitchouk; Anatoly Radyushkin

    2007-03-01

    We extend the analysis of the deeply virtual Compton scattering process to the weak interaction sector in the generalized Bjorken limit. The virtual Compton scattering amplitudes for the weak neutral and charged currents are calculated at the leading twist within the framework of the nonlocal light-cone expansion via coordinate space QCD string operators. Using a simple model, we estimate cross sections for neutrino scattering off the nucleon, relevant for future high intensity neutrino beam facilities.

  9. Λ scattering equations

    NASA Astrophysics Data System (ADS)

    Gomez, Humberto

    2016-06-01

    The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.

  10. Planar-transverse amplitude-phase pattern in nonelastic reactions

    NASA Astrophysics Data System (ADS)

    Arash, Firooz; Moravcsik, Michael J.; Goldstein, Gary R.; Bugg, David V.

    1989-01-01

    The first evidence is presented that the phase pattern of the planar-transverse optimal reaction amplitudes found previously for elastic-scattering strong-interaction reactions also holds for nonelastic reactions. The pattern is observed in the reaction p+p-->d+π in the energy range between 300 and 800 MeV.

  11. Eikonal Scattering at Strong Coupling

    NASA Astrophysics Data System (ADS)

    Irizarry-Gelpi, Melvin Eloy

    The scattering of subatomic particles is a source of important physical phenomena. Decades of work have yielded many techniques for the computation of scattering amplitudes. Most of these techniques involve perturbative quantum field theory and thus apply only at weak coupling. Complementary to scattering is the formation of bound states, which are intrinsically nonperturbative. Regge theory arose in the late 1950s as an attempt to describe, with a single framework, both scattering and the formation of bound states. In Regge theory one obtains an amplitude with bound state poles after analytic continuation of a nonperturbative scattering amplitude, corresponding to a sum of an infinite number of Feynman diagrams at large energy and fixed momentum transfer (but with crossed kinematics). Thus, in order to obtain bound states at fixed energy, one computes an amplitude at large momentum transfer. In this dissertation we calculate amplitudes with bound states in the regime of fixed energy and small momentum transfer. We formulate the elastic scattering problem in terms of many-body path integrals, familiar from quantum mechanics. Then we invoke the semiclassical JWKB approximation, where the path integral is dominated by classical paths. The dynamics in the semiclassical regime are strongly coupled, as found by Halpern and Siegel. When the momentum transfer is small, the classical paths are simple straight lines and the resulting semiclassical amplitudes display a spectrum of bound states that agrees with the spectrum found by solving wave equations with potentials. In this work we study the bound states of matter particles with various types of interactions, including electromagnetic and gravitational interactions. Our work has many analogies with the work started by Alday and Maldacena, who computed scattering amplitudes of gluons at strong coupling with semiclassical quantum mechanics of strings in anti de-Sitter spacetime. We hope that in the future we can apply our

  12. Substorm statistics: Occurrences and amplitudes

    SciTech Connect

    Borovsky, J.E.; Nemzek, R.J.

    1994-05-01

    The occurrences and amplitudes of substorms are statistically investigated with the use of three data sets: the AL index, the Los Alamos 3-satellite geosynchronous energetic-electron measurements, and the GOES-5 and -6 geosynchronous magnetic-field measurements. The investigation utilizes {approximately} 13,800 substorms in AL, {approximately} 1400 substorms in the energetic-electron flux, and {approximately} 100 substorms in the magnetic field. The rate of occurrence of substorms is determined as a function of the time of day, the time of year, the amount of magnetotail bending, the orientation of the geomagnetic dipole, the toward/away configuration of the IMF, and the parameters of the solar wind. The relative roles of dayside reconnection and viscous coupling in the production of substorms are assessed. Three amplitudes are defined for a substorms: the jump in the AL index, the peak of the >30-keV integral electron flux at geosynchronous orbit near midnight, and the angle of rotation of the geosynchronous magnetic field near midnight. The substorm amplitudes are statistically analyzed, the amplitude measurements are cross correlated with each other, and the substorm amplitudes are determined as functions of the solar-wind parameters. Periodically occurring and randomly occurring substorms are analyzed separately. The energetic-particle-flux amplitudes are consistent with unloading and the AL amplitudes are consistent with direct driving plus unloading.

  13. Some tree-level string amplitudes in the NSR formalism

    NASA Astrophysics Data System (ADS)

    Becker, Katrin; Becker, Melanie; Melnikov, Ilarion V.; Robbins, Daniel; Royston, Andrew B.

    2015-12-01

    We calculate tree level scattering amplitudes for open strings using the NSR formalism. We present a streamlined symmetry-based and pedagogical approach to the computations, which we first develop by checking two-, three-, and four-point functions involving bosons and fermions. We calculate the five-point amplitude for massless gluons and find agreement with an earlier result by Brandt, Machado and Medina. We then compute the five-point amplitudes involving two and four fermions respectively, the general form of which has not been previously obtained in the NSR formalism. The results nicely confirm expectations from the supersymmetric F 4 effective action. Finally we use the prescription of Kawai, Lewellen and Tye (KLT) to compute the amplitudes for the closed string sector.

  14. N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops

    SciTech Connect

    Boucher-Veronneau, C.; Dixon, L.J.; /SLAC

    2012-02-15

    We present the full two-loop four-graviton amplitudes in N = 4, 5, 6 supergravity. These results were obtained using the double-copy structure of gravity, which follows from the recently conjectured color-kinematics duality in gauge theory. The two-loop four-gluon scattering amplitudes in N = 0, 1, 2 supersymmetric gauge theory are a second essential ingredient. The gravity amplitudes have the expected infrared behavior: the two-loop divergences are given in terms of the squares of the corresponding one-loop amplitudes. The finite remainders are presented in a compact form. The finite remainder for N = 8 supergravity is also presented, in a form that utilizes a pure function with a very simple symbol.

  15. Measurement of the light-field amplitude-correlation function through joint photon-count distributions.

    NASA Technical Reports Server (NTRS)

    Furcinitti, P.; Kuppenheimer, J. D.; Narducci, L. M.; Tuft , R. A.

    1972-01-01

    When an amplitude-stabilized He-Ne laser beam is scattered by a rotating ground glass with small surface inhomogeneities, the probability density of the instantaneous scattered-wave amplitude is Gaussian. In this paper, we suggest the use of the joint photon-count probability distribution to measure the absolute value of the electric-field amplitude-correlation function for random Gaussian light fields, and report the results of an experiment in which the Gaussian field is produced by scattering a light beam through a rotating ground glass. This procedure offers an alternative to other conventional methods, such as self-beating spectroscopy and irradiance-correlation techniques. The correlation time of the scattered-field amplitude in the present experiment has been measured with an accuracy of approximately 0.8%.

  16. Amplitude path corrections for regional phases in China

    SciTech Connect

    Phillips, W.S.; Velasco, A.A.; Taylor, S.R.; Randall, G.E.

    1998-12-31

    The authors investigate the effectiveness of amplitude path corrections for regional phases on seismic event discrimination and magnitude estimation. Waveform data from digital stations in China for regional, shallow (< 50 km) events were obtained from the IRIS Data Management Center (DMC) for years 1986 to 1996 using the USGS Preliminary Determination of Epicenters (PDE) and the Chinese State Seismological Bureau (SSB) catalogs. For each event, the amplitudes for each regional phase (P{sub n}, P{sub g}, S{sub n}, L{sub g}) were measured, as well as the P{sub g} and L{sub g} coda. Measured amplitudes were corrected for source scaling using estimates of m{sub b} and for distance using a power law that accounts for attenuation and spreading. The amplitude residuals were interpolated and mapped as 2-D amplitude correction surfaces. The authors employ several methods to create the amplitude correction surfaces: a waveguide method, and two interpolation methods (Baysian kriging and a circular moving window mean smoother). They explore the sensitivities of the surfaces to the method and to regional propagation, and apply these surfaces to correct amplitude data to reduce scatter in discrimination ratios and magnitude estimates.

  17. Helicity Amplitudes for Photoproduction of Baryons with J = 1/2 and JP = 3/2+

    NASA Astrophysics Data System (ADS)

    Liu, Lei-Hua

    2015-12-01

    We derive the separate helicity amplitudes using the partial wave analysis in the process of pseudo-scalar meson photoproduction. For JP = 3/2+, we find the amplitude is model independent. According to parity conservation, the general amplitude in the case of JP = 1/2- is obtained. We prove this general amplitude corresponds to the situation of λ = -1 when adopting the circular polarization. Finally, the formulas of scattering amplitudes involving the meson photoproduction with JP = 3/2+ are obtained from the chiral quark model. Supported by the Chinese Scholarship Council (CSC)

  18. Scalar scattering via conformal higher spin exchange

    NASA Astrophysics Data System (ADS)

    Joung, Euihun; Nakach, Simon; Tseytlin, Arkady A.

    2016-02-01

    Theories containing infinite number of higher spin fields require a particular definition of summation over spins consistent with their underlying symmetries. We consider a model of massless scalars interacting (via bilinear conserved currents) with conformal higher spin fields in flat space. We compute the tree-level four-scalar scattering amplitude using a natural prescription for summation over an infinite set of conformal higher spin exchanges and find that it vanishes. Independently, we show that the vanishing of the scalar scattering amplitude is, in fact, implied by the global conformal higher spin symmetry of this model. We also discuss one-loop corrections to the four-scalar scattering amplitude.

  19. One-loop corrections from higher dimensional tree amplitudes

    NASA Astrophysics Data System (ADS)

    Cachazo, Freddy; He, Song; Yuan, Ellis Ye

    2016-08-01

    We show how one-loop corrections to scattering amplitudes of scalars and gauge bosons can be obtained from tree amplitudes in one higher dimension. Starting with a complete tree-level scattering amplitude of n + 2 particles in five dimensions, one assumes that two of them cannot be "detected" and therefore an integration over their LIPS is carried out. The resulting object, function of the remaining n particles, is taken to be four-dimensional by restricting the corresponding momenta. We perform this procedure in the context of the tree-level CHY formulation of amplitudes. The scattering equations obtained in the procedure coincide with those derived by Geyer et al. from ambitwistor constructions and recently studied by two of the authors for bi-adjoint scalars. They have two sectors of solutions: regular and singular. We prove that the contribution from regular solutions generically gives rise to unphysical poles. However, using a BCFW argument we prove that the unphysical contributions are always homogeneous functions of the loop momentum and can be discarded. We also show that the contribution from singular solutions turns out to be homogeneous as well.

  20. Amplitude and phase modulation with waveguide optics

    SciTech Connect

    Burkhart, S.C.; Wilcox, R.B.; Browning, D.; Penko, F.A.

    1996-12-17

    We have developed amplitude and phase modulation systems for glass lasers using integrated electro-optic modulators and solid state high- speed electronics. The present and future generation of lasers for Inertial Confinement Fusion require laser beams with complex temporal and phase shaping to compensate for laser gain saturation, mitigate parametric processes such as transverse stimulated Brillouin scattering in optics, and to provide specialized drive to the fusion targets. These functions can be performed using bulk optoelectronic modulators, however using high-speed electronics to drive low voltage integrated optical modulators has many practical advantages. In particular, we utilize microwave GaAs transistors to perform precision, 250 ps resolution temporal shaping. Optical bandwidth is generated using a microwave oscillator at 3 GHz amplified by a solid state amplifier. This drives an integrated electrooptic modulator to achieve laser bandwidths exceeding 30 GHz.

  1. Rayleigh Scattering.

    ERIC Educational Resources Information Center

    Young, Andrew T.

    1982-01-01

    The correct usage of such terminology as "Rayleigh scattering,""Rayleigh lines,""Raman lines," and "Tyndall scattering" is resolved during an historical excursion through the physics of light-scattering by gas molecules. (Author/JN)

  2. 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.

  3. Scattering equations and global duality of residues

    NASA Astrophysics Data System (ADS)

    Søgaard, Mads; Zhang, Yang

    2016-05-01

    We examine the polynomial form of the scattering equations by means of computational algebraic geometry. The scattering equations are the backbone of the Cachazo-He-Yuan (CHY) representation of the S-matrix. We explain how the Bezoutian matrix facilitates the calculation of amplitudes in the CHY formalism, without explicitly solving the scattering equations or summing over the individual residues. Since for n -particle scattering the size of the Bezoutian matrix grows only as (n -3 )×(n -3 ), our algorithm is very efficient for analytic and numeric amplitude computations.

  4. Shape of Pion Distribution Amplitude

    SciTech Connect

    Radyushkin, Anatoly

    2009-11-01

    A scenario is investigated in which the leading-twist pion distribution amplitude $\\varphi_\\pi (x)$ is approximated by the pion decay constant $f_\\pi$ for all essential values of the light-cone fraction $x$. A model for the light-front wave function $\\Psi (x, k_\\perp)$ is proposed that produces such a distribution amplitude and has a rapidly decreasing (exponential for definiteness) dependence on the light-front energy combination $ k_\\perp^2/x(1-x)$. It is shown that this model easily reproduces the fit of recent large-$Q^2$ BaBar data on the photon-pion transition form factor. Some aspects of scenario with flat pion distribution amplitude are discussed.

  5. Phase coherence and pairing amplitude in photo-excited superconductors

    NASA Astrophysics Data System (ADS)

    Perfetti, Luca; Piovera, Christian; Zhang, Zailan

    2016-05-01

    New data on Bi2Sr2CaCu2O8+δ (Bi2212) reveal interesting aspects of photoexcited superconductors. The electrons dynamics show that inelastic scattering by nodal quasiparticles decreases when the temperature is lowered below the critical value of the superconducting phase transition. This drop of electronic dissipation is astonishingly robust and survives to photoexcitation densities much larger than the value sustained by long-range superconductivity. The unconventional behavior of quasiparticle scattering is ascribed to superconducting correlations extending on a length scale comparable to the inelastic mean-free path. Our measurements indicate that strongly driven superconductors enter in a regime without phase coherence but finite pairing amplitude.

  6. An Analysis of Fundamental Mode Surface Wave Amplitude Measurements

    NASA Astrophysics Data System (ADS)

    Schardong, L.; Ferreira, A. M.; van Heijst, H. J.; Ritsema, J.

    2014-12-01

    Seismic tomography is a powerful tool to decipher the Earth's interior structure at various scales. Traveltimes of seismic waves are widely used to build velocity models, whereas amplitudes are still only seldomly accounted for. This mainly results from our limited ability to separate the various physical effects responsible for observed amplitude variations, such as focussing/defocussing, scattering and source effects. We present new measurements from 50 global earthquakes of fundamental-mode Rayleigh and Love wave amplitude anomalies measured in the period range 35-275 seconds using two different schemes: (i) a standard time-domain amplitude power ratio technique; and (ii) a mode-branch stripping scheme. For minor-arc data, we observe amplitude anomalies with respect to PREM in the range of 0-4, for which the two measurement techniques show a very good overall agreement. We present here a statistical analysis and comparison of these datasets, as well as comparisons with theoretical calculations for a variety of 3-D Earth models. We assess the geographical coherency of the measurements, and investigate the impact of source, path and receiver effects on surface wave amplitudes, as well as their variations with frequency in a wider range than previously studied.

  7. Amplitude relations in non-linear sigma model

    NASA Astrophysics Data System (ADS)

    Chen, Gang; Du, Yi-Jian

    2014-01-01

    In this paper, we investigate tree-level scattering amplitude relations in U( N) non-linear sigma model. We use Cayley parametrization. As was shown in the recent works [23,24], both on-shell amplitudes and off-shell currents with odd points have to vanish under Cayley parametrization. We prove the off-shell U(1) identity and fundamental BCJ relation for even-point currents. By taking the on-shell limits of the off-shell relations, we show that the color-ordered tree amplitudes with even points satisfy U(1)-decoupling identity and fundamental BCJ relation, which have the same formations within Yang-Mills theory. We further state that all the on-shell general KK, BCJ relations as well as the minimal-basis expansion are also satisfied by color-ordered tree amplitudes. As a consequence of the relations among color-ordered amplitudes, the total 2 m-point tree amplitudes satisfy DDM form of color decomposition as well as KLT relation.

  8. K- nuclear potentials based on chiral meson-baryon amplitudes

    NASA Astrophysics Data System (ADS)

    Mareš, J.; Cieplý, A.; Gazda, D.; Friedman, E.; Gal, A.

    2012-09-01

    K- nuclear optical potentials are constructed from in-medium subthreshold K¯N scattering amplitudes within a chirally motivated coupled-channel model. We demonstrate how the strong energy and density dependence of the scattering amplitudes at and below threshold leads to a deep K- nuclear potential VK- for kaonic atoms and K- nuclear quasibound states. Selfconsistent evaluations yield K- potential depths -ReVK- (ρ0) of order 100 MeV. Allowing for K- NN absorption, better agreement with K- atoms data is achieved, leading to increased potential depths, -ReVK- (ρ0) ˜ 175 MeV, in accord with density dependent potentials obtained in purely phenomenological fits. Self consistent dynamical calculations of K- nuclear quasibound states are reported and discussed, as well.

  9. TASI 2014: Lectures on Gauge and Gravity Amplitude Relations

    NASA Astrophysics Data System (ADS)

    Carrasco, John Joseph M.

    In these lectures I talk about simplifications and universalities found in scattering amplitudes for gauge and gravity theories. In contrast to Ward identities, which are understood to arise from familiar symmetries of the classical action, these structures are currently only understood in terms of graphical organizational principles, such as the gauge-theoretic color-kinematics duality and the gravitational double-copy structure, for local representations of multi-loop S-matrix elements. These graphical principles make manifest new relationships in and between gauge and gravity scattering amplitudes. My lectures will focus on arriving at such graphical organizations for generic theories with examples presented from maximal supersymmetry, and their use in unitarity-based multiloop integrand construction.

  10. Positivity of spin foam amplitudes

    NASA Astrophysics Data System (ADS)

    Baez, John C.; Christensen, J. Daniel

    2002-04-01

    The amplitude for a spin foam in the Barrett-Crane model of Riemannian quantum gravity is given as a product over its vertices, edges and faces, with one factor of the Riemannian 10j symbols appearing for each vertex, and simpler factors for the edges and faces. We prove that these amplitudes are always nonnegative for closed spin foams. As a corollary, all open spin foams going between a fixed pair of spin networks have real amplitudes of the same sign. This means one can use the Metropolis algorithm to compute expectation values of observables in the Riemannian Barrett-Crane model, as in statistical mechanics, even though this theory is based on a real-time (eiS) rather than imaginary-time e-S path integral. Our proof uses the fact that when the Riemannian 10j symbols are nonzero, their sign is positive or negative depending on whether the sum of the ten spins is an integer or half-integer. For the product of 10j symbols appearing in the amplitude for a closed spin foam, these signs cancel. We conclude with some numerical evidence suggesting that the Lorentzian 10j symbols are always nonnegative, which would imply similar results for the Lorentzian Barrett-Crane model.

  11. Large amplitude drop shape oscillations

    NASA Technical Reports Server (NTRS)

    Trinh, E. H.; Wang, T. G.

    1982-01-01

    An experimental study of large amplitude drop shape oscillation was conducted in immiscible liquids systems and with levitated free liquid drops in air. In liquid-liquid systems the results indicate the existence of familiar characteristics of nonlinear phenomena. The resonance frequency of the fundamental quadrupole mode of stationary, low viscosity Silicone oil drops acoustically levitated in water falls to noticeably low values as the amplitude of oscillation is increased. A typical, experimentally determined relative frequency decrease of a 0.5 cubic centimeters drop would be about 10% when the maximum deformed shape is characterized by a major to minor axial ratio of 1.9. On the other hand, no change in the fundamental mode frequency could be detected for 1 mm drops levitated in air. The experimental data for the decay constant of the quadrupole mode of drops immersed in a liquid host indicate a slight increase for larger oscillation amplitudes. A qualitative investigation of the internal fluid flows for such drops revealed the existence of steady internal circulation within drops oscillating in the fundamental and higher modes. The flow field configuration in the outer host liquid is also significantly altered when the drop oscillation amplitude becomes large.

  12. Constant-amplitude RC oscillator

    NASA Technical Reports Server (NTRS)

    Kerwin, W. J.; Westbrook, R. M.

    1970-01-01

    Sinusoidal oscillator has a frequency determined by resistance-capacitance /RC/ values of two charge control devices and a constant-amplitude voltage independent of frequency and RC values. RC elements provide either voltage-control, resistance-control, or capacitance-control of the frequency.

  13. N-loop string amplitude

    SciTech Connect

    Mandelstam, S.

    1986-06-01

    Work on the derivation of an explicit perturbation series for string and superstring amplitudes is reviewed. The light-cone approach is emphasized, but some work on the Polyakov approach is also mentioned, and the two methods are compared. The calculation of the measure factor is outlined in the interacting-string picture. (LEW)

  14. Employing helicity amplitudes for resummation

    NASA Astrophysics Data System (ADS)

    Moult, Ian; Stewart, Iain W.; Tackmann, Frank J.; Waalewijn, Wouter J.

    2016-05-01

    Many state-of-the-art QCD calculations for multileg processes use helicity amplitudes as their fundamental ingredients. We construct a simple and easy-to-use helicity operator basis in soft-collinear effective theory (SCET), for which the hard Wilson coefficients from matching QCD onto SCET are directly given in terms of color-ordered helicity amplitudes. Using this basis allows one to seamlessly combine fixed-order helicity amplitudes at any order they are known with a resummation of higher-order logarithmic corrections. In particular, the virtual loop amplitudes can be employed in factorization theorems to make predictions for exclusive jet cross sections without the use of numerical subtraction schemes to handle real-virtual infrared cancellations. We also discuss matching onto SCET in renormalization schemes with helicities in 4- and d -dimensions. To demonstrate that our helicity operator basis is easy to use, we provide an explicit construction of the operator basis, as well as results for the hard matching coefficients, for p p →H +0 , 1, 2 jets, p p →W /Z /γ +0 , 1, 2 jets, and p p →2 , 3 jets. These operator bases are completely crossing symmetric, so the results can easily be applied to processes with e+e- and e-p collisions.

  15. Superstring disk amplitudes in a rolling tachyon background

    SciTech Connect

    Jokela, Niko; Majumder, Jaydeep; Keski-Vakkuri, Esko

    2006-02-15

    We study the tree level scattering or emission of n closed superstrings from a decaying non-BPS brane in Type II superstring theory. We attempt to calculate generic n-point superstring disk amplitudes in the rolling tachyon background. We show that these can be written as infinite power series of Toeplitz determinants, related to expectation values of a periodic function in Circular Unitary Ensembles. Further analytical progress is possible in the special case of bulk-boundary disk amplitudes. These are interpreted as probability amplitudes for emission of a closed string with initial conditions perturbed by the addition of an open string vertex operator. This calculation has been performed previously in bosonic string theory, here we extend the analysis for superstrings. We obtain a result for the average energy of closed superstrings produced in the perturbed background.

  16. Extracting forward strong amplitudes from elastic differential cross sections

    SciTech Connect

    C.M. Chen; D.J. Ernst; Mikkel B. Johnson

    2001-07-01

    The feasibility of a model-independent extraction of the forward strong amplitude from elastic nuclear cross section data in the Coulomb-nuclear interference region is assessed for {pi} and K{sup +} scattering at intermediate energies. Theoretically-generated ''data'' are analyzed to provide criteria for optimally designing experiments to measure these amplitudes, whose energy dependence (particularly that of the real parts) is needed for disentangling various sources of medium modifications of the projectile-nucleon interaction. The issues considered include determining the angular region over which to make the measurements, the role of the most forward angles measured, and the effects of statistical and systematic errors. We find that there is a region near the forward direction where Coulomb-nuclear interference allows reliable extraction of the strong forward amplitude for both pions and the K{sup +} from .3 to 1 GeV/c.

  17. On the four-dimensional formulation of dimensionally regulated amplitudes

    NASA Astrophysics Data System (ADS)

    Fazio, A. R.; Mastrolia, P.; Mirabella, E.; Torres Bobadilla, W. J.

    2014-12-01

    Elaborating on the four-dimensional helicity scheme, we propose a pure four-dimensional formulation (FDF) of the -dimensional regularization of one-loop scattering amplitudes. In our formulation particles propagating inside the loop are represented by massive internal states regulating the divergences. The latter obey Feynman rules containing multiplicative selection rules which automatically account for the effects of the extra-dimensional regulating terms of the amplitude. We present explicit representations of the polarization and helicity states of the four-dimensional particles propagating in the loop. They allow for a complete, four-dimensional, unitarity-based construction of -dimensional amplitudes. Generalized unitarity within the FDF does not require any higher-dimensional extension of the Clifford and the spinor algebra. Finally we show how the FDF allows for the recursive construction of -dimensional one-loop integrands, generalizing the four-dimensional open-loop approach.

  18. Quasi-steady, marginally unstable electron cyclotron harmonic wave amplitudes

    NASA Astrophysics Data System (ADS)

    Zhang, Xiaojia; Angelopoulos, Vassilis; Ni, Binbin; Thorne, Richard M.; Horne, Richard B.

    2013-06-01

    Electron cyclotron harmonic (ECH) waves have long been considered a potential driver of diffuse aurora in Earth's magnetotail. However, the scarcity of intense ECH emissions in the outer magnetotail suggests that our understanding of the amplification and the relative importance of these waves for electron scattering is lacking. We conduct a comprehensive study of wave growth and quasi-linear diffusion to estimate the amplitude of loss-cone-driven ECH waves once diffusion and growth balance but before convection or losses alter the background hot plasma sheet population. We expect this to be the most common state of the plasma sheet between episodes of fast convection. For any given wave amplitude, we model electron diffusion caused by interaction with ECH waves using a 2-D bounce-averaged Fokker-Planck equation. After fitting the resultant electron distributions as a superposition of multicomponent subtracted bi-Maxwellians, we estimate the maximum path-integrated gain using the HOTRAY ray-tracing code. We argue that the wave amplitude during quasi-steady state is the inflection point on a gain-amplitude curve. During quasi-steady state, ECH wave amplitudes can be significant (~1 mV/m) at L ~ 8 but drop to very low values (<~0.1 mV/m) in the outer magnetotail (L ~ 16) and likely fall below the sensitivity of typical instrumentation relatively close to Earth mainly because of the smallness of the loss cone. Our result reinforces the potentially important role of ECH waves in driving diffuse aurora and suggests that careful comparison of theoretical wave amplitude estimates and observations is required for resolving the equatorial scattering mechanism of diffuse auroral precipitation.

  19. True amplitude prestack depth migration

    NASA Astrophysics Data System (ADS)

    Deng, Feng

    Reliable analysis of amplitude variation with offset (or with angle) requires accurate amplitudes from prestack migration. In routine seismic data processing, amplitude balancing and automatic gain control are often used to reduce amplitude lateral variations. However, these methods are empirical and lack a solid physical basis; thus, there are uncertainties that might produce erroneous conclusions, and hence cause economic loss. During wavefield propagation, geometrical spreading, intrinsic attenuation, transmission losses and the energy conversion significantly distort the wavefield amplitude. Most current true-amplitude migrations usually compensate only for geometrical spreading. A new prestack depth migration based on the framework of reverse-time migration in the time-space domain was developed in this dissertation with the aim of compensating all of the propagation effects in one integrated algorithm. Geometrical spreading is automatically included because of the use of full two-way wave extrapolation. Viscoelastic wave equations are solved to handle the intrinsic attenuation with a priori quality factor. Transmission losses for both up- and down-going waves are compensated using a two-pass, recursive procedure based on extracting the angle-dependent reflection/transmission coefficients from prestack migration. The losses caused by the conversion of energy from one elastic model to another are accounted for through elastic wave extrapolation; the influence of the S wave velocity contrast on the P wave reflection coefficient is implicitly included by using the Zoeppritz equations to describe the reflection and transmission at an elastic interface. Only smooth background models are assumed to be known. The contrasts/ratios of the model parameters can be estimated by fitting the compensated angle-dependent reflection coefficients obtained from data for multiple sources. This is one useful by-product of the algorithm. Numerical tests on both 2D and 3D scalar

  20. Randomized gap and amplitude estimation

    NASA Astrophysics Data System (ADS)

    Zintchenko, Ilia; Wiebe, Nathan

    2016-06-01

    We provide a method for estimating spectral gaps in low-dimensional systems. Unlike traditional phase estimation, our approach does not require ancillary qubits nor does it require well-characterized gates. Instead, it only requires the ability to perform approximate Haar random unitary operations, applying the unitary whose eigenspectrum is sought and performing measurements in the computational basis. We discuss application of these ideas to in-place amplitude estimation and quantum device calibration.

  1. Genus dependence of superstring amplitudes

    SciTech Connect

    Davis, Simon

    2006-11-15

    The problem of the consistency of the finiteness of the supermoduli space integral in the limit of vanishing super-fixed point distance and the genus-dependence of the integral over the super-Schottky coordinates in the fundamental region containing a neighborhood of |K{sub n}|=0 is resolved. Given a choice of the categories of isometric circles representing the integration region, the exponential form of bounds for superstring amplitudes is derived.

  2. Pulse amplitude modulated chlorophyll fluorometer

    SciTech Connect

    Greenbaum, Elias; Wu, Jie

    2015-12-29

    Chlorophyll fluorometry may be used for detecting toxins in a sample because of changes in micro algae. A portable lab on a chip ("LOAC") based chlorophyll fluorometer may be used for toxin detection and environmental monitoring. In particular, the system may include a microfluidic pulse amplitude modulated ("PAM") chlorophyll fluorometer. The LOAC PAM chlorophyll fluorometer may analyze microalgae and cyanobacteria that grow naturally in source drinking water.

  3. Wave-scattering from a gently curved surface

    NASA Astrophysics Data System (ADS)

    Bimonte, Giuseppe

    2016-09-01

    We study wave scattering from a gently curved surface. We show that the recursive relations, implied by shift invariance, among the coefficients of the perturbative series for the scattering amplitude allow to perform an infinite resummation of the perturbative series to all orders in the amplitude of the corrugation. The resummed series provides a derivative expansion of the scattering amplitude in powers of derivatives of the height profile, which is expected to become exact in the limit of quasi-specular scattering. We discuss the relation of our results with the so-called small-slope approximation introduced some time ago by Voronovich.

  4. Type 0 open string amplitudes and the tensionless limit

    NASA Astrophysics Data System (ADS)

    Rojas, Francisco

    2014-12-01

    The sum over planar multiloop diagrams in the NS + sector of type 0 open strings in flat spacetime has been proposed by Thorn as a candidate to resolve nonperturbative issues of gauge theories in the large N limit. With S U (N ) Chan-Paton factors, the sum over planar open string multiloop diagrams describes the 't Hooft limit N →∞ with N gs2 held fixed. By including only planar diagrams in the sum the usual mechanism for the cancellation of loop divergences (which occurs, for example, among the planar and Möbius strip diagrams by choosing a specific gauge group) is not available and a renormalization procedure is needed. In this article the renormalization is achieved by suspending total momentum conservation by an amount p ≡∑ i n ki≠0 at the level of the integrands in the integrals over the moduli and analytically continuing them to p =0 at the very end. This procedure has been successfully tested for the 2 and 3 gluon planar loop amplitudes by Thorn. Gauge invariance is respected and the correct running of the coupling in the limiting gauge field theory was also correctly obtained. In this article we extend those results in two directions. First, we generalize the renormalization method to an arbitrary n -gluon planar loop amplitude giving full details for the 4-point case. One of our main results is to provide a fully renormalized amplitude which is free of both UV and the usual spurious divergences leaving only the physical singularities in it. Second, using the complete renormalized amplitude, we extract the high-energy scattering regime at fixed angle (tensionless limit). Apart from obtaining the usual exponential falloff at high energies, we compute the full dependence on the scattering angle which shows the existence of a smooth connection between the Regge and hard scattering regimes.

  5. Surface-integral formulation of scattering theory

    SciTech Connect

    Kadyrov, A.S. Bray, I.; Mukhamedzhanov, A.M.; Stelbovics, A.T.

    2009-07-15

    We formulate scattering theory in the framework of a surface-integral approach utilizing analytically known asymptotic forms of the two-body and three-body scattering wavefunctions. This formulation is valid for both short-range and long-range Coulombic interactions. New general definitions for the potential scattering amplitude are presented. For the Coulombic potentials, the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the Coulomb three-body breakup amplitude are derived. This resolves the problem of the inability of the conventional scattering theory to define the post form of the breakup amplitude for charged particles. The new definitions can be written as surface-integrals convenient for practical calculations. The surface-integral representations are extended to amplitudes of direct and rearrangement scattering processes taking place in an arbitrary three-body system. General definitions for the wave operators are given that unify the currently used channel-dependent definitions.

  6. Massive superstring scatterings in the Regge regime

    SciTech Connect

    He Song; Lee, Jen-Chi; Takahashi, Keijiro; Yang Yi

    2011-03-15

    We calculate four classes of high-energy massive string scattering amplitudes of fermionic string theory at arbitrary mass levels in the Regge regime (RR). We show that all four leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind. Based on the summation algorithm of a set of extended signed Stirling number identities, we show that all four ratios calculated previously by the method of decoupling of zero-norm states among scattering amplitudes in the Gross regime can be extracted from this Kummer function in the RR. Finally, we conjecture and give evidence that the existence of these four Gross regime ratios in the RR persists to subleading orders in the Regge expansion of all high-energy fermionic string scattering amplitudes.

  7. Massive superstring scatterings in the Regge regime

    NASA Astrophysics Data System (ADS)

    He, Song; Lee, Jen-Chi; Takahashi, Keijiro; Yang, Yi

    2011-03-01

    We calculate four classes of high-energy massive string scattering amplitudes of fermionic string theory at arbitrary mass levels in the Regge regime (RR). We show that all four leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind. Based on the summation algorithm of a set of extended signed Stirling number identities, we show that all four ratios calculated previously by the method of decoupling of zero-norm states among scattering amplitudes in the Gross regime can be extracted from this Kummer function in the RR. Finally, we conjecture and give evidence that the existence of these four Gross regime ratios in the RR persists to subleading orders in the Regge expansion of all high-energy fermionic string scattering amplitudes.

  8. The scattering of the screened Coulomb potential

    NASA Astrophysics Data System (ADS)

    Cao, Xin-Wei; Chen, Wen-Li; Li, Yuan-Yuan; Wei, Gao-Feng

    2014-08-01

    We study the scattering states of the screened Coulomb potential in the nonrelativistic frame. The explicitly calculation formula of phase shift is derived and the normalized radial wave functions of scattering states on the ^{\\prime} k/2\\pi scale^{\\prime} are presented. By studying analytical properties of scattering amplitude the screening effects on bound states are discussed numerically. It is shown that the screening effects increase with increasing screened parameter, especially for large quantum states.

  9. Scattering calculations and confining interactions

    NASA Technical Reports Server (NTRS)

    Buck, Warren W.; Maung, Khin M.

    1993-01-01

    Most of the research work performed under this grant were concerned with strong interaction processes ranging from kaon-nucleon interaction to proton-nucleus scattering calculations. Research performed under this grant can be categorized into three groups: (1) parametrization of fundamental interactions, (2) development of formal theory, and (3) calculations based upon the first two. Parametrizations of certain fundamental interactions, such as kaon-nucleon interaction, for example, were necessary because kaon-nucleon scattering amplitude was needed to perform kaon-nucleus scattering calculations. It was possible to calculate kaon-nucleon amplitudes from the first principle, but it was unnecessary for the purpose of the project. Similar work was also done for example for anti-protons and anti-nuclei. Formal developments to some extent were also pursued so that consistent calculations can be done.

  10. Constraints on string resonance amplitudes

    NASA Astrophysics Data System (ADS)

    Cheung, Kingman; Liu, Yueh-Feng

    2005-07-01

    We perform a global analysis of the tree-level open-string amplitudes in the limit s≪M2S. Based on the present data from the Tevatron, HERA, and LEP 2, we set a lower limit on the string scale MS≥0.69 1.96 TeV at 95% confidence level for the Chan-Paton factors |T|=0-4. We also estimate the expected sensitivities at the CERN LHC, which can be as high as 19 TeV for |T|=4.

  11. Zero energy scattering calculation in Euclidean space

    NASA Astrophysics Data System (ADS)

    Carbonell, J.; Karmanov, V. A.

    2016-03-01

    We show that the Bethe-Salpeter equation for the scattering amplitude in the limit of zero incident energy can be transformed into a purely Euclidean form, as it is the case for the bound states. The decoupling between Euclidean and Minkowski amplitudes is only possible for zero energy scattering observables and allows determining the scattering length from the Euclidean Bethe-Salpeter amplitude. Such a possibility strongly simplifies the numerical solution of the Bethe-Salpeter equation and suggests an alternative way to compute the scattering length in Lattice Euclidean calculations without using the Luscher formalism. The derivations contained in this work were performed for scalar particles and one-boson exchange kernel. They can be generalized to the fermion case and more involved interactions.

  12. One-loop amplitudes on the Riemann sphere

    NASA Astrophysics Data System (ADS)

    Geyer, Yvonne; Mason, Lionel; Monteiro, Ricardo; Tourkine, Piotr

    2016-03-01

    The scattering equations provide a powerful framework for the study of scattering amplitudes in a variety of theories. Their derivation from ambitwistor string theory led to proposals for formulae at one loop on a torus for 10 dimensional supergravity, and we recently showed how these can be reduced to the Riemann sphere and checked in simple cases. We also proposed analogous formulae for other theories including maximal super-Yang-Mills theory and supergravity in other dimensions at one loop. We give further details of these results and extend them in two directions. Firstly, we propose new formulae for the one-loop integrands of Yang-Mills theory and gravity in the absence of supersymmetry. These follow from the identification of the states running in the loop as expressed in the ambitwistor-string correlator. Secondly, we give a systematic proof of the non-supersymmetric formulae using the worldsheet factorisation properties of the nodal Riemann sphere underlying the scattering equations at one loop. Our formulae have the same decomposition under the recently introduced Q-cuts as one-loop integrands and hence give the correct amplitudes.

  13. Constructing Amplitudes from Their Soft Limits

    SciTech Connect

    Boucher-Veronneau, Camille; Larkoski, Andrew J.; /SLAC

    2011-12-09

    The existence of universal soft limits for gauge-theory and gravity amplitudes has been known for a long time. The properties of the soft limits have been exploited in numerous ways; in particular for relating an n-point amplitude to an (n-1)-point amplitude by removing a soft particle. Recently, a procedure called inverse soft was developed by which 'soft' particles can be systematically added to an amplitude to construct a higher-point amplitude for generic kinematics. We review this procedure and relate it to Britto-Cachazo-Feng-Witten recursion. We show that all tree-level amplitudes in gauge theory and gravity up through seven points can be constructed in this way, as well as certain classes of NMHV gauge-theory amplitudes with any number of external legs. This provides us with a systematic procedure for constructing amplitudes solely from their soft limits.

  14. Generalized optical theorem for scattering in inhomogeneous media.

    PubMed

    Dacol, Dalcio K; Roy, Dilip G

    2005-09-01

    The scattering of scalar waves by objects embedded in an inhomogeneous medium contained by a bounded volume is discussed using the method of pseudopotentials. The scattering amplitude for the object in an extended uniform medium is assumed known and used as input. The scattering process is described by using an expansion of the scattering amplitude in terms of spherical harmonics. An appropriate multipole decomposition of the Green function in the bounded medium is developed and the effective scattering amplitude in this environment is defined. The generalized optical theorem obeyed by this effective scattering amplitude is obtained and analyzed. The scattering problem is formulated entirely and explicitly in terms of the bounded medium's Green functions. This approach is thus very flexible in regards to the choice of incident field. In the case of waveguides the connection between propagation and scattering is explicit. At the same time it still allows for independent computation of the propagation and scattering aspects of the problem. This is the main advantage of using as input the scattering amplitude in an extended uniform medium. PMID:16241594

  15. Measurements of Dust Oscillations with Laser Heterodyne Receiver of Scattered Radiation

    SciTech Connect

    Serozhkin, Yuriy; Venger, Yevgen

    2011-11-29

    We performed the experiments on measurement of vibration amplitudes for microparticles in gas and water with laser heterodyne receiver of scattered radiation. The measured vibration amplitude values are about 20 nm.

  16. Timelike Compton Scattering

    SciTech Connect

    T. Horn, Y. Illieva, F. J. Klein, P. Nadel‐Turonski, R. Paremuzyan, S. Stepanyan

    2011-10-01

    Generalized Parton Distributions (GPDs) have become a key concept in our studies of hadron structure in QCD. The measurement of suitable experimental observables and the extraction of GPDs from these data is one of the high priority 12 GeV programs at Jefferson Lab. Deeply Virtual Compton Scattering (DVCS) is generally thought of as the most promising channel for probing GPDs in the valence quark region. However, the inverse process, Timelike Compton Scattering (TCS) can provide an important complementary measurement, in particular of the real part of the Compton amplitude and power corrections at intermediate values of Q2. The first studies of TCS using real tagged and quasi-real untagged photons were performed in Hall B at Jefferson Lab.

  17. New identities among gauge theory amplitudes

    NASA Astrophysics Data System (ADS)

    Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Feng, Bo; Søndergaard, Thomas

    2010-08-01

    Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N = 4 super Yang-Mills multiplet.

  18. Multiple scattering and charged-particle - hydrogen-atom collisions

    NASA Technical Reports Server (NTRS)

    Franco, V.; Thomas, B. K.

    1979-01-01

    Glauber-approximation scattering amplitudes for charged-particle - hydrogen-atom elastic and inelastic collisions are derived directly in terms of the known particle-electron and particle-proton Coulomb scattering amplitudes and the known hydrogen-atom form factors. It is shown that the particle-hydrogen amplitude contains no single-scattering term. The double-scattering term is obtained as a two-dimensional integral in momentum space. It is demonstrated how the result can be used as the starting point for an alternative and relatively simple derivation, in closed form, of the Glauber particle-hydrogen scattering amplitude for transitions from the ground state to an arbitrary (nlm) state.

  19. Decoherence due to Elastic Rayleigh Scattering

    NASA Astrophysics Data System (ADS)

    Uys, H.; Biercuk, M. J.; Vandevender, A. P.; Ospelkaus, C.; Meiser, D.; Ozeri, R.; Bollinger, J. J.

    2010-11-01

    We present theoretical and experimental studies of the decoherence of hyperfine ground-state superpositions due to elastic Rayleigh scattering of light off resonant with higher lying excited states. We demonstrate that under appropriate conditions, elastic Rayleigh scattering can be the dominant source of decoherence, contrary to previous discussions in the literature. We show that the elastic-scattering decoherence rate of a two-level system is given by the square of the difference between the elastic-scattering amplitudes for the two levels, and that for certain detunings of the light, the amplitudes can interfere constructively even when the elastic-scattering rates from the two levels are equal. We confirm this prediction through calculations and measurements of the total decoherence rate for a superposition of the valence electron spin levels in the ground state of Be+9 in a 4.5 T magnetic field.

  20. Decoherence due to elastic Rayleigh scattering.

    PubMed

    Uys, H; Biercuk, M J; Vandevender, A P; Ospelkaus, C; Meiser, D; Ozeri, R; Bollinger, J J

    2010-11-12

    We present theoretical and experimental studies of the decoherence of hyperfine ground-state superpositions due to elastic Rayleigh scattering of light off resonant with higher lying excited states. We demonstrate that under appropriate conditions, elastic Rayleigh scattering can be the dominant source of decoherence, contrary to previous discussions in the literature. We show that the elastic-scattering decoherence rate of a two-level system is given by the square of the difference between the elastic-scattering amplitudes for the two levels, and that for certain detunings of the light, the amplitudes can interfere constructively even when the elastic-scattering rates from the two levels are equal. We confirm this prediction through calculations and measurements of the total decoherence rate for a superposition of the valence electron spin levels in the ground state of 9Be+ in a 4.5 T magnetic field. PMID:21231210

  1. Intermediate energy proton-deuteron elastic scattering

    NASA Technical Reports Server (NTRS)

    Wilson, J. W.

    1973-01-01

    A fully symmetrized multiple scattering series is considered for the description of proton-deuteron elastic scattering. An off-shell continuation of the experimentally known twobody amplitudes that retains the exchange symmeteries required for the calculation is presented. The one boson exchange terms of the two body amplitudes are evaluated exactly in this off-shell prescription. The first two terms of the multiple scattering series are calculated explicitly whereas multiple scattering effects are obtained as minimum variance estimates from the 146-MeV data of Postma and Wilson. The multiple scattering corrections indeed consist of low order partial waves as suggested by Sloan based on model studies with separable interactions. The Hamada-Johnston wave function is shown consistent with the data for internucleon distances greater than about 0.84 fm.

  2. Evaluation of the Cachazo-He-Yuan gauge amplitude

    NASA Astrophysics Data System (ADS)

    Lam, C. S.; Yao, York-Peng

    2016-05-01

    The Cachazo-He-Yuan (CHY) formula for n -gluon scattering is known to give the same amplitude as the one obtained from Feynman diagrams, though the former contains neither vertices nor propagators explicitly. The equivalence was shown by indirect means, not by a direct evaluation of the (n -3 )-dimensional integral in the CHY formula. The purpose of this paper is to discuss how such a direct evaluation can be carried out. There are two basic difficulties in the calculation: how to handle the large number of terms in the reduced Pfaffian, and how to carry out the integrations in the presence of a σ dependence much more complicated than the Parke-Taylor form found in a CHY double-color scalar amplitude. We have solved both of these problems, and have formulated a method that can be applied to any n . Many examples are provided to illustrate these calculations.

  3. BPS amplitudes, helicity supertraces and membranes in M-theory

    NASA Astrophysics Data System (ADS)

    Wit, B. d.; Lüst, D.

    2000-03-01

    We study BPS dominated loop amplitudes in M-theory on T2. For this purpose we generalize the concept of helicity supertraces to nine spacetime dimensions. These traces distinguish between various massive supermultiplets and appear as coefficients in their one-loop contributions to n-graviton scattering amplitudes. This can be used to show that only ultrashort BPS multiplets contribute to the R4 term in the effective action, which was first computed by Green, Gutperle and Vanhove. There are two inequivalent ultrashort BPS multiplets which describe the Kaluza-Klein states and the wrapped membranes that cover the torus a number of times. From the perspective of the type-II strings they correspond to momentum and winding states and D0 or D1 branes.

  4. Amplitudes of the two-nucleon interaction at 579 MeV

    NASA Astrophysics Data System (ADS)

    Arash, Firooz; Moravcsik, Michael J.; Goldstein, Gary

    1985-07-01

    A complete amplitude analysis is presented of the 579-MeV data set for p-p elastic scattering. Although all continua of ambiguities are eliminated by the extensive nature of the data, discrete ambiguities remain, as expected from general criteria for such ambiguities. In particular, four solutions are found. Further experiments are specified which can resolve this remaining ambiguity also. A comparison is also made with previous amplitude results at this energy.

  5. Hedgehog bases for A n cluster polylogarithms and an application to six-point amplitudes

    NASA Astrophysics Data System (ADS)

    Parker, Daniel E.; Scherlis, Adam; Spradlin, Marcus; Volovich, Anastasia

    2015-11-01

    Multi-loop scattering amplitudes in N=4 Yang-Mills theory possess cluster algebra structure. In order to develop a computational framework which exploits this connection, we show how to construct bases of Goncharov polylogarithm functions, at any weight, whose symbol alphabet consists of cluster coordinates on the A n cluster algebra. Using such a basis we present a new expression for the 2-loop 6-particle NMHV amplitude which makes some of its cluster structure manifest.

  6. Amplitude and Width Correlations in COBALT-57 and VANADIUM-49.

    NASA Astrophysics Data System (ADS)

    Ramakrishnan, Prabha K.

    Angular distributions of the inelastically scattered protons and of the deexcitation (gamma)-rays in the ('56)Fe(p,p'(gamma)) reaction were measured for d-wave resonances in the proton energy range 3.10 to 4.01 MeV. The experiment was performed with an overall energy resolution of 350 to 400 eV (FWHM) at the Triangle Universities Nuclear Laboratory KN Van de Graaff accelerator and associated high resolution system. Results were obtained for 141 resonances; 83 resonances were assigned J('(pi)) = 5/2('+), while 58 resonances were assigned J('(pi)) = 3/2('+). Mixing parameters for the inelastic decay amplitudes were uniquely determined for the 5/2('+) resonances. For the 3/2('+) resonances sufficient information is not available from this experiment to extract a unique solution for the mixing parameters. Magnitudes and relative signs of three inelastic decay amplitudes were determined for the 5/2('+) resonances in ('57)Co. The angular distributions for the deexcitation (gamma)-rays were measured in coincidence with the inelastically scattered protons for 30 3/2('+) resonances in ('49)V in the proton energy region 2.2 to 3.1 MeV. The singles measurements from a previous experiment were combined with these coincidence measurements to eliminate the ambiguity in the solutions for the mixing parameters. Amplitude and width measurements were determined for the three decay channels for 30 3/2('+) resonances. Statistical analyses were performed on the set of 83 5/2('+) resonances in ('57)Co and on the set of 30 3/2('+) resonances in ('49)V. In both cases, large amplitude and width correlations are observed. These results are interpreted as evidence for direct reactions between the inelastic channels.

  7. Integrable amplitude deformations for N =4 super Yang-Mills and ABJM theory

    NASA Astrophysics Data System (ADS)

    Bargheer, Till; Huang, Yu-Tin; Loebbert, Florian; Yamazaki, Masahito

    2015-01-01

    We study Yangian-invariant deformations of scattering amplitudes in 4d N =4 super Yang-Mills theory and 3d N =6 Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. In particular, we obtain the deformed Graßmannian integral for 4d N =4 supersymmetric Yang-Mills theory, both in momentum and momentum-twistor space. For 3d ABJM theory, we initiate the study of deformed scattering amplitudes. We investigate general deformations of on-shell diagrams, and find the deformed Graßmannian integral for this theory. We furthermore introduce the algebraic R-matrix construction of deformed Yangian invariants for ABJM theory.

  8. Measurements of acoustic pressure at high amplitudes and intensities

    NASA Astrophysics Data System (ADS)

    Crum, L. A.; Bailey, M. R.; Kaczkowski, P.; McAteer, J. A.; Pishchalnikov, Y. A.; Sapozhnikov, O. A.

    2004-01-01

    In our research group, we desire measurements of the large pressure amplitudes generated by the shock waves used in shock wave lithotripsy (SWL) and the large acoustic intensities used in High Intensity Focused Ultrasound (HIFU). Conventional piezoelectric or PVDF hydrophones can not be used for such measurements as they are damaged either by cavitation, in SWL applications, or heat, in HIFU applications. In order to circumvent these difficulties, we have utilized optical fiber hydrophones in SWL that do not cavitate, and small glass probes and a scattering technique for measurements of large HIFU intensities. Descriptions of these techniques will be given as well as some typical data.

  9. Amplitude tests of direct channel resonances: the dibaryon

    SciTech Connect

    Goldstein, G.R.; Moravcsik, M.J.; Arash, F.

    1984-02-01

    A recently formulated polarization amplitude test for the existence of one-particle-exchange mechanisms is modified to deal with direct-channel resonances. The results are applied to proton-proton elastic scattering at and around 800 MeV to test the suggested existence of a dibaryon resonance. This test is sensitive to somewhat different circumstances and parameters than the methods used in the past to find dibaryon resonances. The evidence, on the basis of the SAID data set, is negative for a resonance in any singlet partial wave, but is tantalizingly subliminal for a /sup 3/F/sub 3/ resonance. 7 refs., 4 figs.

  10. Amplitude tests of direct channel resonances: The dibaryon

    NASA Astrophysics Data System (ADS)

    Goldstein, G. R.; Moravosik, M. J.; Arash, F.

    1985-02-01

    A recently formulated polarization amplitude test for the existence of one-particle-exchange mechanisms is modified to deal with direct-channel resonances. The results are applied to proton-proton elastic scattering at and around 800 MeV to test the suggested existence of a dibaryon resonance. This test is sensitive to somewhat different circumstances and parameters than the methods used in the past to find dibaryon resonances. The evidence, on the basis of the SAID data set, is negative for a resonance in any singlet partial wave, but is tantalizingly subliminal for a 3F3 resonance.

  11. Amplitude-phase patterns: A new look at strong interactions

    NASA Astrophysics Data System (ADS)

    Goldstein, Gary R.; Arash, Firooz; Moravcsik, Michael J.

    1994-10-01

    The phases of complex spin-dependent scattering amplitudes for elastic processes NN, πN, πd, along with pp→d π+, are analyzed in various frames of reference for spin quantization. When all available energies and angles are compiled it is seen that the "phase histograms" for each reaction have remarkably simple properties in one choice of optimal frame; the phases tend to be integer multiples of 90°, within existing uncertainties. A two-component model for πN is presented that reproduces the striking pattern of phases and its generalization is discussed.

  12. Transition Distribution Amplitudes for γ⋆γ collisions

    NASA Astrophysics Data System (ADS)

    Lansberg, J. P.; Pire, B.; Szymanowski, L.

    2008-11-01

    We study the exclusive production of ππ and ρπ in hard γ⋆γ scattering in the forward kinematical region where the virtuality of one photon provides us with a hard scale in the process. The newly introduced concept of Transition Distribution Amplitudes (TDA) is used to perform a QCD calculation of these reactions thanks to two simple models for TDAs. The sizable cross sections for ρπ and ππ production may be tested at intense electron-positron colliders such as CLEO and B factories (Belle and BABAR).

  13. BFKL Pomeron and production amplitudes in N = 4 SUSY

    SciTech Connect

    Lipatov, L. N.

    2009-05-14

    Theoretical approaches to the problem of the high energy hadron-hadron scattering in the Regge kinematics are reviewed. It is shown, that the gluon in QCD is reggeized and the Pomeron is a two gluon composite state. Further, the equation for the multi-gluon composite states is integrable at N{sub c}{yields}{infinity}. Due to the AdS/CFT correspondence in N = 4 SUSY the BFKL Pomeron is equivalent to the reggeized graviton. The important properties of the maximal transcendentality and integrability are realized in this model. Multi-gluon scattering amplitudes are investigated in the Regge limit. The BDS ansatz for them is not valid beyond one loop due to the presence of the Mandelstam cuts. The hamiltonian for the corresonding reggeon states coincides with the hamiltonian of an integrable open Heisenberg spin chain.

  14. Amplitude-masked photoacoustic wavefront shaping and application in flowmetry

    PubMed Central

    Tay, Jian Wei; Liang, Jinyang; Wang, Lihong V.

    2014-01-01

    Optical-resolution photoacoustic flowmetry allows non-invasive single-cell flow measurements. However, its operational depth is limited by optical diffusion, which prevents focusing beyond shallow depths in scattering media, as well as reducing the measurement signal-to-noise ratio (SNR). To overcome this limitation, we used binary-amplitude wavefront shaping to enhance light focusing in the presence of scattering. Here, the transmission modes that contributed constructively to the intensity at the optical focus were identified and selectively illuminated, resulting in a 14-fold intensity increase and a corresponding increase in SNR. This technique can potentially extend the operational depth of optical-resolution photoacoustic flowmetry beyond 1 mm in tissue. PMID:25360912

  15. Phase diagram for passive electromagnetic scatterers.

    PubMed

    Lee, Jeng Yi; Lee, Ray-Kuang

    2016-03-21

    With the conservation of power, a phase diagram defined by amplitude square and phase of scattering coefficients for each spherical harmonic channel is introduced as a universal map for any passive electromagnetic scatterers. Physically allowable solutions for scattering coefficients in this diagram clearly show power competitions among scattering and absorption. It also illustrates a variety of exotic scattering or absorption phenomena, from resonant scattering, invisible cloaking, to coherent perfect absorber. With electrically small core-shell scatterers as an example, we demonstrate a systematic method to design field-controllable structures based on the allowed trajectories in this diagram. The proposed phase diagram and inverse design can provide tools to design functional electromagnetic devices. PMID:27136839

  16. Scattering Solutions of Bethe-Salpeter Equation in Minkowski and Euclidean Spaces

    NASA Astrophysics Data System (ADS)

    Carbonell, J.; Karmanov, V. A.

    2016-07-01

    We shortly review different methods to obtain the scattering solutions of the Bethe-Salpeter equation in Minkowski space. We emphasize the possibility to obtain the zero energy observables in terms of the Euclidean scattering amplitude.

  17. Scattering Solutions of Bethe-Salpeter Equation in Minkowski and Euclidean Spaces

    NASA Astrophysics Data System (ADS)

    Carbonell, J.; Karmanov, V. A.

    2016-06-01

    We shortly review different methods to obtain the scattering solutions of the Bethe-Salpeter equation in Minkowski space. We emphasize the possibility to obtain the zero energy observables in terms of the Euclidean scattering amplitude.

  18. Scattering of sound waves by a compressible vortex

    NASA Technical Reports Server (NTRS)

    Colonius, Tim; Lele, Sanjiva K.; Moin, Parviz

    1991-01-01

    Scattering of plane sound waves by a compressible vortex is investigated by direct computation of the two-dimensional Navier-Stokes equations. Nonreflecting boundary conditions are utilized, and their accuracy is established by comparing results on different sized domains. Scattered waves are directly measured from the computations. The resulting amplitude and directivity pattern of the scattered waves is discussed, and compared to various theoretical predictions. For compact vortices (zero circulation), the scattered waves directly computed are in good agreement with predictions based on an acoustic analogy. Strong scattering at about + or - 30 degrees from the direction of incident wave propagation is observed. Back scattering is an order of magnitude smaller than forward scattering. For vortices with finite circulation refraction of the sound by the mean flow field outside the vortex core is found to be important in determining the amplitude and directivity of the scattered wave field.

  19. Coupled-channel scattering on a torus

    SciTech Connect

    Guo, Peng; Dudek, Jozef Jon; Edwards, Robert G.; Szczepaniak, Adam Pawel

    2013-07-01

    Based on the Hamiltonian formalism approach, a generalized Luscher's formula for two particle scattering in both the elastic and coupled-channel cases in moving frames is derived from a relativistic Lippmann-Schwinger equation. Some strategies for extracting scattering amplitudes for a coupled-channel system from the discrete finite-volume spectrum are discussed and illustrated with a toy model of two-channel resonant scattering. This formalism will, in the near future, be used to extract information about hadron scattering from lattice QCD computations.

  20. A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory

    NASA Astrophysics Data System (ADS)

    Badger, Simon; Mogull, Gustav; Ochirov, Alexander; O'Connell, Donal

    2015-10-01

    We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.

  1. Optical scattering methods applicable to drops and bubbles

    NASA Technical Reports Server (NTRS)

    Marston, Philip L.

    1990-01-01

    An overview of optical scattering properties of drops and bubbles is presented. The properties lead to unconventional methods for optically monitoring the size or shape of a scatterer and are applicable to acoustically levitated objects. Several of the methods are applicable to the detection and measurement of small amplitude oscillations. Relevant optical phenomena include: (1) rainbows; (2) diffraction catastrophes from spheroids; (3) critical angle scattering; (4) effects of coatings; (5) glory scattering; and (6) optical levitation.

  2. Toward improving global attenuation models: Interpreting surface-wave amplitudes with approximate theories

    NASA Astrophysics Data System (ADS)

    Dalton, C. A.; Hjorleifsdottir, V.; Ekstrom, G.

    2011-12-01

    Surface-wave amplitudes provide the primary constraint on upper-mantle anelastic structure and are also sensitive to small-scale elastic structure through focusing effects. However, the use of amplitudes for seismic imaging presents several challenges. One, amplitudes are affected not only by propagation through anelastic and elastic heterogeneity but also by uncertainty in the source excitation, local receiver structure, and instrument response. Two, accounting for focusing and defocusing effects, which is important if amplitudes are to be used to study anelasticity, depends considerably on the chosen theoretical treatment. Three, multiple scattering of seismic energy by elastic heterogeneity can be mapped into attenuation, especially at high frequencies. With the objective of improving our ability to image mantle seismic attenuation using real amplitude observations, we investigate how approximations in the theoretical treatment of wave excitation and propagation influence the interpretation of amplitudes. We use a spectral-element wave-propagation solver (SPECFEM3D_GLOBE) to generate accurate seismograms for global Earth models containing one-dimensional attenuation structure and three-dimensional variations in seismic velocity. The seismograms are calculated for 42 realistically distributed earthquakes. Fundamental-mode Rayleigh wave amplitudes in the period range 50--200 seconds are measured using the approach of Ekström et al. (1997), for which PREM is the assumed Earth model. We show that using the appropriate local seismic structure at the source and receiver instead of PREM has a non-negligible effect on the amplitudes and improves their interpretation. The amplitudes due to focusing and defocusing effects are predicted for great-circle ray theory, exact ray theory (JWKB theory), and finite-frequency theory. We assess the ability of each theory to predict amplitudes that agree with those measured from the SPECFEM synthetics for an Earth model that

  3. S-duality and helicity amplitudes

    NASA Astrophysics Data System (ADS)

    Colwell, Kitran; Terning, John

    2016-03-01

    We examine interacting Abelian theories at low energies and show that holomorphically normalized photon helicity amplitudes transform into dual amplitudes under SL(2, {Z} ) as modular forms with weights that depend on the number of positive and negative helicity photons and on the number of internal photon lines. Moreover, canonically normalized helicity amplitudes transform by a phase, so that even though the amplitudes are not duality invariant, their squares are duality invariant. We explicitly verify the duality transformation at one loop by comparing the amplitudes in the case of an electron and the dyon that is its SL(2, {Z} ) image, and extend the invariance of squared amplitudes order by order in perturbation theory. We demonstrate that S-duality is a property of all low-energy effective Abelian theories with electric and/or magnetic charges and see how the duality generically breaks down at high energies.

  4. Discontinuities of multi-Regge amplitudes

    NASA Astrophysics Data System (ADS)

    Fadin, V. S.

    2015-04-01

    In the BFKL approach, discontinuities of multiple production amplitudes in invariant masses of produced particles are discussed. It turns out that they are in evident contradiction with the BDS ansatz for n-gluon amplitudes in the planar N = 4 SYM at n ≥ 6. An explicit expression for the NLO discontinuity of the two-to-four amplitude in the invariant mass of two produced gluons is is presented.

  5. Gravity and Yang-Mills amplitude relations

    SciTech Connect

    Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Soendergaard, Thomas; FengBo

    2010-11-15

    Using only general features of the S matrix and quantum field theory, we prove by induction the Kawai-Lewellen-Tye relations that link products of gauge theory amplitudes to gravity amplitudes at tree level. As a bonus of our analysis, we provide a novel and more symmetric form of these relations. We also establish an infinite tower of new identities between amplitudes in gauge theories.

  6. Minimal Basis for Gauge Theory Amplitudes

    SciTech Connect

    Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Vanhove, Pierre

    2009-10-16

    Identities based on monodromy for integrations in string theory are used to derive relations between different color-ordered tree-level amplitudes in both bosonic and supersymmetric string theory. These relations imply that the color-ordered tree-level n-point gauge theory amplitudes can be expanded in a minimal basis of (n-3)exclamation amplitudes. This result holds for any choice of polarizations of the external states and in any number of dimensions.

  7. Cascaded phase-preserving multilevel amplitude regeneration.

    PubMed

    Roethlingshoefer, Tobias; Onishchukov, Georgy; Schmauss, Bernhard; Leuchs, Gerd

    2014-12-29

    The performance of cascaded in-line phase-preserving amplitude regeneration using nonlinear amplifying loop mirrors has been studied in numerical simulations. As an example of a spectrally efficient modulation format with two amplitude states and multiple phase states, the regeneration performance of a star-16QAM format, basically an 8PSK format with two amplitude levels, was evaluated. An increased robustness against amplified spontaneous emission and nonlinear phase noise was observed resulting in a significantly increased transmission distance. PMID:25607142

  8. Two-photon exchange in electron-trinucleon elastic scattering

    NASA Astrophysics Data System (ADS)

    Kobushkin, A. P.; Timoshenko, Ju. V.

    2013-10-01

    We discuss two-photon exchange (TPE) in elastic electron scattering off the trinucleon systems, 3He and 3H. The calculations are done in the semirelativistic approximation with the trinucleon wave functions obtained with the Paris and CD-Bonn nucleon-nucleon potentials. An applicability area of the model is wide enough and includes the main part of kinematical domain where experimental data exist. All three TPE amplitudes (generalized form factors) for electron 3He elastic scattering are calculated. We find that the TPE amplitudes are a few times more significant in the scattering of electrons off 3He then in the electron-proton scattering.

  9. Wilson lines and gauge invariant off-shell amplitudes

    NASA Astrophysics Data System (ADS)

    Kotko, Piotr

    2014-07-01

    We study matrix elements of Fourier-transformed straight infinite Wilson lines as a way to calculate gauge invariant tree-level amplitudes with off-shell gluons. The off-shell gluons are assigned "polarization vectors" which (in the Feynman gauge) are transverse to their off-shell momenta and define the direction of the corresponding Wilson line operators. The infinite Wilson lines are first regularized to prove the correctness of the method. We have implemented the method in a computer FORM program that can calculate gluonic matrix elements of Wilson line operators automatically. In addition we formulate the Feynman rules that are convenient in certain applications, e.g. proving the Ward identities. Using both the program and the Feynman rules we calculate a few examples, in particular the matrix elements corresponding to gauge invariant g * g * g * g and g * g * g * g * g processes. An immediate application of the approach is in the high energy scattering, as in a special kinematic setup our results reduce to the form directly related to Lipatov's vertices. Thus the results we present can be directly transformed into Lipatov's vertices, in particular into RRRP and RRRRP vertices with arbitrary "orientation" of reggeized gluons. Since the formulation itself is not restricted to high-energy scattering, we also apply the method to a decomposition of an ordinary on-shell amplitude into a set of gauge invariant objects.

  10. Born expansions for charged particle scattering

    SciTech Connect

    Macek, J.H. Oak Ridge National Lab., TN ); Barrachina, R.O. . Centro Atomico Bariloche)

    1989-01-01

    High-order terms in Born expansions of scattering amplitudes in powers of charge are frequently divergent when long-range Coulomb interactions are present asymptotically. Expansions which are free from these logarithmic divergences have been constructed recently. We illustrate these expansions with the simplest example, namely the non-relativistic Rutherford scattering of two charged particles. This approach represents an adequate framework for the calculation of transition amplitudes and a comprehensive starting point for the development of consistent perturbation approximations in multi-channel descriptions of strongly interacting atomic systems. 17 refs.

  11. Three applications of a bonus relation for gravity amplitudes

    NASA Astrophysics Data System (ADS)

    Spradlin, Marcus; Volovich, Anastasia; Wen, Congkao

    2009-04-01

    Arkani-Hamed et al. have recently shown that all tree-level scattering amplitudes in maximal supergravity exhibit exceptionally soft behavior when two supermomenta are taken to infinity in a particular complex direction, and that this behavior implies new non-trivial relations amongst amplitudes in addition to the well-known on-shell recursion relations. We consider the application of these new 'bonus relations' to MHV amplitudes, showing that they can be used quite generally to relate (n - 2) !-term formulas typically obtained from recursion relations to (n - 3) !-term formulas related to the original BGK conjecture. Specifically we provide (1) a direct proof of a formula presented by Elvang and Freedman, (2) a new formula based on one due to Bedford et al., and (3) an alternate proof of a formula recently obtained by Mason and Skinner. Our results also provide the first direct proof that the conjectured BGK formula, only very recently proven via completely different methods, satisfies the on-shell recursion.

  12. Resonances in pi-K scattering

    SciTech Connect

    Wilson, David J.

    2014-06-23

    We have obtained clear signals of resonances in coupled-channel pi K - eta K scattering. Using distillation and a large basis of operators we are able to extract a precise spectrum of energy levels using the variational method. These energies are analysed using inelastic extensions of the Luescher method to obtain scattering amplitudes that clearly describe S, P and D wave resonances, corresponding to the physical K_0^*(1430), the K^*(892) and the K_2^*(1430).

  13. On a Model-Independent Representation for the Real Part of the Elastic Hadron Amplitude

    SciTech Connect

    Fagundes, D. A.; Menon, M. J.

    2010-11-12

    The applicability of Martin's Real Part Formula in model-independent analysis of elastic proton-proton scattering is discussed. Good reproduction of all the differential cross section data at high-energies (19.4-62.5 GeV) is obtained through an empirical parametrization for the imaginary part of the amplitude and the use of a representation for the Martin's formula without the scaling property. According to the fit results, the scattering amplitude is predominantly imaginary, except at the dip region. One zero (change of sign) is observed in the imaginary part of the amplitude (dip region) and two zeros in the real part (at small and intermediate values of the momentum transfer).

  14. Separating Scattering from Intrinsic Attenuation

    NASA Astrophysics Data System (ADS)

    van Wijk, K.; Scales, J. A.

    2003-12-01

    The subsurface appears disordered at all length-scales. Therefore, wave propatation at seismic or ultrasonic frequencies is subject to complicated scatterings. A pulse propagating in the subsurface loses energy at each scattering off an impedance contrast, but also decreases in amplitude as the impulse interacts with fluids in the rock. We call the latter non-elastic effect "intrinsic Q", while the former is "scattering Q". It is often the fluids in the rocks that are of interest, but conventional reflection and transmission of the incident pulse only cannot deceipher the individual components of Q due to scattering and fluid movement in the pore-space. We present an approach that can unravel these two mechanisms, allowing a separate estimate of absorption. This method treats the propagation of the average intensity in the framework of radiative transfer (RT); the arrival of (what is left of) the incident pulse is modeled as the coherent energy, whereas the later arriving multiply scattered events form the incoherent intensity. The coherent pulse decays exponentially due to a combination of scattering and absorption, and so does the incoherent intensity. However, multiple scattering can re-direct energy back to the receiver, supplying a gain-term at later times that makes up the incoherent intensity. Strictly speaking, one can invert for scattering and absorption from the intensity at late times only, often modeled with the late-time equivalent of RT, diffusion. However, we will show that fitting both early- and late-time signal with RT constrains absorption and scattering constants more rigorously. These ideas are illustrated by laboratory and sonic-logging measurements.

  15. Thermal cracking and amplitude dependent attenuation

    SciTech Connect

    Johnston, D.H.; Toksoez, M.N.

    1980-02-10

    The role of crack and grain boundary contacts in determining seismic wave attenuation in rock is investigated by examining Q as a function of thermal cycling (cracking) and wave strain amplitude. Q values are obtained using a longitudinal resonant bar technique in the 10- to 20-kHz range for maximum strain amplitudes varying from roughly 10/sup -8/ to 10/sup -5/. The samples studied include the Berea and Navajo sandstones, Plexiglas, Westerly granite, Solenhofen limestone, and Frederick diabase, the latter two relatively crack free in their virgin state. Measurements were made at room temperature and pressure in air. Q values for both sandstones are constant at low strains (<10/sup -6/) but decrease rapidly with amplitude at higher strains. There is no hysteresis of Q with amplitude. Q values for Plexiglas show no indication of amplitude dependent behavior. The granite, limestone, and diabase are thermally cycled at both fast and slow heating rates in order to induce cracking. Samples slowly cycled at 400/sup 0/C show a marked increase in Q that cannot be entirely explained by outgassing of volatiles. Cycling may also widen thin cracks and grain boundaries, reducing contact areas. Samples heated beyond 400/sup 0/C, or rapidly heated, result in generally decreasing Q values. The amplitude dependence of Q is found to be coupled to the effects of thermal cycling. For rock slowly cycled 400)C or less, the transition from low-amplitude contant Q to high-amplitude variable Q behavior decreases to lower amplitudes as a function of maximum temperature. Above 400/sup 0/C, and possibly in th rapidly heated samples also, the transition moves to higher amplitudes.

  16. Decoherence due to elastic Rayleigh scattering

    NASA Astrophysics Data System (ADS)

    Uys, H.; Biercuk, M. J.; Vandevender, A. P.; Ospelkaus, C.; Bollinger, J. J.; Meiser, D.

    2010-03-01

    Off-resonant light scattering (spontaneous emission) is an important source of decoherence in many coherent control experiments. Typically one focuses on the effects of Raman scattering, in which an atomic state is changed by a single scattering event. We present theoretical and experimental studies of the decoherence of hyperfine ground-state superpositions due to elastic Rayleigh scattering of off-resonant light. By a master equation technique we show that for a two-level superposition the elastic decoherence rate is the square of the difference between the two elastic scattering amplitudes. Thus, if the light detunings for the two states have opposite sign, the amplitudes interfere constructively and can result in a large decoherence rate. We calculate and measure the total decoherence rate for a superposition state of the valence electron spin in the ground state of ^9Be^+ in a 4.5 T magnetic field. We find that for large (˜20 GHz) detunings, decoherence due to elastic Rayleigh scattering can be 5 times larger than decoherence due to Raman scattering. This is in contrast with workootnotetextR. Ozeri, et al., PRL 95, 030403 (2005) at low magnetic field where decoherence was dominated by Raman scattering.

  17. Cross correlation analysis of plasma perturbation in amplitude modulated reactive dusty plasmas

    NASA Astrophysics Data System (ADS)

    Ito, Teppei; Soejima, Masahiro; Yamashita, Daisuke; Seo, Hyunwoong; Itagaki, Naho; Koga, Kazunori; Shiratani, Masaharu; Kobayashi, Tatsuya; Inagaki, Shigeru

    2015-09-01

    Interactions between plasmas and nano-interface are one of the most important issues in plasma processing. We have studied effects of plasma perturbation on growth of nanoparticles in amplitude modulated reactive dusty plasmas and have clarified that amplitude modulation (AM) leads to suppression of growth of nanoparticles [1]. Here we report results of cross correlation analysis of time evolution of laser light scattering intensity from nanoparticles in reactive plasmas. Experiments were carried out using a capacitively-coupled rf discharge reactor with a two-dimensional laser light scattering (LLS) system. We employed Ar +DM-DMOS discharge plasmas to generate nanoparticles. The peaks at higher harmonics and subharmonics in spectra of laser light scattering intensity were detected, suggesting nonlinear coupling between plasma and nanoparticle amount. We found high cross correlation t between waves at AM frequency and its higher harmonics. Namely, perturbation at fAM closely correlates with those at higher harmonics.

  18. Helicity amplitudes on the light-front

    NASA Astrophysics Data System (ADS)

    Cruz Santiago, Christian A.

    Significant progress has been made recently in the field of helicity amplitudes. Currently there are on-shell recursion relations with shifted complex momenta, geometric interpretations of amplitudes and gauge invariant off-shell amplitudes. All this points to helicity amplitudes being a rich field with much more to say. In this work we take initial steps in understanding amplitudes through the light-front formalism for the first time. We begin by looking at crossing symmetry. In the light-front it is not obvious that crossing symmetry should be present as there are non-local energy denominators that mix energies of different states. Nevertheless, we develop a systematic approach to relate, for example, 1 → N gluon processes to 2 → N -- 1 processes. Using this method, we give a perturbative proof of crossing symmetry on the light-front. One important caveat is that the proof requires the amplitudes to be on-shell. We also saw that the analytic continuation from outgoing to incoming particle produces a phase that's dependent on the choice of polarizations. Next, we reproduce the Parke-Taylor amplitudes. For this purpose we found a recursion relation for an off-shell object called the fragmentation function. This recursion relies on the factorization property of the fragmentation functions, and it becomes apparent that this recursion is the light-front analog of the Berends-Giele recursion relation. We also found this object's connection to off-shell and on-shell amplitudes. The solution for the off-shell amplitude, which does reproduce the Parke-Taylor amplitudes in the on-shell limit, turns out to be very interesting. It can be written as a linear sum of off-shell objects with the same structure as MHV amplitudes. Finally, we look at the Wilson line approach to generate gauge invariant off-shell amplitudes. It turns out that the exact same recursion relation appears on both frameworks, thereby providing the interpretation that our recursion relation has it

  19. Location of Tremor and Long Period Events Using Seismic Amplitudes

    NASA Astrophysics Data System (ADS)

    Battaglia, J.; Battaglia, J.; Ferrazzini, V.; Okubo, P. G.

    2001-12-01

    Tremor and Long Period (LP) events are of particular interest for understanding the behavior of volcanoes as it is assumed that they directly involve fluids in their source mechanisms. However, those events are usually difficult or impossible to locate using traditional arrival times methods, because of their emergent onsets or because they are stationary for a long time. While techniques have been proposed using seismic arrays, this task remains problematic using data from classical short period volcano monitoring networks. A method based on the use of seismic amplitudes was developed on the Piton de la Fournaise (Réunion island) for locating tremor, LP events or rockfalls. For each event, seismic amplitudes are corrected for the site effects at each station using coda amplification factors. The spatial amplitude distributions are usually smooth and coherent, and the decay of the amplitude as a function of distance can be used to locate their source. In Réunion, this method was applied to locate the source(s) of eruption tremor. Those sources are usually found at shallow depth and close to the eruptive vents. An application of this characteristic is the possibility of using eruption tremor for locating the eruptive fissures at the beginning of eruptions. We apply this technique in Hawaii for locating LP events at Kilauea volcano. We calculated coda amplification factors for all stations of the network, and coherent and smooth amplitude distributions are also obtained after correcting for the site effect. We located about 150 events which occurred in January 1998 during an increased phase of LP activity. This seismicity, which peaked on January 15, was related to a surge of magma that reached the Pu`u`O`o vent on January 14, following a rapid inflation of Kilauea's summit. The use of the amplitude method provides a new image of the LP activity. The events appear to cluster in a single group, while they are much more scattered when located using arrival times

  20. Elliptic scattering equations

    NASA Astrophysics Data System (ADS)

    Cardona, Carlos; Gomez, Humberto

    2016-06-01

    Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a mathbb{C}{P}^2 space. We show that for the simplest integrand, namely the n - gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ-algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.

  1. Form factor and boundary contribution of amplitude

    NASA Astrophysics Data System (ADS)

    Huang, Rijun; Jin, Qingjun; Feng, Bo

    2016-06-01

    The boundary contribution of an amplitude in the BCFW recursion relation can be considered as a form factor involving boundary operator and unshifted particles. At the tree-level, we show that by suitable construction of Lagrangian, one can relate the leading order term of boundary operators to some composite operators of mathcal{N} = 4 superYang-Mills theory, then the computation of form factors is translated to the computation of amplitudes. We compute the form factors of these composite operators through the computation of corresponding double trace amplitudes.

  2. A link representation for gravity amplitudes

    NASA Astrophysics Data System (ADS)

    He, Song

    2013-10-01

    We derive a link representation for all tree amplitudes in supergravity, from a recent conjecture by Cachazo and Skinner. The new formula explicitly writes amplitudes as contour integrals over constrained link variables, with an integrand naturally expressed in terms of determinants, or equivalently tree diagrams. Important symmetries of the amplitude, such as supersymmetry, parity and (partial) permutation invariance, are kept manifest in the formulation. We also comment on rewriting the formula in a GL( k)-invariant manner, which may serve as a starting point for the generalization to possible Grassmannian contour integrals.

  3. Amplitude- and rise-time-compensated filters

    DOEpatents

    Nowlin, Charles H.

    1984-01-01

    An amplitude-compensated rise-time-compensated filter for a pulse time-of-occurrence (TOOC) measurement system is disclosed. The filter converts an input pulse, having the characteristics of random amplitudes and random, non-zero rise times, to a bipolar output pulse wherein the output pulse has a zero-crossing time that is independent of the rise time and amplitude of the input pulse. The filter differentiates the input pulse, along the linear leading edge of the input pulse, and subtracts therefrom a pulse fractionally proportional to the input pulse. The filter of the present invention can use discrete circuit components and avoids the use of delay lines.

  4. Patterns of high energy massive string scatterings in the Regge regime

    NASA Astrophysics Data System (ADS)

    Ko, Sheng-Lan; Lee, Jen-Chi; Yang, Yi

    2009-06-01

    We calculate high energy massive string scattering amplitudes of open bosonic string in the Regge regime (RR). We found that the number of high energy amplitudes for each fixed mass level in the RR is much more numerous than that of Gross regime (GR) calculated previously. Moreover, we discover that the leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind. In particular, based on a summation algorithm for Stirling number identities developed recently, we discover that the ratios calculated previously among scattering amplitudes in the GR can be extracted from this Kummer function in the RR. We conjecture and give evidences that the existence of these GR ratios in the RR persists to subleading orders in the Regge expansion of all string scattering amplitudes. Finally, we demonstrate the universal power-law behavior for all massive string scattering amplitudes in the RR.

  5. Real Compton scattering via color dipoles

    SciTech Connect

    Kopeliovich, B. Z.; Schmidt, Ivan; Siddikov, M.

    2009-09-01

    We study the photoabsorption reaction and real Compton scattering within the color dipole model. We rely on a photon wave function derived in the instanton-vacuum model and on the energy-dependent phenomenological elastic dipole amplitude. Data for the photoabsorption cross section at high energies agree with our parameter-free calculations. We also provide predictions for the differential real Compton scattering cross section. Although no data for small angle Compton scattering are available so far, this process can be measured in ultraperipheral hadronic and nuclear collisions at the LHC.

  6. Shadowing in Compton scattering on nuclei

    SciTech Connect

    Kopeliovich, B. Z.; Schmidt, Ivan; Siddikov, M.

    2010-05-01

    We evaluate the shadowing effect in deeply virtual and real Compton scattering on nuclei in the framework of the color dipole model. We rely on the soft photon wave function derived in the instanton vacuum model and employ the impact parameter dependent phenomenological elastic dipole amplitude. Both the effects of quark and the gluon shadowing are taken into account.

  7. The isomonodromy method for black hole scattering

    SciTech Connect

    Carneiro da Cunha, Bruno; Novaes, Fábio

    2015-12-17

    We summarize recent results by the authors [7, 8, 35] on the extraction of scattering amplitudes for scalar fields in Kerr/Kerr-de Sitter backgrounds. Analytical, closed forms are found in terms of the Painlevé V and VI transcendents for generic values of the physical parameters.

  8. Asymptotic behaviour of backward elastic scattering

    NASA Astrophysics Data System (ADS)

    Germond, J. F.; Lombard, R. J.

    1988-05-01

    We discuss a compact formula proposed by Dias de Deus and Pimenta for the asymptotic value of the elastic scattering amplitude at backward angles. Improvements and generalization are obtained by means of the saddle-point method which corroborate old calculations by Serber.

  9. Constant-amplitude, frequency- independent phase shifter

    NASA Technical Reports Server (NTRS)

    Deboo, G. J.

    1971-01-01

    Electronic circuit using operational amplifiers provides output with constant phase shift amplitude, with respect to sinusoidal input, over wide range of frequencies. New circuit includes field effect transistor, Q, operational amplifiers, A1 and A2, and phase detector.

  10. Amplitude dynamics favors synchronization in complex networks

    PubMed Central

    Gambuzza, Lucia Valentina; Gómez-Gardeñes, Jesus; Frasca, Mattia

    2016-01-01

    In this paper we study phase synchronization in random complex networks of coupled periodic oscillators. In particular, we show that, when amplitude dynamics is not negligible, phase synchronization may be enhanced. To illustrate this, we compare the behavior of heterogeneous units with both amplitude and phase dynamics and pure (Kuramoto) phase oscillators. We find that in small network motifs the behavior crucially depends on the topology and on the node frequency distribution. Surprisingly, the microscopic structures for which the amplitude dynamics improves synchronization are those that are statistically more abundant in random complex networks. Thus, amplitude dynamics leads to a general lowering of the synchronization threshold in arbitrary random topologies. Finally, we show that this synchronization enhancement is generic of oscillators close to Hopf bifurcations. To this aim we consider coupled FitzHugh-Nagumo units modeling neuron dynamics. PMID:27108847

  11. Azimuthal decorrelation of forward jets in deep inelastic scattering

    SciTech Connect

    Sabio Vera, Agustin; Schwennsen, Florian

    2008-01-01

    We study the azimuthal angle decorrelation of forward jets in deep inelastic scattering. We make predictions for this observable at HERA describing the high energy limit of the relevant scattering amplitudes with quasi-multi-Regge kinematics together with a collinearly-improved evolution kernel for multiparton emissions.

  12. Lorentz violation correction to the Aharonov-Bohm scattering

    NASA Astrophysics Data System (ADS)

    Anacleto, M. A.

    2015-10-01

    In this paper, using a (2 +1 )-dimensional field theory approach, we study the Aharonov-Bohm (AB) scattering with Lorentz symmetry breaking. We obtain the modified scattering amplitude to the AB effect due to the small Lorentz violation correction in the breaking parameter and prove that up to one loop the model is free from ultraviolet divergences.

  13. Symmetry considerations in the scattering of identical composite bodies

    NASA Technical Reports Server (NTRS)

    Norbury, J. W.; Townsend, L. W.; Deutchman, P. A.

    1986-01-01

    Previous studies of the interactions between composite particles were extended to the case in which the composites are identical. The form of the total interaction potential matrix elements was obtained, and guidelines for their explicit evaluation were given. For the case of elastic scattering of identical composites, the matrix element approach was shown to be equivalent to the scattering amplitude method.

  14. Nucleon Distribution Amplitudes from Lattice QCD

    SciTech Connect

    Goeckeler, Meinulf; Kaltenbrunner, Thomas; Warkentin, Nikolaus; Horsley, Roger; Zanotti, James M.; Nakamura, Yoshifumi; Pleiter, Dirk; Schierholz, Gerrit; Rakow, Paul E. L.; Schaefer, Andreas; Stueben, Hinnerk

    2008-09-12

    We calculate low moments of the leading-twist and next-to-leading-twist nucleon distribution amplitudes on the lattice using two flavors of clover fermions. The results are presented in the MS scheme at a scale of 2 GeV and can be immediately applied in phenomenological studies. We find that the deviation of the leading-twist nucleon distribution amplitude from its asymptotic form is less pronounced than sometimes claimed in the literature.

  15. Seismic directional beamforming using cosine amplitude distribution

    NASA Astrophysics Data System (ADS)

    Jiang, T.; Xu, X.; Song, J.; Jia, H.; Ge, L.

    2013-12-01

    o improve the signal-to-noise ratio in seismic exploration, we studied the method of time domain seismic beam-forming based on receiver array (TSBBRA). TSBBRA is useful to extract reflected waves from some target layers and decrease noise from other direction. When noise is strong enough, the control parameter of the method of TSBBRA need to be increased. It means that we have to use more raw records to form a directional seismic record. Therefore, the signal energy in beam is much denser, and the beam becomes narrower accordingly. When the beam can not cover the receiver array, the signal-to-noise ratios in different traces are quite unbalanced and average quality of data probably is still quite low. Therefore, this paper proposes seismic directional beamforming using the cosine amplitude distribution (SDBCAD). SDBCAD can adjust seismic beam shape by introducing cosine amplitude distribution, an amplitude weighting method, in the procedure of beamforming. We studied cosine amplitude weighting function, analyzed the characteristics of uniform and cosine amplitude distribution in beamforming, and compared directivity of beams from the two kind of amplitude pattern. It shows that the main beam of cosine-weighted amplitude is different from uniform distribution. The coverage of main beam from SDBCAD is wider than uniform amplitude, and the width of beam is varied with different number of cosine order. So we simulated the seismic raw record, and used TSBBRA and SDBCAD to process simulated data at the receiving array. The results show that SDBCAD can broaden directional beam, and the main beam from SDBCAD can cover the entire traces instead of partial coverage in TSBBRA. The average signal-to-noise ratio increased 0.2~4.5dB. It concludes that SDBCAD is competent to stretch beam reasonable, and it is useful to boost signal-to-noise ratio when beam from TSBBRA is too narrow to illuminate receiver array properly. Updated results will be presented at the meeting.

  16. The amplitude of quantum field theory

    SciTech Connect

    Medvedev, B.V. ); Pavlov, V.P.; Polivanov, M.K. ); Sukhanov, A.D. )

    1989-05-01

    General properties of the transition amplitude in axiomatic quantum field theory are discussed. Bogolyubov's axiomatic method is chosen as the variant of the theory. The axioms of this method are analyzed. In particular, the significance of the off-shell extension and of the various forms of the causality condition are examined. A complete proof is given of the existence of a single analytic function whose boundary values are the amplitudes of all channels of a process with given particle number.

  17. Twistor-strings and gravity tree amplitudes

    NASA Astrophysics Data System (ADS)

    Adamo, Tim; Mason, Lionel

    2013-04-01

    Recently we discussed how Einstein supergravity tree amplitudes might be obtained from the original Witten and Berkovits twistor-string theory when external conformal gravitons are restricted to be Einstein gravitons. Here we obtain a more systematic understanding of the relationship between conformal and Einstein gravity amplitudes in that twistor-string theory. We show that although it does not in general yield Einstein amplitudes, we can nevertheless obtain some partial twistor-string interpretation of the remarkable formulae recently been found by Hodges and generalized to all tree amplitudes by Cachazo and Skinner. The Hodges matrix and its higher degree generalizations encode the world sheet correlators of the twistor string. These matrices control both Einstein amplitudes and those of the conformal gravity arising from the Witten and Berkovits twistor-string. Amplitudes in the latter case arise from products of the diagonal elements of the generalized Hodges matrices and reduced determinants give the former. The reduced determinants arise if the contractions in the worldsheet correlator are restricted to form connected trees at MHV. The (generalized) Hodges matrices arise as weighted Laplacian matrices for the graph of possible contractions in the correlators and the reduced determinants of these weighted Laplacian matrices give the sum of the connected tree contributions by an extension of the matrix-tree theorem.

  18. Multiple scattering of scalar waves by point scatterers in one dimension. II

    SciTech Connect

    Haacke, E.M.; Foldy, L.L.

    1981-04-01

    In the first paper of this series, we studied the problem of scattering in one dimension of a wave interacting with n randomly distributed pointlike scatterers by delta-function potentials. Averaging the wave function for a constant amplitude transmitted wave over an ensemble of configurations allowed us to obtain an analytic expression for the optical potential which, in certain limits, took the form of the scatterer density (rho) times the scattering strength (GAMMA). We examine the domain in parameter space where rhoGAMMA can be regarded as a good approximation to the optical potential for both this problem and the problem in which the amplitude of the incident wave is constant. The conditions on the parameters are found to be the same in both the preceding problems. We then supplement rhoGAMMA by an appropriate imaginary part. The wave function predicted from this effective potential approximation to the optical potential is in good agreement with that from the exact solution.

  19. The scattering of fast nucleons from nuclei

    SciTech Connect

    Kerman, A. K.; McManus, H.; Thaler, R. M.

    2000-04-10

    The formal theory of the scattering of high-energy nucleons by nuclei is developed in terms of the nucleon nucleon scattering amplitude. The most important approximations necessary to make numerical calculation feasible are then examined. The optical model potential is derived on this basis and compared with the optical model parameters found from experiment. The elastic scattering and polarization of nucleons from light nuclei is predicted and compared with experiment. The effect of nuclear correlations is discussed. The polarization of inelastically scattered nucleons is discussed and predictions compared with experiments. To within the validity of the approximations the experimental data on the scattering of nucleons from nuclei at energies above {approx}100 Mev appears to be consistent with the theory. (c) 2000 Academic Press, Inc.

  20. Ultrasound transmission attenuation tomography using energy-scaled amplitude ratios

    NASA Astrophysics Data System (ADS)

    Chen, Ting; Shin, Junseob; Huang, Lianjie

    2016-04-01

    Ultrasound attenuation of breast tumors is related to their types and pathological states, and can be used to detect and characterize breast cancer. Particularly, ultrasound scattering attenuation can infer the margin properties of breast tumors. Ultrasound attenuation tomography quantitatively reconstructs the attenuation properties of the breast. Our synthetic-aperture breast ultrasound tomography system with two parallel transducer arrays records both ultrasound reflection and transmission signals. We develop an ultrasound attenuation tomography method using ultrasound energy-scaled amplitude decays of ultrasound transmission signals and conduct ultrasound attenuation tomography using a known sound-speed model. We apply our ultrasound transmission attenuation tomography method to a breast phantom dataset, and compare the ultrasound attenuation tomography results with conventional beamforming ultrasound images obtained using reflection signals. We show that ultrasound transmission attenuation tomography complements beamforming images in identifying breast lesions.

  1. Picosecond time-domain electromagnetic scattering from conducting cylinders

    NASA Astrophysics Data System (ADS)

    Robertson, W. M.; Kopcsay, G. V.; Arjavalingam, G.

    1991-12-01

    The microwave scattering properties of conducting cylinders are characterized by measuring their response to picosecond-duration electromagnetic pulses. The ultrafast electromagnetic transients are generated and detected with optoelectronically pulsed antennas. The time-domain response gives physical insight into the scattering process. In addition, Fourier analysis is used to obtain the frequency dependence of the scattered amplitude and phase from 15 to 140 GHz.

  2. VLF scattering from Red Sprites-Theory

    NASA Astrophysics Data System (ADS)

    Rodger, C. J.; Wait, J. R.; Dowden, R. L.

    1998-05-01

    A relatively simple model of Red Sprites as a set of conducting columns reproduces the radio physics properties of VLF sprites. The columnar structure of optical sprites is represented by thin vertical conducting columns (or `Spritelets') in free space, with dimensions taken from optical observations. The scattered field from a set of coupled Spritelets has a complex amplitude pattern which normally includes some deep minima reproducing the `perturbation shadows' seen in some experimental events. It is not uncommon for the back scattered amplitudes to be similar to those for forward scatter in the theoretical model, as in experimental reports. As some sprite events appear to have closely spaced Spritelets, the results presented here indicate that there will be a high degree of electrical shielding. This is an application of the theory presented by[Rodger et al. (1997a)].

  3. New optimal polynomial theory for NN-scattering

    SciTech Connect

    Rijken, T A; Signell, P

    1980-01-01

    A new optimal polynomial theory for nucleon-nucleon scattering is presented. For the first time in nucleon-nucleon scattering, the derivative amplitudes originally introduced by Fubini, Furlan, and Rosetti are applied. Based on the properties of these amplitudes we introduce K-matrix functions which have suitable analyticity properties as functions of cos theta, where theta is the center of mass scattering angle. The K-matrix functions enable introduction of a new set of functions for which the optimal mapping techniques of Cutkosky, Deo and Ciulli can be applied. Results are shown for proton-proton phase shift analyses at 210 and 330 MeV.

  4. Tectonic Tremor Source Amplitude in Northern Cascadia

    NASA Astrophysics Data System (ADS)

    Ulberg, C. W.; Creager, K. C.; Klaus, A. J.; Wech, A.

    2012-12-01

    Most studies of tectonic tremor have focused on tremor location and duration. We examine tremor source amplitude in northern Cascadia, and explore its importance in understanding the physical processes generating tremor and slow slip. In Cascadia, we observe a linear increase in tremor source amplitude during the approximately five-day initiation phase of episodic tremor and slip (ETS) events, apparently associated with a linear increase in the area where tremor is occurring. There is also mounting evidence that tremor amplitude during ETS events is strongly modulated by tidal stresses (e.g. Rubinstein et al, Science, 2008), including the most recent northern Cascadia ETS events of 2010 and 2011. This suggests a low coefficient of friction on the subduction interface. We will extend our existing amplitude catalog of the 2010 and 2011 Cascadia ETS events to include all of 2006 to 2012, incorporating multiple data sets and providing more insight into the spatial distribution of tremor, the initiation phase of ETS events, and tidal forcing of ETS and inter-ETS tremor. Tremor source amplitudes are estimated with a method similar to Maeda and Obara (JGR, 2009), using the proportional relationship between source amplitude and the root-mean square of band-limited (1.5 to 5.5 Hz) ground velocity for every 5-minute window. We use horizontal component seismograms from the CAFE (2006-2008) and Array of Arrays (2009-2011) experiments, as well as permanent PNSN stations. Tremor locations were determined using a waveform envelope cross-correlation method (Wech and Creager, GRL, 2008). We perform an inversion using these tremor locations and station ground velocities to determine the tremor source amplitude and station statics, taking into account geometric spreading and seismic attenuation.

  5. Multichannel 1 → 2 transition amplitudes in a finite volume

    SciTech Connect

    Briceno, Raul A.; Hansen, Maxwell T.; Walker-Loud, Andre

    2015-02-03

    We perform a model-independent, non-perturbative investigation of two-point and three-point finite-volume correlation functions in the energy regime where two-particle states can go on-shell. We study three-point functions involving a single incoming particle and an outgoing two-particle state, relevant, for example, for studies of meson decays (e.g., B⁰ → K*l⁺l⁻) or meson photo production (e.g., πγ* → ππ). We observe that, while the spectrum solely depends upon the on-shell scattering amplitude, the correlation functions also depend upon off-shell amplitudes. The main result of this work is a non-perturbative generalization of the Lellouch-Luscher formula relating matrix elements of currents in finite and infinite spatial volumes. We extend that work by considering a theory with multiple, strongly-coupled channels and by accommodating external currents which inject arbitrary four-momentum as well as arbitrary angular-momentum. The result is exact up to exponentially suppressed corrections governed by the pion mass times the box size. We also apply our master equation to various examples, including two processes mentioned above as well as examples where the final state is an admixture of two open channels.

  6. Involution-dependent constants and the cancellation of divergences in the 1-loop open string amplitude

    SciTech Connect

    Nagao, G.

    1987-12-01

    We recalculate the bosonic 1-loop open string scattering amplitude using the results of the bosonic 1-loop closed string amplitude. The results show explicitly how the cancellation of divergences depends upon of a set of involution-dependent constants which relate the torus to the cylinder and Moebius strip. Such a set of involution-dependent constants exists at each loop level and thus provides a means with which to study the cancellation of divergences and the connection between the world-sheet and internal symmetries. 14 refs., 3 figs.

  7. Minimal unitary (covariant) scattering theory

    SciTech Connect

    Lindesay, J.V.; Markevich, A.

    1983-06-01

    In the minimal three particle equations developed by Lindesay the two body input amplitude was an on shell relativistic generalization of the non-relativistic scattering model characterized by a single mass parameter ..mu.. which in the two body (m + m) system looks like an s-channel bound state (..mu.. < 2m) or virtual state (..mu.. > 2m). Using this driving term in covariant Faddeev equations generates a rich covariant and unitary three particle dynamics. However, the simplest way of writing the relativisitic generalization of the Faddeev equations can take the on shell Mandelstam parameter s = 4(q/sup 2/ + m/sup 2/), in terms of which the two particle input is expressed, to negative values in the range of integration required by the dynamics. This problem was met in the original treatment by multiplying the two particle input amplitude by THETA(s). This paper provides what we hope to be a more direct way of meeting the problem.

  8. A description of seismic amplitude techniques

    NASA Astrophysics Data System (ADS)

    Shadlow, James

    2014-02-01

    The acquisition of seismic data is a non-invasive technique used for determining the sub surface geology. Changes in lithology and fluid fill affect the seismic wavelet. Analysing seismic data for direct hydrocarbon indicators (DHIs), such as full stack amplitude anomalies, or amplitude variation with offset (AVO), can help a seismic interpreter relate the geophysical response to real geology and, more importantly, to distinguish the presence of hydrocarbons. Inversion is another commonly used technique that attempts to tie the seismic data back to the geology. Much has been written about these techniques, and attempting to gain an understanding on the theory and application of them by reading through various journals can be quite daunting. The purpose of this paper is to briefly outline DHI analysis, including full stack amplitude anomalies, AVO and inversion and show the relationship between all three. The equations presented have been included for completeness, but the reader can pass over the mathematical detail.

  9. Periodic amplitude variations in Jovian continuum radiation

    NASA Astrophysics Data System (ADS)

    Kurth, W. S.; Gurnett, D. A.; Scarf, F. L.

    1986-12-01

    An analysis of periodic variations in the amplitude of continuum radiation near 3 kHz trapped in the Jovian magnetosphere shows structure with periods near both 5 and 10 horus. Contrary to a plausible initial idea, the continuum amplitudes are not organized by the position of the observer relative to the dense plasma sheet. Instead, there seem to be perferred orientations of system III longitude with respect to the direction to the sun which account for the peaks. This implies a clocklike modulation of the continuum radiation intensity as opposed to a searchlight effect. The importance of the dipole longitude solar wind alignment to the amplitude of the continuum radiation implies that the source region of the radiation is near the magnetopause and may indirectly tie the generation of the radio waves to the clocklike modulation of energetic electron fluxes from Jupiter.

  10. Cut-constructible part of QCD amplitudes

    SciTech Connect

    Britto, Ruth; Feng Bo; Mastrolia, Pierpaolo

    2006-05-15

    Unitarity cuts are widely used in analytic computation of loop amplitudes in gauge theories such as QCD. We expand upon the technique introduced in hep-ph/0503132 to carry out any finite unitarity cut integral. This technique naturally separates the contributions of bubble, triangle and box integrals in one-loop amplitudes and is not constrained to any particular helicity configurations. Loop momentum integration is reduced to a sequence of algebraic operations. We discuss the extraction of the residues at higher-order poles. Additionally, we offer concise algebraic formulas for expressing coefficients of three-mass triangle integrals. As an application, we compute all remaining coefficients of bubble and triangle integrals for nonsupersymmetric six-gluon amplitudes.