NASA Astrophysics Data System (ADS)
Spinrath, Martin
2016-06-01
There is a wide class of models which give a dynamical description of the origin of flavor in terms of spontaneous symmetry breaking of an underlying symmetry. Many of these models exhibit sum rules which relate on the one hand mixing angles and the Dirac CP phase with each other and/or on the other hand neutrino masses and Majorana phases with each other. We will briefly sketch how this happens and discuss briefly the impact of renormalization group corrections to the mass sum rules.
Exact sum rules for inhomogeneous strings
Amore, Paolo
2013-11-15
We derive explicit expressions for the sum rules of the eigenvalues of inhomogeneous strings with arbitrary density and with different boundary conditions. We show that the sum rule of order N may be obtained in terms of a diagrammatic expansion, with (N−1)!/2 independent diagrams. These sum rules are used to derive upper and lower bounds to the energy of the fundamental mode of an inhomogeneous string; we also show that it is possible to improve these approximations taking into account the asymptotic behavior of the spectrum and applying the Shanks transformation to the sequence of approximations obtained to the different orders. We discuss three applications of these results. -- Highlights: •We derive an explicit expression for the sum rules of an inhomogeneous string. •We obtain a diagrammatic representation for the sum rules of a given order. •We obtain precise bounds on the lowest eigenvalue of the string.
Generalized Thomas-Reiche-Kuhn sum rule
Zhou Binglu; Zhu Jiongming; Yan Zongchao
2006-01-15
The generalized Thomas-Reiche-Kuhn sum rule is established for any Coulombic system with arbitrary masses and charges of its constituent particles. Numerical examples are given for the hydrogen molecular ions.
Systematics of strength function sum rules
NASA Astrophysics Data System (ADS)
Johnson, Calvin W.
2015-11-01
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink-Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink-Axel hypothesis is unsurprising: one expects sum rules to evolve with excitation energy. Furthermore, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).
Exact sum rules for inhomogeneous drums
Amore, Paolo
2013-09-15
We derive general expressions for the sum rules of the eigenvalues of drums of arbitrary shape and arbitrary density, obeying different boundary conditions. The formulas that we present are a generalization of the analogous formulas for one dimensional inhomogeneous systems that we have obtained in a previous paper. We also discuss the extension of these formulas to higher dimensions. We show that in the special case of a density depending only on one variable the sum rules of any integer order can be expressed in terms of a single series. As an application of our result we derive exact sum rules for the homogeneous circular annulus with different boundary conditions, for a homogeneous circular sector and for a radially inhomogeneous circular annulus with Dirichlet boundary conditions. -- Highlights: •We derive an explicit expression for the sum rules of inhomogeneous drums. •We discuss the extension to higher dimensions. •We discuss the special case of an inhomogeneity only along one direction.
Generalized Sum Rules of the Nucleon
NASA Astrophysics Data System (ADS)
Gorshteyn, Mikhail; Szczepaniak, Adam
2008-10-01
We consider doubly virtual Compton scattering (VVCS) off the nucleon with the photon virtualities q1^2=q2^2=-Q^2 and formulate the low energy theorem (LET) for this process. We show that the LET can only be defined at finite momentum transfer t=-2Q^2 which is at variance with existing studies in the literature. Combining LET with dispersion relations for the forward VVCS amplitude, we obtain the new, correct version of the generalized sum rules of the nucleon that state a correspondence between the low energy constants of VVCS and the moments of the DIS structure functions. We notice that the t-channel unitarity is necessary to translate the forward dispersion relations to the low energy limit. This approach leads to a substantial modification of the generalized GDH sum rule at finite Q^2 that undergoes extensive studies at JLab. For the spin-independent VVCS amplitude, the new sum rule for the generalized magnetic susceptibility β(Q^2) is obtained. Our approach provides a consistent, Lorentz invariant formulation of LET for the most general VVCS process that removes inconsistencies that stain the previous studies of the generalized polarizabilities of virtual Compton scattering and the generalized sum rules of the nucleon.
Systematics of strength function sum rules
Johnson, Calvin W.
2015-08-28
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink–Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens,more » violation of the generalized Brink–Axel hypothesis is unsurprising: one expectssum rules to evolve with excitation energy. Moreover, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).« less
Systematics of strength function sum rules
Johnson, Calvin W.
2015-08-28
Sum rules provide useful insights into transition strength functions and are often expressed as expectation values of an operator. In this letter I demonstrate that non-energy-weighted transition sum rules have strong secular dependences on the energy of the initial state. Such non-trivial systematics have consequences: the simplification suggested by the generalized Brink–Axel hypothesis, for example, does not hold for most cases, though it weakly holds in at least some cases for electric dipole transitions. Furthermore, I show the systematics can be understood through spectral distribution theory, calculated via traces of operators and of products of operators. Seen through this lens, violation of the generalized Brink–Axel hypothesis is unsurprising: one expectssum rules to evolve with excitation energy. Moreover, to lowest order the slope of the secular evolution can be traced to a component of the Hamiltonian being positive (repulsive) or negative (attractive).
A cluster version of the GGT sum rule
NASA Astrophysics Data System (ADS)
Hencken, Kai; Baur, Gerhard; Trautmann, Dirk
2004-03-01
We discuss the derivation of a "cluster sum rule" from the Gellmann-Goldberger-Thirring (GGT) sum rule as an alternative to the Thomas-Reiche-Kuhn (TRK) sum rule, which was used as the basis up to now. We compare differences in the assumptions and approximations. Some applications of the sum rule for halo nuclei, as well as, nuclei with a pronounced cluster structure are discussed.
The beauty of impurities: Two revivals of Friedel's virtual bound-state concept
NASA Astrophysics Data System (ADS)
Georges, Antoine
2016-03-01
Jacques Friedel pioneered the theoretical study of impurities and magnetic impurities in metals. He discovered Friedel oscillations, introduced the concept of virtual bound-state, and demonstrated that the charge on the impurity is related to the scattering phase-shift at the Fermi level (Friedel sum-rule). After a brief review of some of these concepts, I describe how they proved useful in two new contexts. The first one concerns the Coulomb blockade in quantum dots, and its suppression by the Kondo effect. The second one is the dynamical mean-field theory of strong electronic correlations. xml:lang="fr"
Tuning sum rules with window functions for optical constant evaluation
NASA Astrophysics Data System (ADS)
Rodríguez-de Marcos, Luis V.; Méndez, José A.; Larruquert, Juan I.
2016-07-01
Sum rules are a useful tool to evaluate the global consistency of a set of optical constants. We present a procedure to spectrally tune sum rules to evaluate the local consistency of optical constants. It enables enhancing the weight of a desired spectral range within the sum-rule integral. The procedure consists in multiplying the complex refractive index with an adapted function, which is named window function. Window functions are constructed through integration of Lorentz oscillators. The asymptotic decay of these window functions enables the derivation of a multiplicity of sum rules akin to the inertial sum rule, along with one modified version of f-sum rule. This multiplicity of sum rules combined with the free selection of the photon energy range provides a double way to tune the spectral contribution within the sum rule. Window functions were applied to reported data of SrF2 and of Al films in order to check data consistency over the spectrum. The use of window functions shows that the optical constants of SrF2 are consistent in a broad spectrum. Regarding Al, some spectral ranges are seen to present a lower consistency, even though the standard sum rules with no window function did not detect inconsistencies. Hence window functions are expected to be a helpful tool to evaluate the local consistency of optical constants.
Charmonium sum rules applied to a holographic model
Hohler, Paul M.
2011-01-15
The heavy-quark QCD sum rules are applied to a model of charmonium based upon the gauge/gravity duality. We find that there is strong agreement between the moments of the polarization function calculated from the holographic model and the experimental data suggesting that the model is consistent with the heavy-quark QCD sum rules at zero temperature.
Exact sum rules for inhomogeneous systems containing a zero mode
Amore, Paolo
2014-10-15
We show that the formulas for the sum rules for the eigenvalues of inhomogeneous systems that we have obtained in two recent papers are incomplete when the system contains a zero mode. We prove that there are finite contributions of the zero mode to the sum rules and we explicitly calculate the expressions for the sum rules of order one and two. The previous results for systems that do not contain a zero mode are unaffected. - Highlights: • We discuss the sum rules of the eigenvalues of inhomogeneous systems containing a zero mode. • We derive the explicit expressions for sum rules of order one and two. • We perform accurate numerical tests of these results for three examples.
QCD sum rules on the complex Borel plane
NASA Astrophysics Data System (ADS)
Araki, Ken-Ji; Ohtani, Keisuke; Gubler, Philipp; Oka, Makoto
2014-07-01
Borel-transformed QCD sum rules conventionally use a real-valued parameter (the Borel mass) for specifying the exponential weight over which hadronic spectral functions are averaged. In this paper, it is shown that the Borel mass can be generalized to have complex values and that new classes of sum rules can be derived from the resulting averages over the spectral functions. The real and imaginary parts of these novel sum rules turn out to have damped oscillating kernels and potentially contain a larger amount of information on the hadronic spectrum than the real-valued QCD sum rules. As a first practical test, we have formulated complex Borel sum rules for the φ -meson channel and have analyzed them using the maximum entropy method, by which we can extract the most probable spectral function from the sum rules without strong assumptions on its functional form. As a result, it is demonstrated that, compared to earlier studies, the complex-valued sum rules allow us to extract the spectral function with a significantly improved resolution and thus to study more detailed structures of the hadronic spectrum than previously possible.
Friedel phase discontinuity and bound states in the continuum in quantum dot systems
NASA Astrophysics Data System (ADS)
Solís, B.; Ladrón de Guevara, M. L.; Orellana, P. A.
2008-06-01
In this Letter we study the Friedel phase of the electron transport in two different systems of quantum dots which exhibit bound states in the continuum (BIC). The Friedel phase jumps abruptly in the energies of the BICs, which is associated to the vanishing width of these states, as shown by Friedrich and Wintgen in [H. Friedrich, D. Wintgen, Phys. Rev. A 31 (1985) 3964]. This odd behavior of the Friedel phase has consequences in the charge through the Friedel sum rule. Namely, if the energy of the BIC drops under the Fermi energy the charge changes abruptly in a unity. We show that this behavior closely relates to discontinuities in the conductance predicted for interacting quantum dot systems.
Quark mixing sum rules and the right unitarity triangle
Antusch, Stefan; Spinrath, Martin; King, Stephen F.; Malinsky, Michal
2010-02-01
In analogy with the recently proposed lepton mixing sum rules, we derive quark mixing sum rules for the case of hierarchical quark mass matrices with 1-3 texture zeros, in which the separate up and down-type 1-3 mixing angles are approximately zero, and V{sub ub} is generated from V{sub cb} as a result of 1-2 up-type quark mixing. Using the sum rules, we discuss the phenomenological viability of such textures, including up to four texture zeros, and show how the right-angled unitarity triangle, i.e., {alpha}{approx_equal}90 deg., can be accounted for by a remarkably simple scheme involving real mass matrices apart from a single element being purely imaginary. In the framework of grand unified theories, we show how the quark and lepton mixing sum rules may combine to yield an accurate prediction for the reactor angle.
Compton scattering from nuclei and photo-absorption sum rules
NASA Astrophysics Data System (ADS)
Gorchtein, Mikhail; Hobbs, Timothy; Londergan, J. Timothy; Szczepaniak, Adam P.
2011-12-01
We revisit the photo-absorption sum rule for real Compton scattering from the proton and from nuclear targets. In analogy with the Thomas-Reiche-Kuhn sum rule appropriate at low energies, we propose a new “constituent quark model” sum rule that relates the integrated strength of hadronic resonances to the scattering amplitude on constituent quarks. We study the constituent quark model sum rule for several nuclear targets. In addition, we extract the α=0 pole contribution for both proton and nuclei. Using the modern high-energy proton data, we find that the α=0 pole contribution differs significantly from the Thomson term, in contrast with the original findings by Damashek and Gilman.
Q^2 dependence of generalized Baldin sum rule
Y. Liang
2005-02-01
The generalized Baldin sum rule for virtual photon, an unpolarized analog of the generalized Gerasimov-Drell-Hearn sum rule, provides an unique way to investigate the transition between the perturbative QCD and hadronic descriptions of nucleon structure. We report on new measurements in Hall C at Jefferson Lab of the generalized Baldin integral for the proton at Q^2 of 0.3-4.0 GeV^2.
Charm and bottom hadronic form factors with QCD sum rules
Bracco, M. E.; Rodrigues, B. O.; Cerqueira, A. Jr.
2013-03-25
We present a brief review of some calculations of form factors and coupling constants in vertices with charm and bottom mesons in the framework of QCD sum rules. We first discuss the motivation for this work, describing possible applications of these form factors to charm and bottom decays processes. We first make a summarize of the QCD sum rules method. We give special attention to the uncertainties of the method introducing by the intrinsic variation of the parameters. Finally we conclude.
Coulomb sum rule for {sup 4}He
J. Carlson; J. Jourdan; R. Schiavilla; I. Sick
2002-10-01
We determine the Coulomb sum for {sup 4}He using world data on {sup 4}He(e, e') and compare the results to calculations based on realistic interactions and including two-body components in the nuclear charge operator. We find good agreement between theory and experiment using free-nucleon form factors. The apparent reduction of the in-medium G{sub ep} implied by IA-interpretation of the L/T-ratios measured in {sup 4}He(e,e'p) and {sup 4}He([vec]e, e'p) is not confirmed.
Additional corrections to the Gross-Llewellyn Smith sum rule
Londergan, J. T.; Thomas, A. W.
2010-12-01
We investigate some QCD corrections that contribute to the Gross-Llewellyn Smith sum rule but have not been included in previous analyses of it. We first review the techniques by which the xF{sub 3} structure function is extracted from combinations of neutrino and antineutrino cross sections. Next we investigate corrections to the Gross-Llewellyn Smith sum rule, with particular attention to contributions arising from strange quark distributions and from charge symmetry violating parton distributions. We find that additional corrections from strange quarks and parton charge symmetry violation are likely to have a small but potentially significant role in decreasing the current discrepancy between the experimental and theoretical estimates of the Gross-Llewellyn Smith sum rule.
Nucleon QCD sum rules in the instanton medium
Ryskin, M. G.; Drukarev, E. G. Sadovnikova, V. A.
2015-09-15
We try to find grounds for the standard nucleon QCD sum rules, based on a more detailed description of the QCD vacuum. We calculate the polarization operator of the nucleon current in the instanton medium. The medium (QCD vacuum) is assumed to be a composition of the small-size instantons and some long-wave gluon fluctuations. We solve the corresponding QCD sum rule equations and demonstrate that there is a solution with the value of the nucleon mass close to the physical one if the fraction of the small-size instantons contribution is w{sub s} ≈ 2/3.
A Derivative of the Gerasimov-Drell-Hearn Sum Rule
Vladimir Pascalutsa; Barry Holstein; Marc Vanderhaeghen
2004-08-01
We derive a sum rule which establishes a linear relation between a particle's anomalous magnetic moment and a quantity connected to the photoabsorption cross-section. This quantity cannot be measured directly. However, it can be computed within a given theory. As an example, we demonstrate validity of the sum rule in QED at tree level---the renowned Schwinger's correction to the anomalous magnetic moment is readily reproduced. In the case of the strong interactions, we also consider the calculation of the nucleon magnetic moment within chiral theories.
Decay Constants of Beauty Mesons from QCD Sum Rules
NASA Astrophysics Data System (ADS)
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2014-11-01
Our recently completed analysis of the decay constants of both pseudoscalar and vector beauty mesons reveals that in the bottom-quark sector two specific features of the sum-rule predictions show up: (i) For the input value of the bottom-quark mass in the M̅S̅ scheme m̅b(m̅b) ≈ 4:18 GeV; the sum-rule result fB ≈ 210-220 MeV for the B meson decay constant is substantially larger than the recent lattice-QCD finding fB ≈ 190 MeV: Requiring QCD sum rules to reproduce the lattice-QCD value of fB yields a significantly larger b-quark mass: m̅b(m̅b) = 4:247 GeV: (ii) Whereas QCD sum-rule predictions for the charmed-meson decay constants fD; fDs, fD* and fDs* are practically independent of the choice of renormalization scale, in the beauty sector the results for the decay constants—and especially for the ratio fB* / fB—prove to be very sensitive to the specific scale setting.
Beauty vector meson decay constants from QCD sum rules
NASA Astrophysics Data System (ADS)
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2016-01-01
We present the outcomes of a very recent investigation of the decay constants of nonstrange and strange heavy-light beauty vector mesons, with special emphasis on the ratio of any such decay constant to the decay constant of the corresponding pseudoscalar meson, by means of Borel-transformed QCD sum rules. Our results suggest that both these ratios are below unity.
Inequalities for frequency-moment sum rules of electron liquids
NASA Technical Reports Server (NTRS)
Iwamoto, N.
1986-01-01
The relations between the various frequency-moment sum rules of electron liquids, which include even-power moments, are systematically examined by using the Cauchy-Schwarz and Hoelder inequalities. A relation involving the isothermal sound velocity and the kinetic and potential energies is obtained from one of the inequalities in the long-wavelength limit, and is generalized to arbitrary spatial dimensions.
Spectral sum rules for confining large- N theories
NASA Astrophysics Data System (ADS)
Cherman, Aleksey; McGady, David A.; Yamazaki, Masahito
2016-06-01
We consider asymptotically-free four-dimensional large- N gauge theories with massive fermionic and bosonic adjoint matter fields, compactified on squashed three-spheres, and examine their regularized large- N confined-phase spectral sums. The analysis is done in the limit of vanishing 't Hooft coupling, which is justified by taking the size of the compactification manifold to be small compared to the inverse strong scale Λ-1. Our results motivate us to conjecture some universal spectral sum rules for these large N gauge theories.
Gottfried sum rule and the ratio Fn2/Fp2
NASA Astrophysics Data System (ADS)
Arash, Firooz
1995-07-01
We describe the nucleon as a bound state of three constituent objects, called ``valons,'' which themselves have structure. At high enough Q2 it is the valon structure, governed by QCD, which is probed and, thus, the nucleon structure is described in terms of its partonic distributions, while at low Q2 the nucleon is described in terms of its valon distributions, independent of a probe and controlled by nonperturbative QCD. The implications of this phenomenological model, then, are applied to the New Muon Collaboration (NMC) data for Fn2/Fp2 and on the Gottfried sum rule. It is shown that the model successfully reproduces the experimental value of the Gottfried sum rule SG[0<=x1,
Otto Stern, the Gdh Sum Rule and Various Spin Crises
NASA Astrophysics Data System (ADS)
Drechsel, D.
2001-02-01
The history of spin and anomalous magnetic moment is full of puzzles and "crises" from the first observations in the 1920's to the present day. The Gerasimov-Drell-Hearn sum rule connects the anomalous magnetic moment with the helicity dependent cross section for photoproduction, and as such checks the internal consistency of our understanding of the nucleon spin structure. Various generalizations of the sum rule have been proposed for the case of virtual photons, thus interpolating from the real photon point to deep inelastic scattering. A series of recent and newly proposed experiments with beam and target/recoil polarization will study this transition between the coherent spin-dependent response and the incoherent response of the partons in the scaling region.
Heavy-meson decay constants from QCD sum rules
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2010-12-22
We sketch a recent sum-rule extraction of the decay constants of the heavy pseudoscalar mesons D, D{sub s}, B, and B{sub s} from the two-point correlator of heavy-light pseudoscalar currents. Our main emphasis lies on the control over all the uncertainties in the decay constants, related both to the input QCD parameters and to the limited accuracy of the method of sum rules. Gaining this control has become possible by application of our new procedure of extracting hadron observables based on a dual threshold depending on the Borel parameter. For the charmed-meson decay constants, we find fD = (206.2{+-}7.3{sub (OPE)}{+-}5.1{sub (syst)}) MeV, fD{sub s} = (245.3{+-}15.7{sub (OPE)}{+-}4.5{sub (syst)}) MeV. For the beauty mesons, the decay constants turn out to be extremely sensitive to the precise value of the {ovr MS} mass of the b-quark, {bar m}{sub b}({bar m}{sub b}). By requiring our sum-rule estimate to match the average of the lattice determinations of f{sub B}, we extract the rather accurate value {bar m}{sub b}({bar m}{sub b}) = (4.245{+-}0.025) GeV. Feeding this parameter value into our sum-rule formalism leads to the beauty-meson decay constants fB = (193.4{+-}12.3{sub (OPE)}{+-}4.3{sub (syst)}) MeV, fB{sub s} = (232.5{+-}18.6{sub (OPE)}{+-}2.4{sub (syst)}) MeV.
On Gravitational Form Factors and Transverse Spin Sum Rule
NASA Astrophysics Data System (ADS)
Chakrabarti, D.; Mondal, C.; Mukherjee, A.
2016-06-01
Using the light front wave functions of the scalar quark-diquark model for nucleon predicted by the soft-wall AdS/QCD, we calculate the flavor dependent gravitational form factors. We evaluate the matrix element of Pauli-Lubanski operator in this model and show that the intrinsic spin sum rule involves the higher twist form factor {bar{C}}. The longitudinal momentum densities in the transverse impact parameter space are also discussed for both unpolarized and transversely polarized nucleons.
Choice of nucleon current in QCD sum rule calculations
Indumathi, D.
1995-06-01
The author studies the correlator occurring in the calculation of nucleon structure functions in the QCD sum rule technique. The author shows+ that the property of gauge invariance of this four-point function in the spin dependent sector uniquely fixes the choice of nucleon current in such computations. No such constraint is obtainable from similar considerations in the spin-independent sector. 14 refs., 5 figs.
A QCD Sum Rules Approach to Mixing of Hadrons
Aliev, T. M.; Ozpineci, A.; Zamiralov, V. S.
2010-12-28
A method for the calculation of the hadronic mixing angles using QCD sum rules is proposed. This method is then applied to predict the mixing angle between the heavy cascade hyperons {Xi}{sub Q} and {Xi}{sub Q}{sup '} where Q = c or Q = b. It is obtained the {theta}{sub b} = 6.4 deg. {+-}1.8 deg. and {theta}{sub c} = 5.5 deg. {+-}1.8 deg.
On the loop approximation in nucleon QCD sum rules
Drukarev, E. G. Ryskin, M. G.; Sadovnikova, V. A.
2015-10-15
There was a general belief that the nucleon QCD sum rules which include only the quark loops and thus contain only the condensates of dimension d = 3 and d = 4 have only a trivial solution. We demonstrate that there is also a nontrivial solution. We show that it can be treated as the lowest order approximation to the solution which includes the higher terms of the Operator Product Expansion. Inclusion of the radiative corrections improves the convergence of the series.
Sum rules for the polarization correlations in photoionization and bremsstrahlung
NASA Astrophysics Data System (ADS)
Pratt, R. H.; Müller, R. A.; Surzhykov, A.
2016-05-01
The polarization correlations in doubly differential cross sections are investigated for photoionization and ordinary bremsstrahlung. These correlations describe the polarization transfer between incident light and ejected photoelectrons as well as between an incoming electron beam and bremsstrahlung light, respectively. They are characterized by a set of seven real parameters Ci j. We show that the squares of these parameters are connected by simple "sum rules." These sum rules can be applied for both one-electron systems and also for atoms, if the latter are described within the independent particle approximation. In particular, they are exact in their simplest form (i) for the photoionization of K -, LI ,I I-, and MI ,I I-atomic shells, as well as (ii) for bremsstrahlung in which the electron is scattered into s1 /2 or p1 /2 states, as in the tip (bremsstrahlung) region. Detailed calculations are performed to verify the derived identities and to discuss their possible applications for the analysis of modern photoionization and bremsstrahlung experiments. In particular, we argue that the sum rules may help to determine the entire set of (significant) polarization correlations in the case when not all Ci j are available for experimental observation.
Relativistic and Nuclear Medium Effects on the Coulomb Sum Rule
NASA Astrophysics Data System (ADS)
Cloët, Ian C.; Bentz, Wolfgang; Thomas, Anthony W.
2016-01-01
In light of the forthcoming high precision quasielastic electron scattering data from Jefferson Lab, it is timely for the various approaches to nuclear structure to make robust predictions for the associated response functions. With this in mind, we focus here on the longitudinal response function and the corresponding Coulomb sum rule for isospin-symmetric nuclear matter at various baryon densities. Using a quantum field-theoretic quark-level approach which preserves the symmetries of quantum chromodynamics, as well as exhibiting dynamical chiral symmetry breaking and quark confinement, we find a dramatic quenching of the Coulomb sum rule for momentum transfers |q |≳0.5 GeV . The main driver of this effect lies in changes to the proton Dirac form factor induced by the nuclear medium. Such a dramatic quenching of the Coulomb sum rule was not seen in a recent quantum Monte Carlo calculation for carbon, suggesting that the Jefferson Lab data may well shed new light on the explicit role of QCD in nuclei.
Radiative corrections to the solar lepton mixing sum rule
NASA Astrophysics Data System (ADS)
Zhang, Jue; Zhou, Shun
2016-08-01
The simple correlation among three lepton flavor mixing angles ( θ 12, θ 13, θ 23) and the leptonic Dirac CP-violating phase δ is conventionally called a sum rule of lepton flavor mixing, which may be derived from a class of neutrino mass models with flavor symmetries. In this paper, we consider the solar lepton mixing sum rule θ 12 ≈ θ 12 ν + θ 13 cos δ, where θ 12 ν stems from a constant mixing pattern in the neutrino sector and takes the value of θ 12 ν = 45 ° for the bi-maximal mixing (BM), {θ}_{12}^{ν } = { tan}^{-1}(1/√{2}) ≈ 35.3° for the tri-bimaximal mixing (TBM) or {θ}_{12}^{ν } = { tan}^{-1}(1/√{5+1}) ≈ 31.7° for the golden-ratio mixing (GR), and investigate the renormalization-group (RG) running effects on lepton flavor mixing parameters when this sum rule is assumed at a superhigh-energy scale. For illustration, we work within the framework of the minimal supersymmetric standard model (MSSM), and implement the Bayesian approach to explore the posterior distribution of δ at the low-energy scale, which becomes quite broad when the RG running effects are significant. Moreover, we also discuss the compatibility of the above three mixing scenarios with current neutrino oscillation data, and observe that radiative corrections can increase such a compatibility for the BM scenario, resulting in a weaker preference for the TBM and GR ones.
Relativistic and Nuclear Medium Effects on the Coulomb Sum Rule.
Cloët, Ian C; Bentz, Wolfgang; Thomas, Anthony W
2016-01-22
In light of the forthcoming high precision quasielastic electron scattering data from Jefferson Lab, it is timely for the various approaches to nuclear structure to make robust predictions for the associated response functions. With this in mind, we focus here on the longitudinal response function and the corresponding Coulomb sum rule for isospin-symmetric nuclear matter at various baryon densities. Using a quantum field-theoretic quark-level approach which preserves the symmetries of quantum chromodynamics, as well as exhibiting dynamical chiral symmetry breaking and quark confinement, we find a dramatic quenching of the Coulomb sum rule for momentum transfers |q|≳0.5 GeV. The main driver of this effect lies in changes to the proton Dirac form factor induced by the nuclear medium. Such a dramatic quenching of the Coulomb sum rule was not seen in a recent quantum Monte Carlo calculation for carbon, suggesting that the Jefferson Lab data may well shed new light on the explicit role of QCD in nuclei. PMID:26849589
Sum rules for M2 and other cases
Kurath, D.
1995-08-01
Sum rules were derived for parity-changing operators consisting of an odd-l spherical harmonic coupled to the spin operator sigma. The conditions are that the valence nucleons are in the oscillator shell with Q quanta and the shell with Q-1 quanta is full and the shell with Q+1 quanta is empty. Thus this applies to the 1p, 2sd and 3pf as valence shells, where the sum rules would be useful for inelastic electron scattering and other reactions. In particular a complete M2 sum rule was derived including the weak contribution from the orbital operator. The contribution from the spurious center-of-mass motion was also derived. The expression was tested by comparing to summations of transition strengths given by shell-model calculations. For nuclei with mass greater than {approximately}A = 70 one would need to include the effect of the intruding level with Q+1 quanta and J = Q+3/2. This problem will be considered in the coming year.
Infrared modified QCD couplings and Bjorken sum rule
NASA Astrophysics Data System (ADS)
Khandramai, V. L.; Teryaev, O. V.; Gabdrakhmanov, I. R.
2016-02-01
We test the recently proposed “Massive” Perturbation Theory (MPT) for the description of the Γ1p-n data at low momentum transfers. The MPT constructed on the two grounds: the first is pQCD with only one parameter added, an effective “glueball mass” mp ≲ Mgl ≲ 1 GeV; serving as an infrared “regulator” the second stems out of the ghost- free Analytic Perturbation Theory comprising non-power perturbative expansion that makes it compatible with linear integral transformations. It is regular in the low-energy region and could serve as a practical means for the analysis of data below 1 GeV up to the IR-limit. We study the non-perturbative Bjorken sum rule higher twists correction by using the MPT, the integral representation for infinite sum of higher twists coefficients and the QCD-inspired model for the Q2-dependence of the generalized Gerasimov-Drell-Hearn sum rule.
3He Spin-Dependent Cross Sections and Sum Rules
Slifer, Karl; Amaryan, Moscov; Amaryan, Moskov; Auerbach, Leonard; Averett, Todd; Berthot, J.; Bertin, Pierre; Bertozzi, William; Black, Tim; Brash, Edward; Brown, D.; Burtin, Etienne; Calarco, John; Cates, Gordon; Chai, Zhengwei; Chen, Jian-Ping; Choi, Seonho; Chudakov, Eugene; Ciofi, Claudio; Cisbani, Evaristo; De Jager, Cornelis; Deur, Alexandre; DiSalvo, R.; Dieterich, Sonja; Djawotho, Pibero; Finn, John; Fissum, Kevin; Fonvieille, Helene; Frullani, Salvatore; Gao, Haiyan; Gao, Juncai; Garibaldi, Franco; Gasparian, Ashot; Gilad, Shalev; Gilman, Ronald; Glamazdin, Oleksandr; Glashausser, Charles; Glockle, W.; Golak, J.; Goldberg, Emma; Gomez, Javier; Gorbenko, Viktor; Hansen, Jens-Ole; Hersman, F.; Holmes, Richard; Huber, Garth; Hughes, Emlyn; Humensky, Thomas; Incerti, Sebastien; Iodice, Mauro; Jensen, S.; Jiang, Xiaodong; Jones, C.; Jones, G.; Jones, Mark; Jutier, Christophe; Kamada, H.; Ketikyan, Armen; Kominis, Ioannis; Korsch, Wolfgang; Kramer, Kevin; Kumar, Krishna; Kumbartzki, Gerfried; Kuss, Michael; Lakuriqi, Enkeleida; Laveissiere, Geraud; LeRose, John; Liang, Meihua; Liyanage, Nilanga; Lolos, George; Malov, Sergey; Marroncle, Jacques; McCormick, Kathy; McKeown, Robert; Meziani, Zein-Eddine; Michaels, Robert; Mitchell, Joseph; Nogga, Andreas; Pace, Emanuele; Papandreou, Zisis; Pavlin, Tina; Petratos, Gerassimos; Pripstein, David; Prout, David; Ransome, Ronald; Roblin, Yves; Rowntree, David; Rvachev, Marat; Sabatie, Franck; Saha, Arunava; Salme, Giovanni; SCOPETTA, S.; Skibinski, R.; Souder, Paul; Saito, Teijiro; Strauch, Steffen; Suleiman, Riad; Takahashi, Kazunori; Todor, Luminita; Tsubota, Hiroaki; Ueno, Hiroaki; Urciuoli, Guido; van der Meer, Rob; Vernin, Pascal; Voskanyan, Hakob; Witala, Henryk; Wojtsekhowski, Bogdan; Xiong, Feng; Xu, Wang; Yang, Jae-Choon; Zhang, Bin; Zolnierczuk, Piotr
2008-07-01
We present a measurement of the spin-dependent cross sections for the \\vec{^3He}(\\vec{e},e')X} reaction in the quasielastic and resonance regions at four-momentum transfer 0.1 < Q^2< 0.9 GeV^2. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt--Cottingham and extended GDH sum rules for the first time. Impulse approximation and exact three-body Faddeev calculations are also compared to the data in the quasielastic region.
Connections between chiral Lagrangians and QCD sum-rules
NASA Astrophysics Data System (ADS)
Fariborz, Amir H.; Pokraka, A.; Steele, T. G.
2016-01-01
In this paper, it is shown how a chiral Lagrangian framework can be used to derive relationships connecting quark-level QCD correlation functions to mesonic-level two-point functions. Crucial ingredients of this connection are scale factor matrices relating each distinct quark-level substructure (e.g. quark-antiquark, four-quark) to its mesonic counterpart. The scale factors and mixing angles are combined into a projection matrix to obtain the physical (hadronic) projection of the QCD correlation function matrix. Such relationships provide a powerful bridge between chiral Lagrangians and QCD sum-rules that are particularly effective in studies of the substructure of light scalar mesons with multiple complicated resonance shapes and substantial underlying mixings. The validity of these connections is demonstrated for the example of the isotriplet a0(980)-a0(1450) system, resulting in an unambiguous determination of the scale factors from the combined inputs of QCD sum-rules and chiral Lagrangians. These scale factors lead to a remarkable agreement between the quark condensates in QCD and the mesonic vacuum expectation values that induce spontaneous chiral symmetry breaking in chiral Lagrangians. This concrete example shows a clear sensitivity to the underlying a0-system mixing angle, illustrating the value of this methodology in extensions to more complicated mesonic systems.
Sum Rules and Moments of the Nucleon Spin Structure Functions
Jian-Ping Chen; Alexandre Deur; Zein-Eddine Meziani
2005-08-01
The nucleon has been used as a laboratory to investigate its own spin structure and Quantum Chromodynamics. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture of the transition region from the confinement regime of the theory to its asymptotic freedom regime. Insight for some aspects of the theory is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e. the Gerasimov-Drell-Hearn, Bjorken and Burkhardt-Cottingham). These moments are expressed in terms of an operator product expansion using quark and gluon degrees of freedom at moderately large momentum transfers. The sum rules are verified to a good accuracy assuming that no singular behavior of the structure functions is present at very high excitation energies. The higher twist contributions have been examined through the moments evolution as the momentum transfer varies from higher to lower values. Furthermore, QCD-inspired low energy effective theories, which explicitly include chiral symmetry breaking, are tested at low momentum transfers. The validity of these theories is further examined as the momentum transfer increases to moderate values. It is found that chiral perturbation calculations agree reasonably well with the first moment of the spin structure function g{sub 1} at momentum transfer of 0.1 GeV{sup 2} but fail to reproduce the neutron data in the case of the generalized polarizability {delta}{sub LT}.
Jacques Friedel and the physics of metals and alloys
NASA Astrophysics Data System (ADS)
Villain, Jacques; Lavagna, Mireille; Bruno, Patrick
2016-03-01
This is an introduction to the theoretical physics of metals for students and physicists from other specialities. Certain simple consequences of the Fermi statistics in pure metals are first addressed, namely the Peierls distortion, Kohn anomalies and the Labbé-Friedel distortion. Then the physics of dilute alloys is discussed. The analogy with nuclear collisions was a fruitful starting point, which suggested one should analyze the effects of impurities in terms of a scattering problem with the introduction of phase shifts. Starting from these concepts, Friedel derived a theory of the resistivity of alloys, and a celebrated sum rule relating the phase shifts at the Fermi level to the number of electrons in the impurity, which turned out to play a prominent role later in the context of correlated impurities, as for instance in the Kondo effect. Friedel oscillations are also an important result, related to incommensurate magnetic structures. It is shown how they can be derived in various ways: from collision theory, perturbation theory, self-consistent approximations and Green's function methods. While collision theory does not permit to take the crystal structure into account, which is responsible for electronic bands, those effects can be included in other descriptions, using for instance the tight binding approximation. xml:lang="fr"
Holographic RG flows, entanglement entropy and the sum rule
NASA Astrophysics Data System (ADS)
Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo
2016-03-01
We calculate the two-point function of the trace of the stress tensor in holographic renormalization group flows between pairs of conformal field theories. We show that the term proportional to the momentum squared in this correlator gives the change of the central charge between fixed points in d = 2 and in d > 2 it gives the holographic entanglement entropy for a planar region. This can also be seen as a holographic realization of the Adler-Zee formula for the renormalization of Newton's constant. Holographic regularization is found to provide a perfect match of the finite and divergent terms of the sum rule, and it is analogous to the regularization of the entropy in terms of mutual information. Finally, we provide a general proof of reflection positivity in terms of stability of the dual bulk action, and discuss the relation between unitarity constraints, the null energy condition and regularity in the interior of the gravity solution.
Moments of Spin Structure Functions: Sum Rules and Polarizabilities
Jian-Ping Chen
2010-10-01
Nucleon structure study is one of the most important research areas in modern physics and has challenged us for decades. Spin has played an essential role and often brought surprises and puzzles to the investigation of the nucleon structure and the strong interaction. New experimental data on nucleon spin structure at low to intermediate momentum transfers combined with existing high momentum transfer data offer a comprehensive picture in the strong region of the interaction and of the transition region from the strong to the asymptotic-free region. Insight for some aspects of the theory for the strong interaction, Quantum Chromodynamics (QCD), is gained by exploring lower moments of spin structure functions and their corresponding sum rules (i.e. the Bjorken, Burkhardt-Cottingham, Gerasimov-Drell-Hearn (GDH), and the generalized GDH). These moments are expressed in terms of an operator-product expansion using quark and gluon degrees of freedom at moderately large momentum transfers.
Sum Rules for Nucleon GPDs and Border Function Formulation
Radyushkin, Anatoly V.
2013-09-01
Recently developed new approach to model nucleon generalized parton distributions (GPDs) H and E is based on two types of their representation in terms of double distributions. Within this approach, we re-consider the derivation of GPD sum rules that allow to use border functions H(x,x) and E(x,x) instead of full GPDs H(x,\\xi) and E(x,\\xi) in the integrals producing Compton form factors of deeply virtual Compton scattering. Using factorized DD Ansatz to model GPDs, we discuss the relation between the border functions and underlying parton densities. We found that substantial contribution to H(x,x) border function comes from the extra term required by new DD representations and related to E(x,\\xi) GPD.
Study of spin sum rules (and the strong coupling constant at large distances)
Alexandre Deur
2009-12-01
We present recent results from Jefferson Lab on sum rules related to the spin structure of the nucleon. We then discuss how the Bjorken sum rule with its connection to the Gerasimov-Drell-Hearn sum, allows us to conveniently define an effective coupling for the strong force at all distances.
Impact of Duality Violations on Spectral Sum Rule analyses
NASA Astrophysics Data System (ADS)
Catà, Oscar
2007-02-01
Recent sum rule analyses on the
Symbolic methods for the evaluation of sum rules of Bessel functions
Babusci, D.; Dattoli, G.; Górska, K.; Penson, K. A.
2013-07-15
The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions. Furthermore, we obtain a set of new closed form sum rules involving various special polynomials and Bessel functions. The examples we consider are relevant for applications ranging from plasma physics to quantum optics.
Comparing T-odd and T-even spin sum rules
Teryaev, O.V.
2015-04-10
Sum rules for T-even and T-odd structure functions and parton distributions are considered. The case of spin-dependent distributions related to energy-momentum tensor (EMT) is specifically addressed. The Burkardt sum rule for T-odd Sivers functions may be related to EMT provided the imaginary prescription for gluonic pole correlator is incorporated. The momentum sum rule for deuteron tensor spin structure function allows one to probe indirectly the gravity couplings to quarks and gluons.
The energy-weighted sum rule and the nuclear radius
NASA Astrophysics Data System (ADS)
Schröder, Hans Peter
2015-09-01
The energy-weighted integrated cross-section for photon absorption --known as sum rule -- is under certain conditions proportional to the mean square nuclear radius (Levinger, Bethe (Phys. Rev. 78, 115 (1950))). Due to the energy weight factor the low-energy absorption components are emphasized and the dipole transitions in the region of giant resonances contribute enhanced at . Thus, the cross-section of the full interaction can be replaced in good approximation by the dipole cross-section. Under these aspects, we have calculated and the radii of various gg-nuclei. For our purpose, we have chosen a simple shell model where the integrals can be solved analytically, and the contributions of uncorrelated functions and correlation corrections can be shown explicitly. The mean square radius as a function of differs by a factor of 1.5/0.87 from the previous result of Levinger and Kent (Phys. Rev. 95, 418 (1954)) without correlation corrections. Plotting the function of the correlation corrections and the uncorrelated function as a ratio it shows that tends towards a limit. Finally, our results for the radii of gg-nuclei are in good agreement with recent experiments (I. Angeli, K.P. Marinova, At. Data Nucl. Data Tables 99, 69 (2013)).
The leptonic Dirac CP-violating phase from sum rules
NASA Astrophysics Data System (ADS)
Girardi, I.; Petcov, S. T.; Titov, A. V.
2016-05-01
In the reference 3-neutrino mixing scheme with three light massive neutrinos, CP-violating effects in neutrino oscillations can be caused by the Dirac CP-violating phase δ present in the unitary neutrino mixing matrix U. Using the fact that U = U†eUv , where Ue and Uv are unitary matrices arising from the diagonalisation, respectively, of the charged lepton and neutrino mass matrices, we consider in a systematic way forms of Ue and Uv allowing us to express δ as a function of the neutrino mixing angles present in U and the angles contained in Uv. After obtaining sum rules for cos δ, we consider several forms of Uv dictated by, or associated with, symmetries, such as tri-bimaximal, bimaximal, etc., for which the angles in Uv are fixed. For each of these forms and forms of Ue allowing to reproduce the measured values of the neutrino mixing angles, we construct the likelihood function for cos δ, using the prospective uncertainties in the determination of the mixing angles. Our results show that the measurement of δ along with improvement of the precision on the neutrino mixing angles can provide unique information about the possible existence of a new fundamental symmetry in the lepton sector.
NASA Astrophysics Data System (ADS)
Lazzeretti, Paolo; Malagoli, Massimo; Zanasi, Riccardo
1991-01-01
The virial theorem has been used to derive sum rules for dipole- and mixed-dipole-quadrupole nuclear electric shieldings and corresponding geometrical derivatives of dipole and quadrupole moments in a molecule. Test calculations have been carried out on a series of first- and second-row hydrides. The virial sum rules can be effective tools to prove the accuracy of theoretical nuclear shieldings and analytic geometrical derivatives. As the latter are related to ir intensities, the virial sum rules can give important indications on the reliability of theoretical predictions for this spectroscopical parameter.
Analysis of quarkonia at finite temperature from complex Borel sum rules
NASA Astrophysics Data System (ADS)
Araki, Ken-Ji; Suzuki, Kei; Guber, Phillip; Oka, Makoto
2014-09-01
Recently, we proposed a new type of QCD sum rules i.e. the complex Borel sum rules (CBSR). It has been found that the CBSR is superior to the conventional QCD sum rules from the point of view of the maximum entropy method (MEM) analysis. Specifically, we have demonstrated that our novel method can be used to study the excited states of hadrons. The suppression of quarkonium states (e.g. J/psi and upsilon) is an important signature of the hot matter produced in relativistic heavy-ion collisions at RHIC and LHC. Recently, the behavior of the excited states at finite temperature, which can be different from the ground state, has attracted much attention. The suppression of the charmonium and bottomonium ground states has already been analyzed by conventional QCD sum rules with MEM. In this talk, we report on the results of a reanalysis by CBSR with MEM to investigate the thermal behavior of the quarkonium excited states.
MathQCDSR: a Mathematica Package for QCD Sum Rules Calculations
NASA Astrophysics Data System (ADS)
Wang, Lai; Lee, Frank X.
2010-02-01
We present a software package written in Mathematica for standard QCD sum rules calculations. Two examples are given to demonstrate how to use the package. One is for the mass spectrum of octet baryons from two-point correlation functions; the other for the magnetic moments of octet baryons in the external-field method. The software package FeynCalc is used to handle the gamma-matrix computations. The derived sum rules can be saved in various forms (native Mathematica, JAVA, Fortran, or Latex). Several notebooks are provided to carry out a Monte-Carlo-based numerical analysis of the sum rules, complete with in-line graphical display of sum rule matching, error distributions, scatter plots for correlations, etc. )
Transition magnetic moment of {Lambda}{yields}{Sigma}{sup 0} in QCD sum rules
Lee, Frank X.; Wang Lai
2011-05-01
The {Lambda}{yields}{Sigma}{sup 0} transition magnetic moment is computed in the QCD sum rules approach. Three independent tensor structures are derived in the external-field method using generalized interpolating fields. They are analyzed together with the {Lambda} and {Sigma}{sup 0} mass sum rules using a Monte-Carlo-based analysis, with attention to operator product expansion convergence, ground-state dominance, and the role of the transitions in the intermediate states. Relations between sum rules for magnetic moments of {Lambda} and {Sigma}{sup 0} and sum rules for transition magnetic moment of {Lambda}{yields}{Sigma}{sup 0} are also examined. Our best prediction for the transition magnetic moment is {mu}{sub {Sigma}}{sup 0}{sub {Lambda}=}1.60{+-}0.07{mu}{sub N}. A comparison is made with other calculations in the literature.
Endpoint behavior of the pion distribution amplitude in QCD sum rules with nonlocal condensates
Mikhailov, S. V.; Pimikov, A. V.; Stefanis, N. G.
2010-09-01
Starting from the QCD sum rules with nonlocal condensates for the pion distribution amplitude, we derive another sum rule for its derivative and its ''integral derivatives''--defined in this work. We use this new sum rule to analyze the fine details of the pion distribution amplitude in the endpoint region x{approx}0. The results for endpoint-suppressed and flattop (or flatlike) pion distribution amplitudes are compared with those we obtained with differential sum rules by employing two different models for the distribution of vacuum-quark virtualities. We determine the range of values of the derivatives of the pion distribution amplitude and show that endpoint-suppressed distribution amplitudes lie within this range, while those with endpoint enhancement--flat-type or Chernyak-Zhitnitsky like--yield values outside this range.
QCD Sum Rules for Magnetically Induced Mixing between ηc and J/ψ
Cho, Sungtae; Hattori, Koichi; Lee, Su Houng; Morita, Kenji; Ozaki, Sho
2014-10-20
We investigate the properties of charmonia in strong magnetic fields by using QCD sum rules. We show how to implement the mixing effects between ηc and J/ψ on the basis of field-theoretical approaches, and then show that the sum rules are saturated by the mixing effects with phenomenologically determined parameters. Consequently, we find that the mixing effects are the dominant contribution to the mass shifts of the static charmonia in strong magnetic fields.
Strong decay constants of heavy tensor mesons in light cone QCD sum rules
NASA Astrophysics Data System (ADS)
Alhendi, H. A.; Aliev, T. M.; Savcı, M.
2016-04-01
Strong decay constants of the heavy tensor to heavy pseudoscalar (vector) and light pseudoscalar mesons are estimated within the light cone QCD sum rules. It is observed that the values of these coupling constants show a significant dependence on the choice of the Lorentz structure. Additionally, the decay widths of these mesons are calculated and discussed within the light of experimental data. A comparison of our results on these coupling constants with the predictions from the 3-point sum rules is performed.
Experimental Tests of the GDH and Other Sum Rules at SLAC
Bosted, P.E.; /Massachusetts U., Amherst
2005-06-14
Recent measurements from SLAC of the polarized nucleon structure functions g{sub 1} and g{sub 2} have been used to experimentally test the Bjorken, Ellis-Jaffe, Burkhardt-Cottingham, and Efremov-Leader-Teryaev sum rules. In the future, the SLAC E159 experiment will extend structure function measurements using real photons to 40 GeV, enabling a definitive test of the high energy convergence of the GDH sum rule for both proton and deuteron targets.
Sum Rules of Charm C P Asymmetries beyond the SU(3 ) F Limit
NASA Astrophysics Data System (ADS)
Müller, Sarah; Nierste, Ulrich; Schacht, Stefan
2015-12-01
We find new sum rules between direct C P asymmetries in D meson decays with coefficients that can be determined from a global fit to branching ratio data. Our sum rules eliminate the penguin topologies P and P A , which cannot be determined from branching ratios. In this way, we can make predictions about direct C P asymmetries in the standard model without ad hoc assumptions on the sizes of penguin diagrams. We consistently include first-order SU(3 ) F breaking in the topological amplitudes extracted from the branching ratios. By confronting our sum rules with future precise data from LHCb and Belle II, one will identify or constrain new-physics contributions to P or P A . The first sum rule correlates the C P asymmetries aCP dir in D0→K+K-, D0→π+π- , and D0→π0π0. We study the region of the aCP dir(D0→π+π-)-aCP dir(D0→π0π0) plane allowed by current data and find that our sum rule excludes more than half of the allowed region at 95% C.L. Our second sum rule correlates the direct C P asymmetries in D+→K¯0K+, Ds+→K0π+, and Ds+→K+π0.
Sum Rules of Charm CP Asymmetries beyond the SU(3)_{F} Limit.
Müller, Sarah; Nierste, Ulrich; Schacht, Stefan
2015-12-18
We find new sum rules between direct CP asymmetries in D meson decays with coefficients that can be determined from a global fit to branching ratio data. Our sum rules eliminate the penguin topologies P and PA, which cannot be determined from branching ratios. In this way, we can make predictions about direct CP asymmetries in the standard model without ad hoc assumptions on the sizes of penguin diagrams. We consistently include first-order SU(3)_{F} breaking in the topological amplitudes extracted from the branching ratios. By confronting our sum rules with future precise data from LHCb and Belle II, one will identify or constrain new-physics contributions to P or PA. The first sum rule correlates the CP asymmetries a_{CP}^{dir} in D^{0}→K^{+}K^{-}, D^{0}→π^{+}π^{-}, and D^{0}→π^{0}π^{0}. We study the region of the a_{CP}^{dir}(D^{0}→π^{+}π^{-})-a_{CP}^{dir}(D^{0}→π^{0}π^{0}) plane allowed by current data and find that our sum rule excludes more than half of the allowed region at 95% C.L. Our second sum rule correlates the direct CP asymmetries in D^{+}→K[over ¯]^{0}K^{+}, D_{s}^{+}→K^{0}π^{+}, and D_{s}^{+}→K^{+}π^{0}. PMID:26722915
Finite temperature effects and the validity of the Weinberg sum rules
NASA Astrophysics Data System (ADS)
Ayala, Alejandro; Dominguez, C. A.; Loewe, M.; Zhang, Y.
2016-05-01
Using resent independent results from QCD sum rules for the thermal evolution of hadronic parameters in the vector and the axial-vector channels, we discuss the saturation of the two Weinberg sum rules. It turn out that both sum rules are quite well satisfied in a wide range from T = 0 up to T/T c ≃ 0.7 — 0.8. At higher temperatures, coming closer to Tc , there is an asymmetry between both channels since in the vector case there is a leading order effect, proportional to T2 , due to a one loop pion contribution in the space-like region, which is absent in the axial-vector case. This leads then to a small deviation. More important, though, in this region the QCD sum rules for the hadronic parameters begin to have no solutions since the widths of the ρ and the a1-mesons diverge signaling the occurrence of deconfinement. Close to and at Tc there are no pions left in the medium and chiral symmetry is restored so that the Weinberg sum rules are trivially satisfied.
Charge form factor and sum rules of electromagnetic response functions in $^{12}$C
Lovato, Alessandro; Gandolfi, Stefano; Carlson, Joseph A.; Butler, Ralph; Lusk, Ewing; Pieper, Steven C.; Schiavilla, Rocco
2013-08-01
An {\\it ab initio} calculation of the $^{12}$C elastic form factor, and sum rules of longitudinal and transverse response functions measured in inclusive (e,e') scattering, is reported, based on realistic nuclear potentials and electromagnetic currents. The longitudinal elastic form factor and sum rule are found to be in satisfactory agreement with available experimental data. A direct comparison between theory and experiment is difficult for the transverse sum rule. However, it is shown that the calculated one has large contributions from two-body currents, indicating that these mechanisms lead to a significant enhancement of the quasi-elastic transverse response. This fact may have implications for the anomaly observed in recent neutrino quasi-elastic charge-changing scattering data off $^{12}$C.
Thermal behaviors of light unflavored tensor mesons in the framework of QCD sum rule
NASA Astrophysics Data System (ADS)
Azizi, K.; Türkan, A.; Sundu, H.; Veli Veliev, E.; Yazıcı, E.
2014-12-01
In this paper, we investigated the sensitivity of the masses and decay constants of f2(1270) and a2(1320) tensor mesons to the temperature using OCD sum rule approach. In our calculations, we take into account new additional operators appearing in operator product expansion (OPE). At the end of numerical analyses we show that at deconfinement temperature the decay constants and masses decreased by 6% and 96% of their vacuum values, respectively. Our results on the masses and decay constants at zero temperature of the tensor mesons are consistent with the experimental data as well as the vacuum sum rules predictions.
Incomplete fusion studies near Coulomb barrier: a modified sum rule model
NASA Astrophysics Data System (ADS)
Bhujang, Bhushan; Das, Pragya; Singh, R. P.; Tripathi, R.; Tomar, B. S.
2013-03-01
The excitation functions of the evaporation residues, produced via complete fusion and incomplete fusion reactions of 11B + 122Sn, were measured for the projectile energy of around 6 MeV/A by the off-line gamma spectrometry. The cross sections have been compared with the statistical model code Projected Angular Momentum Coupled Evaporation (PACE4). The original sum rule model underestimated the ICF cross sections. We therefore made modification in the model mainly to incorporate the energy dependence in the definition of critical angular momentum. Using this modified sum rule model, we found a significant improvement in the results.
Sum rules for invariance of the fourth-rank hypermagnetisability in a gauge translation
NASA Astrophysics Data System (ADS)
Pagola, G. I.; Caputo, M. C.; Ferraro, M. B.; Lazzeretti, P.
2005-06-01
The conditions for invariance in a gauge translation of the fourth-rank molecular hypermagnetisability tensor, introduced to rationalize the cubic response of a molecule in the presence of an external magnetic field, are discussed in terms of quantum mechanical sum rules. Eight relationships, connecting electric dipole polarisability, polarisability of magnetisability, and other third- and fourth-rank tensors that can be regarded as intrinsic molecular properties tout court, have been obtained. Numerical tests have been carried out to determine the Hartree-Fock limit for the sum-rules in a set of small molecules.
Energy-weighted sum rules connecting ΔZ = 2 nuclei within the SO(8) model
Štefánik, Dušan; Šimkovic, Fedor; Faessler, Amand
2013-12-30
Energy-weighted sum rules associated with ΔZ = 2 nuclei are obtained for the Fermi and the Gamow-Teller operators within the SO(8) model. It is found that there is a dominance of contribution of a single state of the intermediate nucleus to the sum rule. The results confirm founding obtained within the SO(5) model that the energy-weighted sum rules of ΔZ = 2 nuclei are governed by the residual interactions of nuclear Hamiltonian. A short discussion concerning some aspects of energy weighted sum rules in the case of realistic nuclei is included.
Complex-energy approach to sum rules within nuclear density functional theory
Hinohara, Nobuo; Kortelainen, Markus; Nazarewicz, Witold; Olsen, Erik
2015-04-27
The linear response of the nucleus to an external field contains unique information about the effective interaction, correlations governing the behavior of the many-body system, and properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or nuclear energy density functional (EDF). But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. To establish anmore » efficient framework to compute energy-weighted sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy finite-amplitude method (FAM) based on the quasiparticle random- phase approximation. The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method is very efficient and well-adaptable to parallel computing. As a result, the FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and external field cannot be used.« less
Comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule
NASA Astrophysics Data System (ADS)
Luo, Yousong; Eberhard, Andrew
2005-07-01
A comparison principle for viscosity sub- and super-solutions of second order elliptic partial differential equations is derived using the "fuzzy sum rule" of non-smooth calculus. This method allows us to weaken the assumptions made on the function F when the equation F(x,u,=u,=2u)=0 is under consideration.
Complex-energy approach to sum rules within nuclear density functional theory
Hinohara, Nobuo; Kortelainen, Markus; Nazarewicz, Witold; Olsen, Erik
2015-04-27
The linear response of the nucleus to an external field contains unique information about the effective interaction, correlations governing the behavior of the many-body system, and properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or nuclear energy density functional (EDF). But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. To establish an efficient framework to compute energy-weighted sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy finite-amplitude method (FAM) based on the quasiparticle random- phase approximation. The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method is very efficient and well-adaptable to parallel computing. As a result, the FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and external field cannot be used.
Radiative decays of the heavy flavored baryons in light cone QCD sum rules
Aliev, T. M.; Azizi, K.; Ozpineci, A.
2009-03-01
The transition magnetic dipole and electric quadrupole moments of the radiative decays of the sextet heavy flavored spin 3/2 to the heavy spin 1/2 baryons are calculated within the light cone QCD sum rules approach. Using the obtained results, the decay rate for these transitions are also computed and compared with the existing predictions of the other approaches.
Iso-vector form factors of the delta and nucleon in QCD sum rules
Ozpineci, A.
2012-10-23
Form factors are important non-perturbative properties of hadrons. They give information about the internal structure of the hadrons. In this work, iso-vector axial-vector and iso-vector tensor form factors of the nucleon and the iso-vector axial-vector {Delta}{yields}N transition form factor calculations in QCD Sum Rules are presented.
A QCD Sum Rule Approach with an Explicit Di-quark field
Kim, Kyung-il; Jido, Daisuke; Lee, Su Houng
2011-10-21
In hadron phenomenology, diquark structures can be an important degree of freedom in certain configurations. We investigate the possibility that the diquark structure can be treated as an elementary field in certain configurations. To start with, we assume that {Lambda} is composed of a spectator strange quark and a diquark. We construct a QCD sum rule for {Lambda}, where the input parameters are the diquark mass and its condensate, in addition to other parameters of QCD sum rules. We find good Borel curve for the {Lambda} mass for certain combinations of the diquark mass and condensate, and that smaller diquark condensate is needed when the diquark mass is increased to maintain the good Borel curve. The same sets of diquark mass and condensate are found to work well for {Lambda}{sub c} and {Lambda}{sub b}.
Nucleon form factors to next-to-leading order with light-cone sum rules
Passek-Kumericki, K.; Peters, G.
2008-08-01
We have calculated the leading-twist next-to-leading order (NLO), i.e., O({alpha}{sub s}), correction to the light-cone sum rules prediction for the electromagnetic form factors of the nucleon. We have used the Ioffe nucleon interpolation current and worked in M{sub N}=0 approximation, with M{sub N} being the mass of the nucleon. In this approximation, only the Pauli form factor F{sub 2} receives a correction and the calculated correction is quite sizable (ca. 60%). The numerical results for the proton form factors show the improved agreement with the experimental data. We also discuss the problems encountered when going away from M{sub N}=0 approximation at NLO, as well as gauge invariance of the perturbative results. This work presents the first step towards the NLO accuracy in the light-cone sum rules for baryon form factors.
Coset construction and character sum rules for the doubly extended N = 4 superconformal algebras
NASA Astrophysics Data System (ADS)
Petersen, Jens Lyng; Taormina, Anne
1993-06-01
Character sum rules associated with the realization of the N = 4 superconformal algebra Ãγ on manifolds corresponding to the group cosets SU(3) k˜+ / U(1) are derived and developed as an important tool in obtaining the modular properties of Ãγ characters as well as information on certain extensions of that algebra. Their structure strongly suggests the existence of rational conformal field theories with central charges in the range 1 ⪕ c ⪕ 4. The corresponding characters appear in the massive sector of the sum rules and are completely specified in terms of the characters for the parafermionic theory SU(3)/(SU(2)×U(1)) and in terms of the branching functions of massless Ãγ characters into SU(2) k˜+× SU(2) 1 characters.
QCD sum rules for D and B mesons in nuclear matter
Hilger, T.; Thomas, R.; Kaempfer, B.
2009-02-15
QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D-D and B-B mesons as a function of the nuclear matter density; extrapolated to saturation density it is in the order of 60 and 130 MeV, respectively, driven essentially by the condensates ,
, and
may leave room for an even larger D-D mass splitting. The genuine chiral condensate
Sum rules for interaction of ϒ resonances with Zbπ
NASA Astrophysics Data System (ADS)
Voloshin, M. B.
2016-07-01
The strength of the amplitudes for the coupling between the bottomonium ϒ (n S ) states, the bottomonium-like isovector resonances Zb and a pion, ϒ (n S )Zbπ , is considered. These amplitudes describe the decays Zb→ϒ (n S )π for n =1 , 2, 3, and the processes ϒ (n S )→Zbπ for n =5 ,6 ,… with either Zb(10610 ) or Zb(10650 ). It is pointed out that analyticity and unitarity impose a sum rule for these couplings to each of the Zb resonances. With the currently available data it appears to be difficult or impossible to simultaneously satisfy the sum rules for the Zb(10610 ) and Zb(10650 ) resonances. This difficulty can be resolved if there is a considerable dissimilarity in the yield of the states Zb(10610 )π and Zb(10650 )π in the e+e- annihilation at energies above the ϒ (5 S ) resonance.
{Sigma}{sub b,c} to Nucleon Transitions in Light Cone QCD Sum Rules
Bayar, M.; Azizi, K.; Zeyrek, M. T.
2011-05-23
The loop level flavor changing neutral current transitions of the {Sigma}{sub b}{yields}nl{sup +}l{sup -} and {Sigma}{sub c}{yields}pl{sup +}l{sup -} are investigated in the light cone QCD sum rules approach. Using the most general form of the interpolating current for {Sigma}{sub Q}, Q = b or c, the transition form factors are calculated using two sets of input parameters entering the nucleon distribution amplitudes, namely, QCD sum rules and lattice QCD inputs. The obtained results are used to estimate the decay rates of the corresponding transitions. Since such type transitions occurred at loop level in the standard model, they can be considered as good candidates to search for the new physics effects beyond the SM.
The Q^2 Evolution of the GDH sum Rule (on 3He and the Neutron)
Gordon Cates
2002-06-01
We discuss the extention of the Gerasimov-Drell-Hearn (GDH) sum rule, which pertains to real photons, to include scattering due to virtual photons. We present data from Jefferson Laboratory experiment E94-010 which measured the inclusive scattering of polarized electrons from a polarized 3He target over the quasielastic and resonance regions. From these data we exctract the transverse-transverse interference cross section {sigma}{prime}_TT', and compute the Q^2 depenent extended GDH integral.
Dynamic properties of one-component strongly coupled plasmas: The sum-rule approach
Arkhipov, Yu. V.; Askaruly, A.; Davletov, A. E.; Ballester, D.; Tkachenko, I. M.
2010-02-15
The dynamic characteristics of strongly coupled one-component plasmas are studied within the moment approach. Our results on the dynamic structure factor and the dynamic local-field correction satisfy the sum rules and other exact relations automatically. A quantitative agreement is obtained with numerous simulation data on the plasma dynamic properties, including the dispersion and decay of collective modes. Our approach allows us to correct and complement the results previously found with other treatments.
Low x Behavior of the Isovector Nucleon Polarized Structure Function and the Bjorken Sum Rule
NASA Astrophysics Data System (ADS)
Buccella, Franco; Pisanti, Ofelia; Santorelli, Pietro
The combination gp1(x)-gn_1(x) is derived from SLAC data on polarized proton and deuteron targets, evaluated at Q2=10 GeV2, and compared with the results of SMC experiment. The agreement is satisfactory except for the points at the three lowest x, which have an important role in the SMC evaluation on the L.H.S. of the Bjorken sum rule.
Fourth Moment Sum Rule for the Charge Correlations of a Two-Component Classical Plasma
NASA Astrophysics Data System (ADS)
Alastuey, Angel; Fantoni, Riccardo
2016-05-01
We consider an ionic fluid made with two species of mobile particles carrying either a positive or a negative charge. We derive a sum rule for the fourth moment of equilibrium charge correlations. Our method relies on the study of the system response to the potential created by a weak external charge distribution with slow spatial variations. The induced particle densities, and the resulting induced charge density, are then computed within density functional theory, where the free energy is expanded in powers of the density gradients. The comparison with the predictions of linear response theory provides a thermodynamical expression for the fourth moment of charge correlations, which involves the isothermal compressibility as well as suitably defined partial compressibilities. The familiar Stillinger-Lovett condition is also recovered as a by-product of our method, suggesting that the fourth moment sum rule should hold in any conducting phase. This is explicitly checked in the low density regime, within the Abe-Meeron diagrammatical expansions. Beyond its own interest, the fourth-moment sum rule should be useful for both analyzing and understanding recently observed behaviours near the ionic critical point.
Nature of the X(5568) — A critical Laplace sum rule analysis at N2LO
NASA Astrophysics Data System (ADS)
Albuquerque, R.; Narison, S.; Rabemananjara, A.; Rabetiarivony, D.
2016-06-01
We scrutinize recent QCD spectral sum rules (QSSR) results to lowest order (LO) predicting the masses of the BK molecule and (su)(bd¯) four-quark states. We improve these results by adding NLO and N2LO corrections to the PT contributions giving a more precise meaning on the b-quark mass definition used in the analysis. We extract our optimal predictions using Laplace sum rule (LSR) within the standard stability criteria versus the changes of the external free parameters (τ-sum rule variable, tc continuum threshold and subtraction constant μ). The smallness of the higher order PT corrections justifies (a posteriori) the LO order results ⊕ the uses of the ambiguous heavy quark mass to that order. However, our predicted spectra in the range (5173 ˜ 5226) MeV, summarized in Table 7, for exotic hadrons built with four different flavors (buds), do not support some previous interpretations of the D0 candidate,1 X(5568), as a pure molecule or a four-quark state. If experimentally confirmed, it could result from their mixing with an angle: sin 2𝜃 ≈ 0.15. One can also scan the region (2327 ˜ 2444) MeV (where the Ds0∗(2317) might be a good candidate) and the one (5173 ˜ 5226) MeV for detecting these (cuds) and (buds) unmixed exotic hadrons (if any) via, eventually, their radiative or π+hadrons decays.
Heavy-Quark Mass and Heavy-Meson Decay Constants from QCD Sum Rules
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2011-05-23
We present a sum-rule extraction of decay constants of heavy mesons from the two-point correlator of heavy-light pseudoscalar currents. Our primary concern is to control the uncertainties of the decay constants, induced by both input QCD parameters and limited accuracy of the sum-rule method. Gaining this control is possible by applying our novel procedure for the extraction of hadron observables utilizing Borel-parameter-depending dual thresholds. For the charmed mesons, we obtain f{sub D} (206.2{+-}7.3{sub (OPE){+-}}5.1{sub (syst)}) MeV and f{sub D{sub s}} (245.3{+-}15.7{sub (OPE){+-}}4.5{sub (syst)}) MeV. In the case of the beauty mesons, the decay constants prove to be extremely sensitive to the exact value of the b-quark MS mass m-bar{sub b}(m-bar{sub b}). By matching our sum-rule prediction for f{sub B} to the lattice outcomes, the very accurate b-mass value m-bar{sub b}(m-bar{sub b}) = (4.245{+-}0.025) GeV is found, which yields f{sub B} = (193.4{+-}12.3{sub (OPE){+-}}4.3{sub (syst)}) MeV and f{sub B{sub s}} (232.5{+-}18.6{sub (OPE){+-}}2.4{sub (syst)}) MeV.
Ultrafast zero balance of the oscillator-strength sum rule in graphene
Kim, Jaeseok; Lim, Seong Chu; Chae, Seung Jin; Maeng, Inhee; Choi, Younghwan; Cha, Soonyoung; Lee, Young Hee; Choi, Hyunyong
2013-01-01
Oscillator-strength sum rule in light-induced transitions is one general form of quantum-mechanical identities. Although this sum rule is well established in equilibrium photo-physics, an experimental corroboration for the validation of the sum rule in a nonequilibrium regime has been a long-standing unexplored question. The simple band structure of graphene is an ideal system for investigating this question due to the linear Dirac-like energy dispersion. Here, we employed both ultrafast terahertz and optical spectroscopy to directly monitor the transient oscillator-strength balancing between quasi-free low-energy oscillators and high-energy Fermi-edge ones. Upon photo-excitation of hot Dirac fermions, we observed that the ultrafast depletion of high-energy oscillators precisely complements the increased terahertz absorption oscillators. Our results may provide an experimental priori to understand, for example, the intrinsic free-carrier dynamics to the high-energy photo-excitation, responsible for optoelectronic operation such as graphene-based phototransistor or solar-energy harvesting devices. PMID:24036567
Predictions for the Dirac Phase in the Neutrino Mixing Matrix and Sum Rules
NASA Astrophysics Data System (ADS)
Girardi, I.; Petcov, S. T.; Titov, A. V.
2015-07-01
Using the fact that the neutrino mixing matrix U = U†eUν, where Ue and Uv result from the diagonalisation of the charged lepton and neutrino mass matrices, we analyse the sum rules which the Dirac phase δ present in U satisfies when Uv has a form dictated by, or associated with, discrete symmetries and Ue has a “minimal” form (in terms of angles and phases it contains) that can provide the requisite corrections to Uv, so that reactor, atmospheric and solar neutrino mixing angles θ13, θ23 and θ12 have values compatible with the current data. The following symmetry forms are considered: i) tri-bimaximal (TBM), ii) bimaximal (BM) (or corresponding to the conservation of the lepton charge L' = Le — Lμ — Lτ (LC)), iii) golden ratio type A (GRA), iv) golden ratio type B (GRB), and v) hexagonal (HG). We investigate the predictions for 5 in the cases of TBM, BM (LC), GRA, GRB and HG forms using the exact and the leading order sum rules for cos δ proposed in the literature, taking into account also the uncertainties in the measured values of sin2 θ12, sin2 θ23 and sin2 θ13. This allows us, in particular, to assess the accuracy of the predictions for cos δ based on the leading order sum rules and its dependence on the values of the indicated neutrino mixing parameters when the latter are varied in their respective 3σ experimentally allowed ranges.
Perturbative corrections to Λ b → Λ form factors from QCD light-cone sum rules
NASA Astrophysics Data System (ADS)
Wang, Yu-Ming; Shen, Yue-Long
2016-02-01
We compute radiative corrections to Λ b → Λ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with Λ b -baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-Λ b -baryon correlation function is justified at leading power in Λ /m b , with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to- B-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at {O}({α}_s) shift the Λ b → Λ from factors at large recoil significantly and the dominant contribution originates from the next-to-leading order jet function instead of the hard coefficient functions. Having at hand the sum rule predictions for the Λ b → Λ from factors we further investigate several decay observables in the electro-weak penguin Λ b → Λ ℓ + ℓ - transitions in the factorization limit (i.e., ignoring the "non-factorizable" hadronic effects which cannot be expressed in terms of the Λ b → Λ from factors), including the invariant mass distribution of the lepton pair, the forward-backward asymmetry in the dilepton system and the longitudinal polarization fraction of the leptonic sector.
QCD corrections to B → π form factors from light-cone sum rules
NASA Astrophysics Data System (ADS)
Wang, Yu-Ming; Shen, Yue-Long
2015-09-01
We compute perturbative corrections to B → π form factors from QCD light-cone sum rules with B-meson distribution amplitudes. Applying the method of regions we demonstrate factorization of the vacuum-to-B-meson correlation function defined with an interpolating current for pion, at one-loop level, explicitly in the heavy quark limit. The short-distance functions in the factorization formulae of the correlation function involves both hard and hard-collinear scales; and these functions can be further factorized into hard coefficients by integrating out the hard fluctuations and jet functions encoding the hard-collinear information. Resummation of large logarithms in the short-distance functions is then achieved via the standard renormalization-group approach. We further show that structures of the factorization formulae for fBπ+ (q2) and fBπ0 (q2) at large hadronic recoil from QCD light-cone sum rules match that derived in QCD factorization. In particular, we perform an exploratory phenomenological analysis of B → π form factors, paying attention to various sources of perturbative and systematic uncertainties, and extract |Vub | = (3.05-0.38+0.54|th. ± 0.09|exp.) ×10-3 with the inverse moment of the B-meson distribution amplitude ϕB+ (ω) determined by reproducing fBπ+ (q2 = 0) obtained from the light-cone sum rules with π distribution amplitudes. Furthermore, we present the invariant-mass distributions of the lepton pair for B → πℓνℓ (ℓ = μ, τ) in the whole kinematic region. Finally, we discuss non-valence Fock state contributions to the B → π form factors fBπ+ (q2) and fBπ0 (q2) in brief.
NASA Technical Reports Server (NTRS)
Berk, A.; Temkin, A.
1985-01-01
A sum rule is derived for the auxiliary eigenvalues of an equation whose eigenspectrum pertains to projection operators which describe electron scattering from multielectron atoms and ions. The sum rule's right-hand side depends on an integral involving the target system eigenfunctions. The sum rule is checked for several approximations of the two-electron target. It is shown that target functions which have a unit eigenvalue in their auxiliary eigenspectrum do not give rise to well-defined projection operators except through a limiting process. For Hylleraas target approximations, the auxiliary equations are shown to contain an infinite spectrum. However, using a Rayleigh-Ritz variational principle, it is shown that a comparatively simple aproximation can exhaust the sum rule to better than five significant figures. The auxiliary Hylleraas equation is greatly simplified by conversion to a square root equation containing the same eigenfunction spectrum and from which the required eigenvalues are trivially recovered by squaring.
NASA Astrophysics Data System (ADS)
Henderson, D.; Plischke, M.
1987-04-01
Starting from well-known relations for the derivatives of the radial distribution functions of a mixture of fluids, and allowing the diameter of one particle to become exceedingly large, three sum rules for a fluid with density inhomogeneities are obtained. None of these sum rules are new. However, the relation between the Lovett-Mou-Buff-Wertheim and the Born-Green hierarchy of equations seems not well known. The accuracy of a recent parametrization of the pair correlation of hard spheres near a hard wall and of the solutions of the Percus-Yevick and hypernetted-chain equation for this same function are examined by determination of how well these functions satisfy these sum rules and the accuracy of their surface tension, calculated from the sum rule of Triezenberg and Zwanzig. Generally speaking, the Percus-Yevick theory gives the best results and the hypernetted-chain approximation gives the worst results with the parametrization being intermediate.
{sup 3}He Spin-Dependent Cross Sections and Sum Rules
Slifer, K.; Auerbach, L.; Choi, Seonho; Incerti, S.; Lakuriqi, E.; Meziani, Z.-E.; Amarian, M.; Ketikyan, A.; Voskanian, H.; Averett, T.; Berthot, J.; Bertin, P.; DiSalvo, R.; Fonvieille, H.; Laveissiere, G.; Roblin, Y.
2008-07-11
We present a measurement of the spin-dependent cross sections for the {sup 3}He-vector (e-vector,e{sup '})X reaction in the quasielastic and resonance regions at a four-momentum transfer 0.1{<=}Q{sup 2}{<=}0.9 GeV{sup 2}. The spin-structure functions have been extracted and used to evaluate the nuclear Burkhardt-Cottingham and extended Gerasimov-Drell-Hearn sum rules for the first time. The data are also compared to an impulse approximation calculation and an exact three-body Faddeev calculation in the quasielastic region.
B ---> pi and B ---> K transitions from QCD sum rules on the light cone
Ball, P.
1998-09-01
I calculate the form factors describing semileptonic and penguin-induced decays of B mesons into light pseudoscalar mesons. The form factors are calculated from QCD sum rules on the light-cone including contributions up to twist 4, radiative corrections to the leading twist contribution and SU(3)-breaking effects. The theoretical uncertainty is estimated to be \\sim 15%. The heavy-quark-limit relations between semileptonic and penguin form factors are found to be valid in the full accessible range of momentum transfer.
NASA Astrophysics Data System (ADS)
Huitu, Katri; Pandita, P. N.; Tiitola, Paavo
2015-10-01
We examine the deflected mirage mediation supersymmetry breaking (DMMSB) scenario, which combines three supersymmetry breaking scenarios, namely anomaly mediation, gravity mediation and gauge mediation using the one-loop renormalization group invariants (RGIs). We examine the effects on the RGIs at the threshold where the gauge messengers emerge, and derive the supersymmetry breaking parameters in terms of the RGIs. We further discuss whether the supersymmetry breaking mediation mechanism can be determined using a limited set of invariants, and derive sum rules valid for DMMSB below the gauge messenger scale. In addition we examine the implications of the measured Higgs mass for the DMMSB spectrum.
Limitations of the semirelativistic approach in sum rules and related calculations in atomic physics
NASA Technical Reports Server (NTRS)
Rustgi, M. L.; Leung, P. T.; Long, S. A. T.
1988-01-01
The semirelativistic approach, as applied to sum-rule calculations, can yield very inaccurate results for high-Z systems; the apparently good agreement previously reported is fortuitous, due to the application of an approximate eigenstate of the semirelativistic Hamiltonian. Attention is given to one-electron atomic systems, and the results obtained are discussed with a view to their implications for many-electron systems. The many-electron problem is complicated by a lack of clarity as to the relative importance of contributions due to correlation effects among the electrons, their effect on the E2 oscillator strength, and the retardation correction to the E1 transition.
Analysis of the vertices BsBK* and DsDK* with QCD Sum Rules
NASA Astrophysics Data System (ADS)
Cerqueira, A., Jr.; Osório Rodrigues, B.; Bracco, M. E.
2015-07-01
In this work, we calculated the form factors and coupling constant of the vertex DsDK* using the QCD Sum Rules. The calculation of the form factors were performed for the cases D, Ds and K* off shell. Using the similarities between B and D mesons, we also calculated the form factors and coupling constant of the vertex BsBK*. The coupling constants of the vertices BsBK* and DsDK* were compared with each other through the Heavy Hadron Chiral Perturbation Theory(HHChPT). We found a difference of 19% between BsBK* and DsDK* coupling constants using the HHChPT relation.
Analysis of the Heavy Pseudoscalar Mesons with Thermal QCD Sum Rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Bin; Wang, Zhi-Gang
2016-07-01
In this article, we calculate the contributions of the condensates up to dimension-6, including the one-loop corrections to the quark condensates, in the operator product expansion in a consistent way, and study the masses and decay constants of the heavy pseudoscalar mesons with the thermal QCD sum rules. We reproduce the experimental values of the masses of the D, D s , B and B s and obtain the decay constants at zero temperature. Then we study the thermal behaviors of the masses and decay constants, which are useful in explaining the heavy-ion collision experiments.
{kappa}K{sup +{pi}-} vertex in light cone QCD sum rules
Baytemir, G.; Sarac, Y.; Yilmaz, O.
2010-05-01
In this work we study the {kappa}K{sup +{pi}-} vertex in the framework of light cone QCD sum rules. We predict the coupling constant g{sub {kappa}K}{sup +}{sub {pi}}{sup -} to be g{sub {kappa}K}{sup +}{sub {pi}}{sup -}=(6.0{+-}1.0) GeV and estimate the scalar f{sub 0}-{sigma} mixing angle from the experimental ratio g{sup 2}({kappa}{yields}K{pi})/g{sup 2}({sigma}{yields}{pi}{pi}).
Magnetic moment for the negative parity Λ → Σ0 transition in light cone QCD sum rules
NASA Astrophysics Data System (ADS)
Aliev, T. M.; Savcı, M.
2016-07-01
The magnetic moment of the Λ →Σ0 transition between negative parity baryons is calculated in framework of the QCD sum rules approach by using the general form of the interpolating currents. The pollution arising from the positive-to-positive, and positive-to-negative parity baryons is eliminated by constructing the sum rules for different Lorentz structures. A comparison of our result with the predictions of the results of other approaches for the positive parity baryons is presented.
Up- and down-quark masses from finite-energy QCD sum rules to five loops
Dominguez, C. A.; Nasrallah, N. F.; Roentsch, R. H.; Schilcher, K.
2009-01-01
The up- and down-quark masses are determined from an optimized QCD finite-energy sum rule involving the correlator of axial-vector divergences, to five-loop order in perturbative QCD, and including leading nonperturbative QCD and higher order quark-mass corrections. This finite-energy sum rule is designed to reduce considerably the systematic uncertainties arising from the (unmeasured) hadronic resonance sector, which in this framework contributes less than 3-4% to the quark mass. This is achieved by introducing an integration kernel in the form of a second degree polynomial, restricted to vanish at the peak of the two lowest lying resonances. The driving hadronic contribution is then the pion pole, with parameters well known from experiment. The determination is done in the framework of contour improved perturbation theory, which exhibits a very good convergence, leading to a remarkably stable result in the unusually wide window s{sub 0}=1.0-4.0 GeV{sup 2}, where s{sub 0} is the radius of the integration contour in the complex energy (squared) plane. The results are m{sub u}(Q=2 GeV)=2.9{+-}0.2 MeV, m{sub d}(Q=2 GeV)=5.3{+-}0.4 MeV, and (m{sub u}+m{sub d})/2=4.1{+-}0.2 MeV (at a scale Q=2 GeV)
J-pairing interaction, number of states, and nine-j sum rules of four identical particles
Zhao, Y.M.; Arima, A.
2005-11-01
We study the J-pairing Hamiltonian and find that the sum of eigenvalues of spin-I states equals the sum of the norm matrix elements within the pair basis for four identical particles such as four fermions in a single-j shell or four bosons with spin l. We relate the number of states to sum rules of nine-j coefficients. We obtained sum rules for nine-j coefficients <(jj)J,(jj)K:I|(jj)J,(jj)K:I> and <(ll)J,(ll)K:I|(ll)J,(ll)K:I> summing over (1) even J and even K, (2) even J and odd K, (3) odd J and odd K, and (4) both even and odd values for J and K, where j is a half integer and l is an integer.
Mass tensor in the Bohr Hamiltonian from the nondiagonal energy weighted sum rules
Jolos, R. V.; Brentano, P. von
2009-04-15
Relations are derived in the framework of the Bohr Hamiltonian that express the matrix elements of the deformation-dependent components of the mass tensor through the experimental data on the energies and the E2 transitions relating the low-lying collective states. These relations extend the previously obtained results for the intrinsic mass coefficients of the well-deformed axially symmetric nuclei on nuclei of arbitrary shape. The expression for the mass tensor is suggested, which is sufficient to satisfy the existing experimental data on the energy weighted sum rules for the E2 transitions for the low-lying collective quadrupole excitations. The mass tensor is determined for {sup 106,108}Pd, {sup 108-112}Cd, {sup 134}Ba, {sup 150}Nd, {sup 150-154}Sm, {sup 154-160}Gd, {sup 164}Dy, {sup 172}Yb, {sup 178}Hf, {sup 188-192}Os, and {sup 194-196}Pt.
Study of the D*ρ system using QCD sum rules
Torres, A. Martínez; Khemchandani, K. P.; Nielsen, M.; Navarra, F. S.; Oset, E.
2014-11-11
In this proceeding we present a study of the D*ρ system made by using the method of QCD sum rules. Considering isospin and spin projectors, we investigate the different configurations and obtain three D* mesons with isospin I = 1/2, spin S = 0, 1, 2 and with masses 2500±67 MeV, 2523±60 MeV, and 2439±119 MeV, respectively. The last state can be related to D{sub 2}{sup *} (2460) (spin 2) listed by the Particle Data Group, while one of the first two might be associated with D*(2640), whose spin-parity is unknown. In the case of I = 3/2 we also find evidences of three states with spin 0, 1 and 2, respectively, with masses 2467±82 MeV, 2420±128 MeV, and 2550±56 MeV.
Pinched weights and duality violation in QCD sum rules: A critical analysis
Gonzalez-Alonso, Martin; Pich, Antonio; Prades, Joaquim
2010-07-01
We analyze the so-called pinched weights, that are generally thought to reduce the violation of quark-hadron duality in finite-energy sum rules. After showing how this is not true in general, we explain how to address this question for the left-right correlator and any particular pinched weight, taking advantage of our previous work [1], where the possible high-energy behavior of the left-right spectral function was studied. In particular, we show that the use of pinched weights allows to determine with high accuracy the dimension six and eight contributions in the operator-product expansion, O{sub 6}=(-4.3{sub -0.7}{sup +0.9})x10{sup -3} GeV{sup 6} and O{sub 8}=(-7.2{sub -5.3}{sup +4.2})x10{sup -3} GeV{sup 8}.
Temperature Dependence of Decuplet Baryon Masses from Thermal QCD Sum Rules
NASA Astrophysics Data System (ADS)
Xu, Yong-Jiang; Liu, Yong-Lu; Huang, Ming-Qiu
2015-02-01
In the present work, the masses of the decuplet baryons at finite temperature are investigated using thermal QCD sum rules. Making use of the quark propagator at finite temperature, we calculate the spectral functions to T8 order, and find that there are no contributions to the spectral functions at T8 order and the temperature corrections mainly come from that containing T4 ones. The calculations show very little temperature dependence of the masses below T = 0.11 GeV. While above that value, the masses decrease with increasing temperature. The results indicate that the hadron-quark phase transition temperature may be Tc >= 0.11 GeV for the decuplet bayons.
Atomic partial charges in condensed phase from an exact sum rule for infrared absorption
NASA Astrophysics Data System (ADS)
Vuilleumier, Rodolphe
2014-05-01
A general sum rule for infrared intensities provides a definition of effective partial charges which can be experimentally obtained using isotopic substitutions and is valid in both gas and condensed phases. Of particular interest is the case of molecular liquids. We have, therefore, determined the hydrogen partial charges in liquid methanol and liquid water from the available literature. The resulting charges are 0.63 e and 0.14 e for hydrogen atoms bounded to the methanol oxygen and carbon atoms, respectively, and 0.55 e for hydrogen atoms in liquid water. The effective partial charges in liquid water were also computed from density functional based ab initio molecular dynamics simulations and found in good agreement with experiment.
Malila, Jussi; McGraw, Robert; Laaksonen, Ari; Lehtinen, Kari E. J.
2015-01-07
Despite recent advances in monitoring nucleation from a vapor at close-to-molecular resolution, the identity of the critical cluster, forming the bottleneck for the nucleation process, remains elusive. During past twenty years, the first nucleation theorem has been often used to extract the size of the critical cluster from nucleation rate measurements. However, derivations of the first nucleation theorem invoke certain questionable assumptions that may fail, e.g., in the case of atmospheric new particle formation, including absence of subcritical cluster losses and heterogeneous nucleation on pre-existing nanoparticles. Here we extend the kinetic derivation of the first nucleation theorem to give a general framework to include such processes, yielding sum rules connecting the size dependent particle formation and loss rates to the corresponding loss-free nucleation rate and the apparent critical size from a naïve application of the first nucleation theorem that neglects them.
Sum rules related to third-order properties: a numerical check
NASA Astrophysics Data System (ADS)
Caputo, M. C.; Lazzeretti, P.
2003-03-01
Although electrodynamics is formally invariant in a gauge transformation, the values of some physical quantities, e.g., magnetic properties, depend on the approximation employed to calculate them. The conditions for gauge independence of third-rank tensor properties that describe the response of a molecule in the presence of three perturbations, that is, external electric and magnetic field, and intramolecular nuclear magnetic dipoles, are discussed. The relationships for invariance of the physical properties to a gauge translation are exactly the same as the constraints for charge conservation. They are expressed in terms of second-rank response properties, namely electric polarizabilities and electric shielding at the nuclei. An extended numerical test has been carried out to determine the Hartree-Fock limit for a series of quantities entering the gauge-invariance sum rules.
Sum rules and spectral density flow in QCD and in superconformal theories
NASA Astrophysics Data System (ADS)
Costantini, Antonio; Delle Rose, Luigi; Serino, Mirko
2014-11-01
We discuss the signature of the anomalous breaking of the superconformal symmetry in N = 1 super Yang Mills theory and its manifestation in the form of anomaly poles. Moreover, we describe the massive deformations of the N = 1 theory and the spectral densities of the corresponding anomaly form factors. These are characterized by spectral densities which flow with the mass deformation and turn the continuum contributions from the two-particle cuts of the intermediate states into poles, with a single sum rule satisfied by each component. The poles can be interpreted as signaling the exchange of a composite axion/dilaton/dilatino (ADD) multiplet in the effective Lagrangian. We conclude that global anomalous currents characterized by a single flow in the perturbative picture always predict the existence of composite interpolating fields.
Malila, Jussi; McGraw, Robert; Laaksonen, Ari; Lehtinen, Kari E. J.
2015-01-07
Despite recent advances in monitoring nucleation from a vapor at close-to-molecular resolution, the identity of the critical cluster, forming the bottleneck for the nucleation process, remains elusive. During past twenty years, the first nucleation theorem has been often used to extract the size of the critical cluster from nucleation rate measurements. However, derivations of the first nucleation theorem invoke certain questionable assumptions that may fail, e.g., in the case of atmospheric new particle formation, including absence of subcritical cluster losses and heterogeneous nucleation on pre-existing nanoparticles. Here we extend the kinetic derivation of the first nucleation theorem to give amore » general framework to include such processes, yielding sum rules connecting the size dependent particle formation and loss rates to the corresponding loss-free nucleation rate and the apparent critical size from a naïve application of the first nucleation theorem that neglects them.« less
QCD sum rule study of a charged bottom-strange scalar meson
NASA Astrophysics Data System (ADS)
Zanetti, C. M.; Nielsen, M.; Khemchandani, K. P.
2016-05-01
Using the QCD sum rule approach, we investigate the possible four-quark structure for the new observed Bs0π± narrow structure (D0). We use a diquak-antidiquark scalar current and work to the order of ms in full QCD, without relying on 1 /mQ expansion. Our study indicates that although it is possible to obtain a stable mass in agreement with the state found by the D0 collaboration, more constraint analysis (simultaneous requirement of the OPE convergence and the dominance of the pole on the phenomenological side) leads to a higher mass. We also predict the masses of the bottom scalar tetraquark resonances with zero and two strange quarks.
QCD sum rule calculation of quark-gluon three-body components in the B-meson wave function
Nishikawa, Tetsuo; Tanaka, Kazuhiro
2011-10-21
We discuss the QCD sum rule calculation of the heavy-quark effective theory parameters {lambda}{sub E} and {lambda}{sub H}, which represent quark-gluon three-body components in the B-meson wave function. We update the sum rules for {lambda}{sub E,H} calculating the new higher-order contributions to the operator product expansion for the corresponding correlator, i.e., the order {alpha}{sub s} radiative corrections to the Wilson coefficients associated with the dimension-5 quark-gluon mixed condensate, and the power corrections due to the dimension-6 vacuum condensates. We find that the new radiative corrections significantly improve stability of the corresponding Borel sum rules, modifying the values of {lambda}{sub E,H}.
Wilson coefficients and four-quark condensates in QCD sum rules for medium modifications of D mesons
NASA Astrophysics Data System (ADS)
Buchheim, T.; Hilger, T.; Kämpfer, B.
2015-01-01
Wilson coefficients of light four-quark condensates in QCD sum rules are evaluated for pseudoscalar D mesons, thus pushing the sum rules toward mass dimension 6. In contrast to the situation for q ¯q mesons, the impact of the four-quark condensates for vacuum as well as in-medium situations is found to be rather small within the Borel window used in previous analyses. The complete four-quark condensate contributions enable us to identify candidates for an order parameter of spontaneous chiral symmetry breaking and/or restoration as well as to evaluate stability criteria of operator product expansions.
Yan, Xin -Hu; Ye, Yun -Xiu; Chen, Jian -Ping; Lu, Hai -Jiang; Zhu, Peng -Jia; Jiang, Feng -Jian
2015-07-17
The radiation and ionization energy loss are presented for single arm Monte Carlo simulation for the GDH sum rule experiment in Hall-A at Jefferson Lab. Radiation and ionization energy loss are discussed formore » $$^{12}C$$ elastic scattering simulation. The relative momentum ratio $$\\frac{\\Delta p}{p}$$ and $$^{12}C$$ elastic cross section are compared without and with radiation energy loss and a reasonable shape is obtained by the simulation. The total energy loss distribution is obtained, showing a Landau shape for $$^{12}C$$ elastic scattering. This simulation work will give good support for radiation correction analysis of the GDH sum rule experiment.« less
Yan, Xin -Hu; Ye, Yun -Xiu; Chen, Jian -Ping; Lu, Hai -Jiang; Zhu, Peng -Jia; Jiang, Feng -Jian
2015-07-17
The radiation and ionization energy loss are presented for single arm Monte Carlo simulation for the GDH sum rule experiment in Hall-A at Jefferson Lab. Radiation and ionization energy loss are discussed for $^{12}C$ elastic scattering simulation. The relative momentum ratio $\\frac{\\Delta p}{p}$ and $^{12}C$ elastic cross section are compared without and with radiation energy loss and a reasonable shape is obtained by the simulation. The total energy loss distribution is obtained, showing a Landau shape for $^{12}C$ elastic scattering. This simulation work will give good support for radiation correction analysis of the GDH sum rule experiment.
NASA Astrophysics Data System (ADS)
Kataev, A. L.
2014-02-01
Conformal symmetry-based relations between concrete perturbative QED and QCD approximations for the Bjorken , the Ellis-Jaffe sum rules of polarized lepton- nucleon deep-inelastic scattering (DIS), the Gross-Llewellyn Smith sum rules of neutrino-nucleon DIS, and for the Adler functions of axial-vector and vector channels are derived. They result from the application of the operator product expansion to three triangle Green functions, constructed from the non-singlet axial-vector, and two vector currents, the singlet axial-vector and two non-singlet vector currents and the non-singlet axial-vector, vector and singlet vector currents in the limit, when the conformal symmetry of the gauge models with fermions is considered unbroken. We specify the perturbative conditions for this symmetry to be valid in the case of the U(1) and SU( N c) models. The all-order perturbative identity following from the conformal invariant limit between the concrete contributions to the Bjorken, the Ellis-Jaffe and the Gross-Llewellyn Smith sum rules is proved. The analytical and numerical O( α 4) and conformal symmetry based approximations for these sum rules and for the Adler function of the non-singlet vector currents are summarized. Possible theoretical applications of the results presented are discussed.
Sum Rule Constraints and the Quality of Approximate Kubo-Transformed Correlation Functions.
Hernández de la Peña, Lisandro
2016-02-11
In this work, a general protocol for evaluating the quality of approximate Kubo correlation functions of nontrivial systems in many dimensions is discussed. We first note that the generalized deconvolution of the Kubo transformed correlation function onto a time correlation function at a given value τ in imaginary time, such that 0 < τ < βℏ, leads to a series of sum rules applicable to the nth derivative of the Kubo function and whose iterative extension allows us to link derivatives of different order in the corresponding correlation functions. We focus on the case when τ = βℏ/2, for which all deconvolution kernels become real valued functions and their asymptotic behavior at long times exhibits a polynomial divergence. It is then shown that thermally symmetrized static averages, and the averages of the corresponding time derivatives, are ideally suited to investigate the quality of approximate Kubo correlation functions at successively larger (and up to arbitrarily long) times. This overall strategy is illustrated analytically for a harmonic system and numerically for a multidimensional double-well potential and a Lennard-Jones fluid. The analysis includes an assessment of RPMD position autocorrelation results as a function of the number of dimensions in a double-well potential and of the RPMD velocity autocorrelation function of liquid neon at 30 K. PMID:26786406
Infrared Refractive Index of Silicon: Parity and Sum-Rule Tests
NASA Astrophysics Data System (ADS)
Karstens, William; Inokuti, Mitio; Smith, David Y.
2012-02-01
We have resolved conflicting reports for the IR refractive index of silicon using general considerations of linear response theory. We find that use of unphysical series expansions in the analysis of channel spectra has been a significant source of systematic error. Recognition that the index is an even function of photon energy is crucial for analysis of these measurements and clarifies data presentation. In the region of high IR transparency of elemental semiconductors, the index may be expanded in a rapidly convergent Taylor series. Coefficients of terms in the (2n)^th power of energy are proportional to the (2n+1)^th inverse moment of the electronic absorption spectrum. In the favorable case of intrinsic Si, the electronic absorption is sufficiently well known that independent values of the intercept, slope and curvature of plots of index vs. the square of photon energy may be calculated. Index data sets with parameters significantly different from these suffer from systematic errors or refer to impure samples. Using these parity and sum-rule tests we have prepared a composite index data set for intrinsic silicon that represents a best fit to reliable measurements from microwaves to the visible. Applications to germanium and diamond will be discussed.
Mass modification of /D-meson at finite density in QCD sum rule
NASA Astrophysics Data System (ADS)
Hayashigaki1, A.
2000-08-01
We evaluate the mass shift of isospin-averaged /D-meson in the nuclear medium. Borel-transformed QCD sum rules are used to describe an interaction between the /D-meson and a nucleon by taking into account all the lowest dimension-4 operators in the operator product expansion (OPE). We find at normal matter density the /D-meson mass shift is about /10 times (/~50 MeV) larger than that of /J/ψ. This originates from the fact that the dominant contribution in the OPE for the /D-meson is the nucleon matrix element of mcq¯q, where mc is the charm-quark mass and /q denotes light quarks. We also discuss that the mass shift of the /D-meson in nuclear matter may cause the level crossings of the charmonium states and the /DD¯ threshold. This suggests an additional mechanism of the /J/ψ suppression in high energy heavy-ion collisions.
Unitarity sum rules, three-site moose model, and the ATLAS 2 TeV diboson anomalies
NASA Astrophysics Data System (ADS)
Abe, Tomohiro; Nagai, Ryo; Okawa, Shohei; Tanabashi, Masaharu
2015-09-01
We investigate W' interpretations for the ATLAS 2 TeV diboson anomalies. The roles of the unitarity sum rules, which ensure the perturbativity of the longitudinal vector boson scattering amplitudes, are emphasized. We find the unitarity sum rules and the custodial symmetry are powerful enough to predict various nontrivial relations among W W Z', W Z W', W W h , W W'h and Z Z'h coupling strengths in a model independent manner. We also perform surveys in the general parameter space of W' models and find the ATLAS 2 TeV diboson anomalies may be interpreted as a W' particle of the three-site moose model, i.e., a Kaluza-Klein like particle in a deconstructed extra dimension model. It is also shown that the nonstandard-model-like Higgs boson is favored by the present data to interpret the ATLAS diboson anomalies as the consequences of the W' and Z' bosons.
Baikov, P A; Chetyrkin, K G; Kühn, J H
2010-04-01
We compute, for the first time, the order alpha(s)(4) contributions to the Bjorken sum rule for polarized electron-nucleon scattering and to the (nonsinglet) Adler function for the case of a generic color gauge group. We confirm at the same order a (generalized) Crewther relation which provides a strong test of the correctness of our previously obtained results: the QCD Adler function and the five-loop beta function in quenched QED. In particular, the appearance of an irrational contribution proportional to zeta(3) in the latter quantity is confirmed. We obtain the commensurate scale equation relating the effective strong coupling constants as inferred from the Bjorken sum rule and from the Adler function at order alpha(s)(4). PMID:20481875
NASA Astrophysics Data System (ADS)
Yan, Xin-Hu; Ye, Yun-Xiu; Chen, Jian-Ping; Lu, Hai-Jiang; Zhu, Peng-Jia; Jiang, Feng-Jian
2015-07-01
The radiation and ionization energy loss are presented for single arm Monte Carlo simulation for the GDH sum rule experiment in Hall-A at the Jefferson Lab. Radiation and ionization energy loss are discussed for 12C elastic scattering simulation. The relative momentum ratio \\frac{{Δ p}}{p} and 12C elastic cross section are compared without and with radiative energy loss and a reasonable shape is obtained by the simulation. The total energy loss distribution is obtained, showing a Landau shape for 12C elastic scattering. This simulation work will give good support for radiation correction analysis of the GDH sum rule experiment. Supported by National Natural Science Foundation of China (11135002, 11275083), US Department of Energy contract DE-AC05-84ER-40150 under which Jefferson Science Associates operates the Thomas Jefferson National Accelerator Facility and Natural Science Foundation of An'hui Educational Committee (KJ2012B179)
K 0- overlineK0 mixing and the CKM parameters (ϱ, η) from the Laplace sum rules
NASA Astrophysics Data System (ADS)
Narison, S.
1995-02-01
Using the Laplace sum rule (LSR) approach, which is less affected by the contribution of the higher mass hadronic states than the Finite Energy Sum Rule (FESR), we test the reliability of the existing estimate of the K 0- overlineK0 mixing parameter from the four-quark two-point correlator. We obtain, for the renormalization group invariant B-parameter [ {f K}/{(1.2f π) }] 2B̂K, the upper bound: 0.83 and the conservative estimate: 0.58 ± 0.22 from the LSR method. Combining the previous estimate with the updated value of f BB B=(1.49±0.14)f π obtained from the same LSR method, one can deduce the fitted values ( ϱ, η) f (0.09, 0.41) of the CKM parameters.
Analyses of gD*sDK and gB*sBK vertices in QCD sum rules
NASA Astrophysics Data System (ADS)
Süngü, J. Y.; Sundu, H.; Azizi, K.
2012-02-01
The coupling constants gD*sDK and gB*sBK are calculated in the framework of QCD sum rules. We evaluate the correlation functions of these vertices considering both D(B) and K mesons off-shell and obtain the results as gD*sDK = (2.89 ± 0.25) and gB*sBK = (3.01 ± 0.28).
{lambda}{sub b}{yields}p, {lambda} transition form factors from QCD light-cone sum rules
Wang Yuming; Lue Caidian; Shen Yuelong
2009-10-01
Light-cone sum rules for the {lambda}{sub b}{yields}p, {lambda} transition form factors are derived from the correlation functions expanded by the twist of the distribution amplitudes of the {lambda}{sub b} baryon. In terms of the {lambda}{sub b} three-quark distribution amplitude models constrained by the QCD theory, we calculate the form factors at small momentum transfers and compare the results with those estimated in the conventional light-cone sum rules (LCSR) and perturbative QCD approaches. Our results indicate that the two different versions of sum rules can lead to the consistent numbers of form factors responsible for {lambda}{sub b}{yields}p transition. The {lambda}{sub b}{yields}{lambda} transition form factors from LCSR with the asymptotic {lambda} baryon distribution amplitudes are found to be almost 1 order larger than those obtained in the {lambda}{sub b}-baryon LCSR, implying that the preasymptotic corrections to the baryonic distribution amplitudes are of great importance. Moreover, the SU(3) symmetry breaking effects between the form factors f{sub 1}{sup {lambda}{sub b}}{sup {yields}}{sup p} and f{sub 1}{sup {lambda}{sub b}}{sup {yields}}{sup {lambda}} are computed as 28{sub -8}{sup +14}% in the framework of {lambda}{sub b}-baryon LCSR.
B{sub (s)}{yields}S transitions in the light cone sum rules with the chiral current
Sun Yanjun; Li Zuohong; Huang Tao
2011-01-15
We make a QCD light-cone sum rule assessment of B{sub (s)} semileptonic decays to a light scalar meson, B{sub (s)}{yields}Sl{nu}{sub l}, Sll(l=e,{mu},{tau}). Chiral current correlators are used and calculations are performed at leading order in {alpha}{sub s}. Having little knowledge of the ingredients of the scalar mesons, we confine ourself to the two-quark picture for them and work with the two possible scenarios. The resulting sum rules for the form factors receive no contributions from the twist-3 distribution amplitudes, in comparison with the calculation of the conventional light-cone sum rule approach where the twist-3 parts usually play an important role. We specify the range of the squared momentum transfer q{sup 2}, in which the operator product expansion for the correlators remains valid approximately. It is found that the form factors satisfy a relation consistent with the prediction of soft collinear effective theory. In the effective range we investigate behaviors of the form factors and differential decay widths and compare our calculations with the observations from other approaches.
NASA Astrophysics Data System (ADS)
Yu, Z.; Baym, G.
2006-06-01
The spin response functions measured in multicomponent fermion gases by means of rf transitions between hyperfine states are strongly constrained by the symmetry of the interatomic interactions. Such constraints are reflected in the spin f -sum rule that the response functions must obey. In particular, only if the effective interactions are not fully invariant in SU(2) spin space, are the response functions sensitive to mean field and pairing effects. We demonstrate, via a self-consistent calculation of the spin-spin correlation function within the framework of Hartree-Fock-BCS theory, how one can derive a correlation function explicitly obeying the f -sum rule. By contrast, simple one-loop approximations to the spin response functions do not satisfy the sum rule, except in special cases. As we show, the emergence of a second peak at higher frequency in the rf spectrum, as observed in a recent experiment in trapped Li6 , can be understood as the contribution from the paired fermions, with a shift of the peak from the normal particle response proportional to the square of the BCS pairing gap.
A QCD sum rule calculation of the X± (5568) → Bs0 π± decay width
NASA Astrophysics Data System (ADS)
Dias, J. M.; Khemchandani, K. P.; Martínez Torres, A.; Nielsen, M.; Zanetti, C. M.
2016-07-01
To understand the nature of the X (5568), recently observed in the mass spectrum of the Bs0 π± system by the D0 Collaboration, we have investigated, in a previous work, a scalar tetraquark (diquak-antidiquark) structure for it, within the two-point QCD sum rules method. We found that it is possible to obtain a stable value of the mass compatible with the D0 result, although a rigorous QCD sum rule constrained analysis led to a higher value of mass. As a continuation of our investigation, we calculate the width of the tetraquark state with same quark content as X (5568), to the channel Bs0 π±, using the three-point QCD sum rule. We obtain a value of (20.4 ± 8.7) MeV for the mass ∼ 5568 MeV, which is compatible with the experimental value of 21.9 ± 6.4 (sta)-2.5+5.0 (syst) MeV /c2. We find that the decay width to Bs0 π± does not alter much for a higher mass state.
NASA Astrophysics Data System (ADS)
Delion, Doru S.; Schuck, Peter; Tohyama, Mitsuru
2016-02-01
The Self-Consistent RPA (SCRPA) approach is elaborated for cases with a continuously broken symmetry, this being the main focus of the present article. Correlations beyond standard RPA are summed up correcting for the quasi-boson approximation in standard RPA. Desirable properties of standard RPA such as fulfillment of energy weighted sum rule and appearance of Goldstone (zero) modes are kept. We show theoretically and, for a model case, numerically that, indeed, SCRPA maintains all properties of standard RPA for practically all situations of spontaneously broken symmetries. A simpler approximate form of SCRPA, the so-called renormalised RPA, also has these properties. The SCRPA equations are first outlined as an eigenvalue problem, but it is also shown how an equivalent many body Green's function approach can be formulated.
Babusci, D.; Giordano, G.; Baghaei, H.; Cichocki, A.; Blecher, M.; Breuer, M.; Commeaux, C.; Didelez, J.P.; Caracappa, A.; Fan, Q.
1995-12-31
Energy weighted integrals of the difference in helicity-dependent photo-production cross sections ({sigma}{sub {1/2}} - {sigma}{sub 3/2}) provide information on the nucleon`s Spin-dependent Polarizability ({gamma}), and on the spin-dependent part of the asymptotic forward Compton amplitude through the Drell-Hearn-Gerasimov (DHG) sum rule. (The latter forms the Q{sup 2}=0 limit of recent spin-asymmetry experiments in deep-inelastic lepton-scattering.) There are no direct measurements of {sigma}{sub {1/2}} or {sigma}{sub 3/2}, for either the proton or the neutron. Estimates from current {pi}-photo-production multipole analyses, particularly for the proton-neutron difference, are in good agreement with relativistic-l-loop Chiral calculations ({chi}PT) for {gamma} but predict large deviations from the DHG sum rule. Either (a) both the 2-loop corrections to the Spin-Polarizability are large and the existing multipoles are wrong, or (b) modifications to the Drell-Hearn-Gerasimov sum rule are required to fully describe the isospin structure of the nucleon. The helicity-dependent photo-reaction amplitudes, for both the proton and the neutron, will be measured at LEGS from pion-threshold to 470 MeV. In these double-polarization experiments, circularly polarized photons from LEGS will be used with SPHICE, a new frozen-spin target consisting of {rvec H} {center_dot} {rvec D} in the solid phase. Reaction channels will be identified in SASY, a large detector array covering about 80% of 4{pi}. A high degree of symmetry in both target and detector will be used to minimize systematic uncertainties.
Investigation of the D*s2(2573)+D+K0 vertex via QCD sum rules
NASA Astrophysics Data System (ADS)
Sarac, Y.; Azizi, K.; Sundu, H.
2014-12-01
In this work the D*s2(2573)+D+K0 vertex is studied and the coupling constant corresponding to the D*s2(2573)+ → D+K0 transition is calculated. The calculation is performed using three point QCD sum rules method and the value of the coupling constant is obtained as gD*s2DK = (12.85 ± 3.85) GeV-1. The coupling constant is also used to calculate the decay width and the branching ratio of the considered transition.
{sigma}{sub Q}{lambda}{sub Q}{pi} coupling constant in light cone QCD sum rules
Azizi, K.; Bayar, M.; Ozpineci, A.
2009-03-01
The strong coupling constants g{sub {sigma}{sub Q}}Q{sub {lambda}{sub Q}}{sub {pi}} (Q=b and c) are studied in the framework of the light cone QCD sum rules using the most general form of the baryonic currents. The predicted coupling constants are used to estimate the decay widths for the {sigma}{sub Q}{yields}{lambda}{sub Q}{pi} decays which are compared with the predictions of the other approaches and existing experimental data.
Energy-weighted sum rules and the analysis of vibrational structure in molecular spectra
NASA Astrophysics Data System (ADS)
Smith, W. L.
2015-10-01
The energy-weighted sum SV = Σn (E‧n - E″m)|<ψ″m|ψ‧n>|2 = <ψ″m|ΔV|ψ″m> for the vibrational potential functions V‧, V″ associated with transitions between two electronic states of diatomic molecular species is investigated and specific formulae are given using Morse functions for V‧ and V″. It is found that these formulae are useful approximations which provide a convenient way to analyse the vibrational structure of real spectra to give estimates of molecular parameters such as the change in internuclear distance accompanying a transition.
The spin structure function g1p of the proton and a test of the Bjorken sum rule
NASA Astrophysics Data System (ADS)
Adolph, C.; Akhunzyanov, R.; Alexeev, M. G.; Alexeev, G. D.; Amoroso, A.; Andrieux, V.; Anosov, V.; Austregesilo, A.; Azevedo, C.; Badełek, B.; Balestra, F.; Barth, J.; Baum, G.; Beck, R.; Bedfer, Y.; Bernhard, J.; Bicker, K.; Bielert, E. R.; Birsa, R.; Bisplinghoff, J.; Bodlak, M.; Boer, M.; Bordalo, P.; Bradamante, F.; Braun, C.; Bressan, A.; Büchele, M.; Burtin, E.; Capozza, L.; Chang, W.-C.; Chiosso, M.; Choi, I.; Chung, S. U.; Cicuttin, A.; Crespo, M. L.; Curiel, Q.; Dalla Torre, S.; Dasgupta, S. S.; Dasgupta, S.; Denisov, O. Yu.; Dhara, L.; Donskov, S. V.; Doshita, N.; Duic, V.; Dziewiecki, M.; Efremov, A.; Eversheim, P. D.; Eyrich, W.; Ferrero, A.; Finger, M.; Finger, M.; Fischer, H.; Franco, C.; du Fresne von Hohenesche, N.; Friedrich, J. M.; Frolov, V.; Fuchey, E.; Gautheron, F.; Gavrichtchouk, O. P.; Gerassimov, S.; Giordano, F.; Gnesi, I.; Gorzellik, M.; Grabmüller, S.; Grasso, A.; Grosse-Perdekamp, M.; Grube, B.; Grussenmeyer, T.; Guskov, A.; Haas, F.; Hahne, D.; von Harrach, D.; Hashimoto, R.; Heinsius, F. H.; Herrmann, F.; Hinterberger, F.; Horikawa, N.; d'Hose, N.; -Yu Hsieh, C.; Huber, S.; Ishimoto, S.; Ivanov, A.; Ivanshin, Yu.; Iwata, T.; Jahn, R.; Jary, V.; Jörg, P.; Joosten, R.; Kabuß, E.; Ketzer, B.; Khaustov, G. V.; Khokhlov, Yu. A.; Kisselev, Yu.; Klein, F.; Klimaszewski, K.; Koivuniemi, J. H.; Kolosov, V. N.; Kondo, K.; Königsmann, K.; Konorov, I.; Konstantinov, V. F.; Kotzinian, A. M.; Kouznetsov, O.; Krämer, M.; Kremser, P.; Krinner, F.; Kroumchtein, Z. V.; Kuchinski, N.; Kunne, F.; Kurek, K.; Kurjata, R. P.; Lednev, A. A.; Lehmann, A.; Levillain, M.; Levorato, S.; Lichtenstadt, J.; Longo, R.; Maggiora, A.; Magnon, A.; Makins, N.; Makke, N.; Mallot, G. K.; Marchand, C.; Martin, A.; Marzec, J.; Matousek, J.; Matsuda, H.; Matsuda, T.; Meshcheryakov, G.; Meyer, W.; Michigami, T.; Mikhailov, Yu. V.; Miyachi, Y.; Nagaytsev, A.; Nagel, T.; Nerling, F.; Neyret, D.; Nikolaenko, V. I.; Novy, J.; Nowak, W.-D.; Nunes, A. S.; Olshevsky, A. G.; Orlov, I.; Ostrick, M.; Panzieri, D.; Parsamyan, B.; Paul, S.; Peng, J.-C.; Pereira, F.; Pesek, M.; Peshekhonov, D. V.; Platchkov, S.; Pochodzalla, J.; Polyakov, V. A.; Pretz, J.; Quaresma, M.; Quintans, C.; Ramos, S.; Regali, C.; Reicherz, G.; Riedl, C.; Rocco, E.; Rossiyskaya, N. S.; Ryabchikov, D. I.; Rychter, A.; Samoylenko, V. D.; Sandacz, A.; Santos, C.; Sarkar, S.; Savin, I. A.; Sbrizzai, G.; Schiavon, P.; Schmidt, K.; Schmieden, H.; Schönning, K.; Schopferer, S.; Selyunin, A.; Shevchenko, O. Yu.; Silva, L.; Sinha, L.; Sirtl, S.; Slunecka, M.; Sozzi, F.; Srnka, A.; Stolarski, M.; Sulc, M.; Suzuki, H.; Szabelski, A.; Szameitat, T.; Sznajder, P.; Takekawa, S.; ter Wolbeek, J.; Tessaro, S.; Tessarotto, F.; Thibaud, F.; Tosello, F.; Tskhay, V.; Uhl, S.; Veloso, J.; Virius, M.; Weisrock, T.; Wilfert, M.; Windmolders, R.; Zaremba, K.; Zavertyaev, M.; Zemlyanichkina, E.; Ziembicki, M.; Zink, A.
2016-02-01
New results for the double spin asymmetry A1p and the proton longitudinal spin structure function g1p are presented. They were obtained by the COMPASS Collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH3 target. The data were collected in 2011 and complement those recorded in 2007 at 160 GeV, in particular at lower values of x. They improve the statistical precision of g1p (x) by about a factor of two in the region x ≲ 0.02. A next-to-leading order QCD fit to the g1 world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, ΔΣ, ranging from 0.26 to 0.36, and to a re-evaluation of the first moment of g1p. The uncertainty of ΔΣ is mostly due to the large uncertainty in the present determinations of the gluon helicity distribution. A new evaluation of the Bjorken sum rule based on the COMPASS results for the non-singlet structure function g1NS (x ,Q2) yields as ratio of the axial and vector coupling constants |gA /gV | = 1.22 ± 0.05 (stat.) ± 0.10 (syst.), which validates the sum rule to an accuracy of about 9%.
NASA Astrophysics Data System (ADS)
Jin, Hong-Ying; Zhang, Jin; Zhang, Zhu-Feng; Steele, T. G.
2010-03-01
Motivated by the similar mass splitting in light-light and heavy-light JP=0- and JP=0+ mesons, the SU(3)-symmetry breaking effects splitting the masses in the 0- and 0+ channels of the D meson are analyzed in the framework of QCD sum rules with an underlying cq¯ structure. We take into account operator mixing to obtain an infrared stable operator-product expansion method including complete nonperturbative and perturbative O(mq) corrections to the correlation function. With the same threshold for both channels, the mass splitting arising from the sum rules has the same behavior as the observed spectrum. In particular, we obtain mDs-mDd˜35MeV in the 0- channel and mDd-mDs˜12MeV in the 0+ channel at a renormalization scale μ=1GeV. The splitting can be attributed to the different roles of mass effects and the parity-dependent “force” induced from nonperturbative QCD vacuum. Further analysis shows that due to this parity-dependent force it is natural that the mass gap of the two states in the 0- channel is larger than the 0+ channel. When we increase the renormalization scale to μ=1.3GeV the splitting remains unchanged which demonstrates a correct scale invariance. Combined with heavy quark effective theory, generalizations to other channels of charmed mesons and b-systems are briefly discussed.
OPE, charm-quark mass, and decay constants of D and Ds mesons from QCD sum rules
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2011-01-01
We present a sum-rule extraction of the decay constants of the charmed mesons D and Ds from the two-point correlator of pseudoscalar currents. First, we compare the perturbative expansion for the correlator and the decay constant performed in terms of the pole and the running MS¯ masses of the charm quark. The perturbative expansion in terms of the pole mass shows no signs of convergence whereas reorganizing this very expansion in terms of the MS¯ mass leads to a distinct hierarchy of the perturbative expansion. Furthermore, the decay constants extracted from the pole-mass correlator turn out to be considerably smaller than those obtained by means of the MS¯-mass correlator. Second, making use of the OPE in terms of the MS¯ mass, we determine the decay constants of both D and Ds mesons with an emphasis on the uncertainties in these quantities related both to the input QCD parameters and to the limited accuracy of the method of sum rules. PMID:21949465
Quasielastic /sup 3/Hp and /sup 3/Hep scattering at intermediate energies and the Glauber sum rules
Blinov, A.V.; Vanyushin, I.A.; Grechko, V.E.; Drobot, V.V.; Ergakov, B.A.; Zombkovskii, S.M.; Kondratyuk, L.A.; Korolev, Y.V.; Selektor, Y.M.; Solov'ev, V.V.
1984-09-01
The differential cross sections and the average energy loss of fast protons in the reactions p+/sup 3/H..-->..p/sub F/+X and p+/sup 3/He..-->..p/sub F/+X are investigated by means of a liquid-hydrogen bubble chamber at the Institute of Theoretical and Experimental Physics of diameter 80 cm, exposed in a beam of 2.5 GeV/c tritium nuclei (primary-proton kinetic energy in the rest system of the nucleus T/sub p/ = 0.318 GeV) and in a beam of 5-GeV/c /sup 3/He nuclei (T/sub p/ = 0.978 GeV). The experimental results are compared with the predictions based on sum rules for differential cross sections and average energy loss in the Glauber-Sitenko theory of multiple scattering and with use of the completeness condition for the wave functions of the excited states of the nucleus and locality of the nuclear potential. Good agreement between the data and the theoretical predictions is observed at 2.5 GeV/c. A discrepancy between the Glauber sum-rule predictions and the data at 5 GeV/c is explained by the production of the ..delta.. isobar in the intermediate state. It is established that the possible admixture of six-quark bags in the nuclei /sup 3/H and /sup 3/He does not exceed 5%.
Improved fD(s)∗, fB(s)∗ and fBc from QCD Laplace sum rules
NASA Astrophysics Data System (ADS)
Narison, Stephan
2015-07-01
Anticipating future precise measurements of the D- and B-like (semi)leptonic and hadronic decays for alternative determinations of the CKM mixing angles, we pursue our program on the D- and B-like mesons by improving the estimates of fD(s)∗ and fB(s)∗ (analogue to fπ) by using the well-established (inverse) Laplace sum rules (LSR) and/or their suitable ratios less affected by the systematics, which are known to N2LO pQCD and where the complete d = 6 nonperturbative condensate contributions are included. The convergence of the PT series is analyzed by an estimate of the N3LO terms based on geometric growth of the coefficients. In addition to the standard LSR variable τ and the QCD continuum threshold tc stability criteria, we extract our optimal results by also requiring stability on the variation of the arbitrary QCD subtraction point μ which reduces the errors in the analysis. We complete the study of the open bottom states by an estimate of fBc. Our results summarized in Tables 3 and 4 are compared with some other recent sum rules and lattice estimates.
Friedel-Crafts Acylation with Amides
Raja, Erum K.; DeSchepper, Daniel J.; Nilsson Lill, Sten O.; Klumpp, Douglas A.
2012-01-01
Friedel-Crafts acylation has been known since the 1870s and it is an important organic synthetic reaction leading to aromatic ketone products. Friedel-Crafts acylation is usually done with carboxylic acid chlorides or anhydrides while amides are generally not useful substrates in these reactions. Despite being the least reactive carboxylic acid derivative, we have found a series of amides capable of providing aromatic ketones in good yields (55–96%, 17 examples). We propose a mechanism involving diminished C-N resonance through superelectrophilic activation and subsequent cleavage to acyl cations. PMID:22690740
NASA Astrophysics Data System (ADS)
Jugeau, F.; Le Yaouanc, A.; Oliver, L.; Raynal, J.-C.
2006-01-01
Within the OPE, we formulate new sum rules in Heavy Quark Effective Theory in the heavy quark limit and at order 1/mQ, using the non-forward amplitude. In the heavy quark limit, these sum rules imply that the elastic Isgur-Wise function ξ(w) is an alternate series in powers of (w - 1). Moreover, one gets that the n-th derivative of ξ(w) at w = 1 can be bounded by the (n - 1)-th one, and the absolute lower bound for the n-th derivative (-1)nξ(n)(1) ⩾ (2n+1)!!/22n. Moreover, for the curvature we find ξ″(1) ⩾ 1/5[4ρ2 + 3(ρ2)2] where ρ2 = -ξ'(1). These results are consistent with the dispersive bounds, and they strongly reduce the allowed region of the latter for ξ(w). The method is extended to the subleading quantities in 1/mQ. Concerning the perturbations of the Current, we derive new simple relations between the functions ξ3(w) and Λ¯ξ(w) and the sums ∑ n ΔEj(n)τj(n)(1)τj(n)(w) (j = 1/2, 3/2), that involve leading quantities, Isgur-Wise functions τj(n)(w) and level spacings ΔEj(n). Our results follow because the non-forward amplitude depends on three variables (wi, wf, wif) = (vi ṡ v', vf ṡ v', vi ṡ vf), and we consider the zero recoil frontier (w, 1, w) where only a finite number of jP states contribute (1/2+, 3/2+). We also obtain new sum rules involving the elastic subleading form factors χi(w) (i = 1, 2, 3) at order 1/mQ that originate from the Lkin and Lmag perturbations of the Lagrangian. To the sum rules contribute only the same intermediate states (jP, JP) = (1/2-, 1-),(3/2-, 1-) that enter in the 1/mQ2 corrections of the axial form factor hA1(w) at zero recoil. This allows to obtain a lower bound on -δ1/m2(A1) in terms of the χi(w) and the shape of the elastic IW function ξ(w). An important theoretical implication is that χ1'(1), χ2(1) and χ3'(1)(χ1(1) = χ3(1) = 0 from Luke theorem) must vanish when the slope and the curvature attain their lowest values ρ2 → 3/4, σ2 → 15/16. These constraints should be taken
Finite size effect and Friedel oscillations for a Friedel-Anderson impurity by FAIR method
NASA Astrophysics Data System (ADS)
Tao, Yaqi
A compact solution consisting of 4-8 Slater states (FAIR solution) is introduced to treat the Friedel Anderson and Kondo impurity problem. The ground state energy is obtained with impressively high accuracy. Net integrated polarization density is calculated and it confirms the existence of Kondo cloud. Finite size effect in the impurity problem is studied using FAIR method. It is shown that the formation of a Kondo ground state requires a minimum sample size and is accompanied by the presence of Kondo cloud. The Friedel Oscillations in the vicinity of a Friedel-Anderson impurity are investigated by FAIR method. The development of Friedel oscillation with a phase shift of pi/2 outside the Kondo radius is confirmed. And the amplitude A(xi) of the Friedel oscillations show a very similar behavior to that of a simple non-interacting Friedel impurity with a narrow resonance at the Fermi level. This similarity supports the concept of a "Kondo" resonance. And the Kondo resonance half width GammaFA is suggested to be GammaFA ≈ Echi/2.4, where Echi is the Kondo energy calculated from susceptibility.
NASA Astrophysics Data System (ADS)
Holas, A.; March, N. H.; Rubio, Angel
2005-11-01
Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force Fxc(r)=-∇υxc(r) associated with the xc potential υxc(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule ⟨nFxc⟩=0 relating the xc force with the ground-state density n(r ). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions.
A measurement of {alpha}{sub s}(Q{sup 2}) from the Gross Llewellyn Smith sum rule
Harris, D.A.; Auchincloss, P.; Arroyo, C.G.
1995-06-01
The Gross Llewellyn Smith sum rule has been measured at different values of four-momentum transfer squared (Q{sup 2}) by combining the precise CCFR neutrino data with data from other deep-inelastic scattering experiments at lower values of Q{sup 2}. A comparison with the {Omicron} ({alpha}{sub s}{sup 3}) predictions of perturbative QCD yields a determination of {alpha}{sub s} and its dependence on Q{sup 2} in the range 1GeV{sup 2} < Q{sup 2} < 20 GeV{sup 2}. Low Q{sup 2} tests have greater sensitivity to {alpha}{sub s} (M{sub Z}{sup 2}) than high Q{sup 2} tests, since at low Q{sup 2} {alpha}{sub s} is large and changing rapidly.
Adler function, sum rules and Crewther relation of order O(αs4): The singlet case
NASA Astrophysics Data System (ADS)
Baikov, P. A.; Chetyrkin, K. G.; Kühn, J. H.; Rittinger, J.
2012-07-01
The analytic result for the singlet part of the Adler function of the vector current in a general gauge theory is presented in five-loop approximation. Comparing this result with the corresponding singlet part of the Gross-Llewellyn Smith sum rule (Baikov et al., 2010 [1]), we successfully demonstrate the validity of the generalized Crewther relation for the singlet part. This provides a non-trivial test of both our calculations and the generalized Crewther relation. Combining the result with the already available non-singlet part of the Adler function (Baikov et al., 2008 [2], Baikov et al., 2010 [3]) we arrive at the complete O(αs4) expression for the Adler function and, as a direct consequence, at the complete O(αs4) correction to the e+e- annihilation into hadrons in a general gauge theory.
D → a1, f1 transition form factors and semileptonic decays via 3-point QCD sum rules
NASA Astrophysics Data System (ADS)
Zuo, Yabing; Hu, Yue; He, Linlin; Yang, Wei; Chen, Yan; Hao, Yannan
2016-07-01
By using the 3-point QCD sum rules, we calculate the transition form factors of D decays into the spin triplet axial vector mesons a1(1260), f1(1285), f1(1420). In the calculations, we consider the quark contents of each meson in detail. In view of the fact that the isospin of a1(1260) is one, we calculate the D+ → a 10(1260) and D0 → a 1‑(1260) transition form factors separately. In the case of f1(1285), f1(1420), the mixing between light flavor SU(3) singlet and octet is taken into account. Based on the form factors obtained here, we give predictions for the branching ratios of relevant semileptonic decays, which can be tested in the future experiments.
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang
2016-03-01
In this article, we construct both the axialvector-diquark-axialvector-diquark-antiquark type and the axialvector-diquark-scalar-diquark-antiquark type interpolating currents, then calculate the contributions of the vacuum condensates up to dimension 10 in the operator product expansion, and we study the masses and pole residues of the J^P={1/2}^± hidden-charm pentaquark states with the QCD sum rules in a systematic way. In calculations, we use the formula μ =sqrt{M^2P-(2{{M}}_c)^2} to determine the energy scales of the QCD spectral densities. We take into account the SU(3) breaking effects of the light quarks, and we obtain the masses of the hidden-charm pentaquark states with the strangeness S=0,-1,-2,-3, which can be confronted with the experimental data in the future.
Analysis of the {1/2}^{± } pentaquark states in the diquark model with QCD sum rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang; Huang, Tao
2016-01-01
In this article, we present the scalar-diquark-scalar-diquark-antiquark type and scalar-diquark-axialvector-diquark-antiquark type pentaquark configurations in the diquark model, and study the masses and pole residues of the J^P={1/2}^± hidden-charm pentaquark states in detail with the QCD sum rules by extending our previous work on the J^P={3/2}^- and {5/2}+ hidden-charm pentaquark states. We calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion by constructing both the scalar-diquark-scalar-diquark-antiquark type and the scalar-diquark-axialvector-diquark-antiquark type interpolating currents. The present predictions of the masses can be confronted to the LHCb experimental data in the future.
Holas, A; March, N H; Rubio, Angel
2005-11-15
Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions. PMID:16321073
Kominis, Ioannis
2001-01-31
This thesis presents the results of E-94010, an experiment at Thomas Jefferson National Accelerator Facility (TJNAF) designed to study the spin structure of the neutron at low momentum transfer, and to test the “extended” Gerasimov-Drell-Hearn (GDH) sum rule. The first experiment of its kind, it was performed in experimental Hall-A of TJNAF using a new polarized 3He facility. It has recently been shown that the GDH sum rule and the Bjorken sum rule are both special examples of a more general sum rule that applies to polarized electron scattering off nucleons. This generalized sum rule, due to Ji and Osborne, reduces to the GDH sum rule at Q2 = 0 and to the Bjorken sum rule at Q2 >> 1 GeV2. By studying the Q2 evolution of the extended GDH sum, one learns about the transition from quark-like behavior to hadronic-like behavior. We measured inclusive polarized cross sections by scattering high energy polarized electrons off the new TJNAF polarized 3He target with both longitudinal and transverse target orientations. The high density 3He target, based on optical pumping and spin exchange, was used as an effective neutron target. The target maintained a polarization of about 35% at beam currents as high as 151tA. We describe the precision 3He polarimetry leading to a systematic uncertainty of the target polarization of 4% (relative). A strained GaAs photocathode was utilized in the polarized electron gun, which provided an electron beam with a polarization of about 70%, known to 3% (relative). By using six different beam energies (between 0.86 and 5.06 GeV) and a fixed scattering angle of 15.5°, a wide kinematic coverage was achieved, with 0.02 GeV2< Q2 <1 GcV2 and 0.5 GeV< W < 2.5 GeV for the squared momentum transfer and invariant mass, respectively. From the measured cross sections we extract the 3He spin structure functions He and g1e Finally, we determine the extended GDH sum for the range 0.1 GeV2< Q2 <1 GeV2 for 3He and the neutron.
Gubler, Philipp; Yamamoto, Naoki; Hatsuda, Tetsuo; Nishida, Yusuke
2015-05-15
Making use of the operator product expansion, we derive a general class of sum rules for the imaginary part of the single-particle self-energy of the unitary Fermi gas. The sum rules are analyzed numerically with the help of the maximum entropy method, which allows us to extract the single-particle spectral density as a function of both energy and momentum. These spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations.
First Measurement of the Gerasimov-Drell-Hearn Sum Rule for 1H from 0.7 to 1.8 GeV at ELSA.
Dutz, H; Helbing, K; Krimmer, J; Speckner, T; Zeitler, G; Ahrens, J; Altieri, S; Annand, J R M; Anton, G; Arends, H-J; Beck, R; Bock, A; Bradtke, C; Braghieri, A; v Drachenfels, W; Frommberger, F; Godo, M; Goertz, S; Grabmayr, P; Hasegawa, S; Hansen, K; Harmsen, J; Heid, E; Hillert, W; Holvoet, H; Horikawa, N; Iwata, T; Van Hoorebeke, L; d'Hose, N; Jennewein, P; Kiel, B; Klein, F; Kondratiev, R; Lang, M; Lannoy, B; Leukel, R; Lisin, V; Menze, D; Meyer, W; Michel, T; Naumann, J; Panzeri, A; Pedroni, P; Pinelli, T; Preobrajenski, I; Radtke, E; Reicherz, G; Rohlof, C; Rostomyan, T; Sauer, M; Schoch, B; Schumacher, M; Tamas, G; Thomas, A; van de Vyver, R; Weihofen, W; Zapadtka, F
2003-11-01
To verify the fundamental Gerasimov-Drell-Hearn (GDH) sum rule for the first time experimentally, we measured the helicity dependent total photoabsorption cross section with circularly polarized real photons and longitudinally polarized nucleons in the photon energy range 0.68-1.82 GeV with the tagged photon facility at ELSA. The experiment was carried out with a 4pi detection system, a circularly polarized tagged photon beam, and a frozen spin polarized proton target. The contribution to the GDH sum rule in this photon energy range is [49.9+/-2.4(stat)+/-2.2(syst)] microb. PMID:14611575
NASA Astrophysics Data System (ADS)
Corianò, Claudio; Costantini, Antonio; Rose, Luigi Delle; Serino, Mirko
2014-06-01
We discuss the signature of the anomalous breaking of the superconformal symmetry in = 1 super Yang Mills theory, mediated by the Ferrara-Zumino hypercurrent () with two vector () supercurrents () and its manifestation in the anomaly action, in the form of anomaly poles. This allows to investigate in a unified way both conformal and chiral anomalies. The analysis is performed in parallel to the Standard Model, for comparison. We investigate, in particular, massive deformations of the = 1 theory and the spectral densities of the anomaly form factors which are extracted from the components of this correlator. In this extended framework it is shown that all the anomaly form factors are characterized by spectral densities which flow with the mass deformation. In particular, the continuum contributions from the two-particle cuts of the intermediate states turn into poles in the zero mass limit, with a single sum rule satisfied by each component. Non anomalous form factors, instead, in the same anomalous correlators, are characterized by non-integrable spectral densities. These tend to uniform distributions as one moves towards the conformal point, with a clear dual behaviour. As in a previous analysis of the dilaton pole of the Standard Model, also in this case the poles can be interpreted as signaling the exchange of a composite dilaton/axion/dilatino (ADD) multiplet in the effective Lagrangian. The pole-like behaviour of the anomaly form factors is shown to be a global feature of the correlators, present at all energy scales, due to the sum rules. A similar behaviour is shown to be present in the Konishi current, which identifies additional composite states. We conclude that global anomalous currents characterized by a single flow in the perturbative picture always predict the existence of composite interpolating fields. In case of gauging of these currents, as in superconformal theories coupled to gravity, we show that the cancellation of the corresponding anomalies
Catalytic Friedel-Crafts reaction of aminocyclopropanes.
de Nanteuil, Florian; Loup, Joachim; Waser, Jérôme
2013-07-19
A Lewis acid catalyzed Friedel-Crafts reaction between donor-acceptor aminocyclopropanes and indoles and other electron-rich aromatic compounds is reported. Indole alkylation at the C3 position was generally obtained for a broad range of functional groups and substitution patterns. In the case of C3-substituted indoles, C2 alkylation was observed. The reaction gives a rapid access to gamma amino acid derivatives present in numerous bioactive molecules. PMID:23815365
Form factors in Bbar0 →π+π0 ℓνbarℓ from QCD light-cone sum rules
NASA Astrophysics Data System (ADS)
Hambrock, Christian; Khodjamirian, Alexander
2016-04-01
The form factors of the semileptonic B → ππℓ ν bar decay are calculated from QCD light-cone sum rules with the distribution amplitudes of dipion states. This method is valid in the kinematical region, where the hadronic dipion state has a small invariant mass and simultaneously a large recoil. The derivation of the sum rules is complicated by the presence of an additional variable related to the angle between the two pions. In particular, we realize that not all invariant amplitudes in the underlying correlation function can be used, some of them generating kinematical singularities in the dispersion relation. The two sum rules that are free from these ambiguities are obtained in the leading twist-2 approximation, predicting the Bbar0 →π+π0 form factors F⊥ and F∥ of the vector and axial b → u current, respectively. We calculate these form factors at the momentum transfers 0
Precision calculation of threshold πd scattering, πN scattering lengths, and the GMO sum rule
NASA Astrophysics Data System (ADS)
Baru, V.; Hanhart, C.; Hoferichter, M.; Kubis, B.; Nogga, A.; Phillips, D. R.
2011-12-01
We use chiral perturbation theory (ChPT) to calculate the πd scattering length with an accuracy of a few percent, including isospin-violating corrections in both the two- and three-body sectors. In particular, we provide the technical details of a recent letter (Baru et al., 2011) [1], where we used data on pionic deuterium and pionic hydrogen atoms to extract the isoscalar and isovector pion-nucleon scattering lengths a and a. We study isospin-breaking contributions to the three-body part of a due to mass differences, isospin violation in the πN scattering lengths, and virtual photons. This last class of effects is ostensibly infrared enhanced due to the smallness of the deuteron binding energy. However, we show that the leading virtual-photon effects that might undergo such enhancement cancel, and hence the standard ChPT counting provides a reliable estimate of isospin violation in a due to virtual photons. Finally, we discuss the validity of the Goldberger-Miyazawa-Oehme sum rule in the presence of isospin violation, and use it to determine the charged-pion-nucleon coupling constant.
Friedel oscillations: Decoding the hidden physics
NASA Astrophysics Data System (ADS)
Bena, Cristina
2016-03-01
We show that the impurity-induced Friedel oscillations allow one to probe in an unexpected and quite remarkable manner the electronic properties of two-dimensional systems such as graphene or high-temperature superconductors. In particular, we show that by studying these oscillations, one can get access not only to the constant-energy maps, but also to more hidden information such as the chiral properties of Dirac electrons in graphene, which cannot be observed directly by other methods. For graphene, this hidden information is revealed by comparing the theoretical predictions with scanning tunneling microscopy experimental measurements of the local density of states. xml:lang="fr"
Friedel oscillations as a probe of fermionic quasiparticles
NASA Astrophysics Data System (ADS)
Dalla Torre, Emanuele G.; Benjamin, David; He, Yang; Dentelski, David; Demler, Eugene
2016-05-01
When immersed in a sea of electrons, local impurities give rise to density modulations known as Friedel oscillations. In spite of the generality of this phenomenon, the exact shape of these modulations is usually computed only for noninteracting electrons with a quadratic dispersion relation. In actual materials, Friedel oscillations are a viable way to access the properties of electronic quasiparticles, including their dispersion relation, lifetime, and pairing. In this work we analyze the signatures of Friedel oscillations in STM and x-ray scattering experiments, focusing on the concrete example of cuprate superconductors. We identify signatures of Friedel oscillations seeded by impurities and vortices, and explain experimental observations that have been previously attributed to a competing charge order.
NASA Technical Reports Server (NTRS)
Ying, Hao
1993-01-01
The fuzzy controllers studied in this paper are the ones that employ N trapezoidal-shaped members for input fuzzy sets, Zadeh fuzzy logic and a centroid defuzzification algorithm for output fuzzy set. The author analytically proves that the structure of the fuzzy controllers is the sum of a global nonlinear controller and a local nonlinear proportional-integral-like controller. If N approaches infinity, the global controller becomes a nonlinear controller while the local controller disappears. If linear control rules are used, the global controller becomes a global two-dimensional multilevel relay which approaches a global linear proportional-integral (PI) controller as N approaches infinity.
g{sub {Sigma}{sub Q{Sigma}{sub Q{pi}}}}coupling constant via light cone QCD sum rules
Azizi, K.; Bayar, M.; Ozpineci, A.; Sarac, Y.
2010-10-01
Using the most general form of the interpolating currents, the coupling constants g{sub {Sigma}{sub b{Sigma}{sub b{pi}}}}and g{sub {Sigma}{sub c{Sigma}{sub c{pi}}}}are calculated within the light cone QCD sum rules approach. It is found that g{sub {Sigma}{sub c{Sigma}{sub c{pi}=}}}-8.0{+-}1.7 and g{sub {Sigma}{sub b{Sigma}{sub b{pi}=}}}-11.0{+-}2.1.
NASA Astrophysics Data System (ADS)
Cvetič, Gorazd; Kataev, A. L.
2016-07-01
We consider a new form of analytical perturbation theory expansion in the massless S U (Nc) theory, for the nonsinglet part of the e+e--annihilation to hadrons Adler function Dn s and of the Bjorken sum rule of the polarized lepton-hadron deep-inelastic scattering Cns B j p, and demonstrate its validity at the O (αs4)-level at least. It is a two-fold series in powers of the conformal anomaly and of S U (Nc) coupling αs. Explicit expressions are obtained for the {β }-expanded perturbation coefficients at O (αs4) level in MS ¯ scheme, for both considered physical quantities. Comparisons of the terms in the {β }-expanded coefficients are made with the corresponding terms obtained by using extra gluino degrees of freedom, or skeleton-motivated expansion, or Rδ-scheme motivated expansion in the Principle of Maximal Conformality. Relations between terms of the {β }-expansion for the Dn s- and Cns B j p-functions, which follow from the conformal symmetry limit and its violation, are presented. The relevance to the possible new analyses of the experimental data for the Adler function and Bjorken sum rule is discussed.
Parameterisation of [σ1/2-σ3/2] for Q2>=0 and non-resonance contribution to the GDH sum rule
NASA Astrophysics Data System (ADS)
Bianchi, N.; Thomas, E.
1999-03-01
A description of the virtual photon absorption cross section difference [σ1/2-σ3/2] for the proton and neutron is obtained with a parameterisation based on a Regge type approach. The parametrisation is obtained from global fits to the cross section data derived from the spin asymmetries measured in deep inelastic scattering of longitudinally polarised leptons from polarised 1H, 3He and 2H targets in the range 0.3 GeV2
NASA Astrophysics Data System (ADS)
Kumar, Ashok; Thakkar, Ajit J.
2010-02-01
The construction of the dipole oscillator strength distribution (DOSD) from theoretical and experimental photoabsorption cross sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule and molar refractivity data is a well-established technique that has been successfully applied to more than 50 species. Such DOSDs are insufficiently accurate at large photon energies. A novel iterative procedure is developed that rectifies this deficiency by using the high-energy asymptotic behavior of the dipole oscillator strength density as an additional constraint. Pilot applications are made for the neon, argon, krypton, and xenon atoms. The resulting DOSDs improve the agreement of the predicted S2 and S1 sum rules with ab initio calculations while preserving the accuracy of the remainder of the moments. Our DOSDs exploit new and more accurate experimental data. Improved estimates of dipole properties for these four atoms and of dipole-dipole C6 and triple-dipole C9 dispersion coefficients for the interactions among them are reported.
Kumar, Ashok; Thakkar, Ajit J.
2010-02-21
The construction of the dipole oscillator strength distribution (DOSD) from theoretical and experimental photoabsorption cross sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule and molar refractivity data is a well-established technique that has been successfully applied to more than 50 species. Such DOSDs are insufficiently accurate at large photon energies. A novel iterative procedure is developed that rectifies this deficiency by using the high-energy asymptotic behavior of the dipole oscillator strength density as an additional constraint. Pilot applications are made for the neon, argon, krypton, and xenon atoms. The resulting DOSDs improve the agreement of the predicted S{sub 2} and S{sub 1} sum rules with ab initio calculations while preserving the accuracy of the remainder of the moments. Our DOSDs exploit new and more accurate experimental data. Improved estimates of dipole properties for these four atoms and of dipole-dipole C{sub 6} and triple-dipole C{sub 9} dispersion coefficients for the interactions among them are reported.
Jeffries, J R; Moore, K T; Butch, N P; Maple, M B
2010-05-19
We examine the degree of 5f electron localization in URu{sub 2}Si{sub 2} using spin-orbit sum rule analysis of the U N{sub 4,5} (4d {yields} 5f) edge. When compared to {alpha}-U metal, US, USe, and UTe, which have increasing localization of the 5f states, we find that the 5f states of URu{sub 2}Si{sub 2} are more localized, although not entirely. Spin-orbit analysis shows that intermediate coupling is the correct angular momentum coupling mechanism for URu{sub 2}Si{sub 2} when the 5f electron count is between 2.6 and 2.8. These results have direct ramifications for theoretical assessment of the hidden order state of URu{sub 2}Si{sub 2}, where the degree of localization of the 5f electrons and their contribution to the Fermi surface are critical.
Application of the QCD light cone sum rule to tetraquarks: The strong vertices XbXbρ and XcXcρ
NASA Astrophysics Data System (ADS)
Agaev, S. S.; Azizi, K.; Sundu, H.
2016-06-01
The full version of the QCD light-cone sum rule method is applied to tetraquarks containing a single heavy b or c quark. To this end, investigations of the strong vertices XbXbρ and XcXcρ are performed, where Xb=[s u ][b ¯ d ¯ ] and Xc=[s u ][c ¯d ¯] are the exotic states built of four quarks of different flavors. The strong coupling constants GXbXbρ and GXcXcρ corresponding to these vertices are found using the ρ -meson leading- and higher-twist distribution amplitudes. In the calculations, Xb and Xc are treated as scalar bound states of a diquark and antidiquark.
Analysis of P_c(4380) and P_c(4450) as pentaquark states in the diquark model with QCD sum rules
NASA Astrophysics Data System (ADS)
Wang, Zhi-Gang
2016-02-01
In this article, we construct the diquark-diquark-antiquark type interpolating currents, and we study the masses and pole residues of the J^P={3/2}^- and {5/2}^+ hidden charm pentaquark states in detail with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in the operator product expansion. In the calculations, we use the formula μ =√{M^2_{P_c}-(2{{M}}_c)^2} to determine the energy scales of the QCD spectral densities. The present predictions favor assigning P_c(4380) and P_c(4450) to be the {3/2}^- and {5/2}^+ pentaquark states, respectively.
The Friedel-Crafts Reaction - A Sixth Form Project
ERIC Educational Resources Information Center
Hodson, D.
1973-01-01
Suggests that the Friedel-Crafts reaction, used for synthesizing a wide range of aromatic compounds, is an ideal vehicle for extended senior high school project work in chemistry. Provides a theoretical discussion of the reaction, suggests a number of suitable investigations, and outlines the experimental details. (JR)
Accurate decay-constant ratios fB*/fB and fBs*/fBs from Borel QCD sum rules
NASA Astrophysics Data System (ADS)
Lucha, Wolfgang; Melikhov, Dmitri; Simula, Silvano
2015-06-01
We present our analysis of the decay constants of the beauty vector mesons B* and Bs* within the framework of dispersive sum rules for the two-point correlator of vector currents in QCD. While the decay constants of the vector mesons fB* and fBs* —similar to the decay constants of the pseudoscalar mesons fB and fBs—individuallyhave large uncertainties induced by theory parameters not known with a satisfactory precision, these uncertainties almost entirely cancel out in the ratios of vector over pseudoscalar decay constants. These ratios, thus, may be predicted with very high accuracy due to the good control over the systematic uncertainties of the decay constants gained upon application of our hadron-parameter extraction algorithm. Our final results read fB*/fB=0.944 ±0.01 1OPE±0.01 8syst and fBs*/fB s=0.947 ±0.02 3OPE±0.02 0syst . Thus, both fB*/fB and fBs*/fBs are less than unity at 2.5 σ and 2 σ level, respectively.
NASA Astrophysics Data System (ADS)
Bakulev, A. P.; Mikhailov, S. V.; Pimikov, A. V.; Stefanis, N. G.
2011-10-01
A global fit to the data from different collaborations (CELLO, CLEO, BaBar) on the pion-photon transition form factor is carried out using light-cone sum rules. The analysis includes the next-to-leading QCD radiative corrections and the twist-four contributions, while the main next-to-next-to-leading term and the twist-six contribution are taken into account in the form of theoretical uncertainties. We use the information extracted from the data to investigate the pivotal characteristics of the pion distribution amplitude. This is done by dividing the data into two sets: one containing all data up to 9 GeV 2, whereas the other incorporates also the high- Q tail of the BaBar data. We find that it is not possible to accommodate into the fit these BaBar data points with the same accuracy and conclude that it is difficult to explain these data in the standard scheme of OCD.
Moore, K; der Laan, G v; Haire, R; Wall, M; Schwartz, A
2005-10-07
Transmission electron microscopy is used to acquire electron energy-loss spectra from phase-specific regions of Pu and U metal, PuO{sub 2} and UO{sub 2}, and aged, self-irradiated Pu metal. The N{sub 4,5} (4d {yields} 5f) spectra are analyzed using the spin-orbit sum rule. Our results show that the technique is sensitive enough to detect changes in the branching ratio of the white-line peaks between the metal and dioxide of both U and Pu. There is a small change in the branching ratio between different Pu metals, and the data trends as would be expected for varying f electron localization, i.e., {alpha}-Pu, {delta}-Pu, aged {delta}-Pu. Moreover, our results suggest that the metal-oxide bonds in UO{sub 2} and PuO{sub 2} are strongly covalent in nature and do not exhibit an integer valence change as would be expected from purely ionic bonding.
Lvov, A.I.; Scopetta, S. |; Drechsel, D.; Scherer, S.
1998-01-01
Photoproduction of e{sup +}e{sup {minus}} pairs at small angles is investigated as a tool to determine the functions f{sub 1} and f{sub 2} entering the real-photon forward Compton scattering amplitude. The method is based on an interference of the Bethe-Heitler and the virtual Compton scattering mechanisms, generating an azimuthal asymmetry in the e{sup +} versus e{sup {minus}} yield. The general case of a circularly polarized beam and a longitudinally polarized target allows one to determine both the real and imaginary parts of f{sub 1} as well as f{sub 2}. The imaginary part of f{sub 2} requires target polarization only. We calculate cross sections and asymmetries of the reaction p({gamma},e{sup +}e{sup {minus}})p, estimate corrections and backgrounds, and propose suitable kinematical regions to perform the experiment. Our investigation shows that photoproduction of e{sup +}e{sup {minus}}-pairs off the proton and light nuclei may serve as a rather sensitive test of the validity of the Gerasimov-Drell-Hearn sum rule. {copyright} {ital 1998} {ital The American Physical Society}
NASA Astrophysics Data System (ADS)
Mikhailov, S. V.; Pimikov, A. V.; Stefanis, N. G.
2016-06-01
We consider the calculation of the pion-photon transition form factor Fγ*γπ0(Q2) within light-cone sum rules focusing attention to the low-mid region of momenta. The central aim is to estimate the theoretical uncertainties which originate from a wide variety of sources related to (i) the relevance of next-to-next-to-leading order radiative corrections (ii) the influence of the twist-four and the twist-six term (iii) the sensitivity of the results on auxiliary parameters, like the Borel scale M2, (iv) the role of the phenomenological description of resonances, and (v) the significance of a small but finite virtuality of the quasireal photon. Predictions for Fγ*γπ0(Q2) are presented which include all these uncertainties and found to comply within the margin of experimental error with the existing data in the Q2 range between 1 and 5 GeV2 , thus justifying the reliability of the applied calculational scheme. This provides a solid basis for confronting theoretical predictions with forthcoming data bearing small statistical errors.
Friedel oscillations at the surfaces of rhombohedral N -layer graphene
NASA Astrophysics Data System (ADS)
Dutreix, C.; Katsnelson, M. I.
2016-01-01
The low-energy physics of rhombohedral N -layer graphene mainly arises on the external layers, where most of the π electrons are located. Their Bloch band structure defines a two-band semimetal; the dispersion relation scales as ±qN with the momentum norm q in the vicinity of two nonequivalent valleys. In this paper, we address the problem of elastic scattering through a localized impurity located either on the surface of the material or within the bulk, and focus on the quantum interferences it induces on the two external layers. It is apprehended in the framework of a T -matrix approach, both numerically and analytically, regardless of the impurity magnitude, which enables the description of realistic scatters. In rhombohedral multilayer graphene, the impurity induces Friedel oscillations that always decay as 1 /r . As a result, monolayer graphene is the only material of the rhombohedral class that exhibits 1 /r2 -decaying Friedel oscillations. The interference patterns are subsequently analyzed in momentum space. This analysis enables a clear distinction between monolayer graphene and multilayer graphene. It also shows that the interference pattern reveals the whole Bloch band structure, and highlights the number of layers stacked in the material, as well as the π -quantized Berry phases that characterize the existence of nodal points in the semimetallic spectrum. Experimentally, these features may be probed from scanning tunneling microscopy, when imaging the local density of states at the surfaces of suspended rhombohedral N -layer graphene.
Impurity scattering and Friedel oscillations in monolayer black phosphorus
NASA Astrophysics Data System (ADS)
Zou, Yong-Lian; Song, Juntao; Bai, Chunxu; Chang, Kai
2016-07-01
We study the impurity scattering effect in black phosphorene (BP) in this work. For a single impurity, we calculate the impurity-induced local density of states (LDOS) in momentum space numerically based on a tight-binding Hamiltonian. In real space, we calculate the LDOS and Friedel oscillation analytically. The LDOS shows strong anisotropy in BP. Many impurities in BP are investigated using the T -matrix approximation when the density is low. Midgap states appear in the band gap with peaks in the DOS. The peaks of midgap states are dependent on the impurity potential. For finite positive potential, the impurity tends to bind negative charge carriers and vice versa. The infinite-impurity-potential problem is related to chiral symmetry in BP.
Sundu, Hayriye; Bayar, Melahat; Azizi, Kazem
2010-12-22
The form factors of the semileptonic B{sub c{yields}}S(AV)l{nu} (l = {tau},{mu},e) transitions, where S and AV denote the scalar {Chi}{sub c0} and axial vector ({Chi}{sub c1},h{sub c}) mesons, are calculated within the framework of the three-point QCD sum rules. The results of form factors are used to estimate the total decay widths and branching ratios of these transitions. A comparison of our results on branching ratios with the predictions of other approaches is also presented.
Hypercrosslinked polymeric foams prepared by Friedel-Crafts polycondensation
Steckle, W.P. Jr.; Mitchell, M.A.; Apen, P.G.
1995-12-31
Porous materials are widely used in industry and government for chemical separations, processing and monitoring, environmental cleanup and remediation, energy efficiency, and conservation. Porous materials used in these applications include: foams, filters, membranes, absorbents, ion exchange resins, molecular sieves, zeolites, catalyst supports, sensors, and electrodes. Organic analogues to inorganic zeolites would be a significant step forward in engineered porous materials and would provide advantages in range, selectivity, tailorability and processing. A novel process for preparing hypercross linked polymeric foams has been developed via a Friedel-Crafts polycondensation reaction. A series of rigid hypercrosslinked foams have been prepared using simple rigid polyaromatic hydrocarbons such as benzene, biphenyl, mterphenyl, diphenylmethane, and polystyrene, with p-dichloroxylene as the crosslinking agent. After drying the gels, the resulting foams are robust and rigid; densities range from 0.3 to 0.g/cc. Nitrogen adsorption studies have shown that by judiciously selecting monomers and crosslinking agent along with the level of crosslinking, the pore size and distribution along with total surface area of the foam can be tailored. Surface areas range from 160 to 1,200 m{sup 2}/g with pore sizes ranging from 6{Angstrom} to 250{Angstrom}. Further evidence of this has been confirmed by high resolution TEM.
Gan Longfei; Huang Mingqiu
2010-09-01
We present an analysis of semileptonic decays of orbitally, P-wave excited B{sub s} meson states B{sub s}**, including the newly found narrow B{sub s1}(5830) and B{sub s2}*(5840) states, into low-lying D{sub s} mesons (D{sub s}(1968), D{sub s}*(2112), D{sub sJ}(2317), D{sub sJ}(2460)) within the framework of the heavy quark effective theory. The relevant universal form factors are estimated using QCD sum rules at the leading order of the heavy quark expansion. The decay widths are predicted and the branching ratios are estimated.
NASA Astrophysics Data System (ADS)
Blümlein, Johannes; Falcioni, Giulio; De Freitas, Abilio
2016-09-01
We calculate analytically the flavor non-singlet O (αs2) massive Wilson coefficients for the inclusive neutral current non-singlet structure functions F1,2,Lep (x ,Q2) and g1,2ep (x ,Q2) and charged current non-singlet structure functions F1,2,3ν (ν bar) p (x ,Q2), at general virtualities Q2 in the deep-inelastic region. Numerical results are presented. We illustrate the transition from low to large virtualities for these observables, which may be contrasted to basic assumptions made in the so-called variable flavor number scheme. We also derive the corresponding results for the Adler sum rule, the unpolarized and polarized Bjorken sum rules and the Gross-Llewellyn Smith sum rule. There are no logarithmic corrections at large scales Q2 and the effects of the power corrections due to the heavy quark mass are of the size of the known O (αs4) corrections in the case of the sum rules. The complete charm and bottom corrections are compared to the approach using asymptotic representations in the region Q2 ≫mc,b2. We also study the target mass corrections to the above sum rules.
Djawotho, Pibero
2002-12-01
This dissertation presents results of experiment E94-010 performed at Jefferson Laboratory (simply known as JLab) in Hall A. The experiment aimed to measure the low Q^{2} evolution of the Gerasimov-Drell-Hearn (GDH) integral from Q^{2} = 0.1 to 0.9 GeV^{2}. The GDH sum rule at the real photon point provides an important test of Quantum Chromodynamics (QCD). The low Q^{2} evolution of the GDH integral contests various resonance models, Chiral Perturbation Theory ({chi} PT) and lattice QCD calculations, but more importantly, it helps us understand the transition between partonic and hadronic degrees of freedom. At high Q^{2}, beyond 1 GeV^{2}, the difference of the GDH integrals for the proton and the neutron is related to the Bjorken sum rule, another fundamental test of QCD. In addition, results of the measurements for the spin structure functions g_{1} and g_{2}, cross sections, and asymmetries are presented. E94-010 was the first experiment of its kind at JLab. It used a high-pressure, polarized ^{3}He target with a gas pressure of 10 atm and average target polarization of 35%. For the first time, the polarized electron source delivered an average beam polarization of 70% with a beam current of 15 micro A. The limit on the beam current was only imposed by the target. The experiment required six different beam energies from 0.86 to 5.1 GeV. This was the first time the accelerator ever reached 5.1 GeV. Both High-Resolution Spectrometers of Hall A, used in singles mode, were positioned at 15.5 ° each.
Condensed matter physics in the 21st century: The legacy of Jacques Friedel
NASA Astrophysics Data System (ADS)
Bouchiat, Hélène; Villain, Jacques
2016-03-01
The purpose of this dossier of Comptes rendus Physique devoted to the memory of Jacques Friedel is to give a panorama of his exceptional and numerous contributions to modern condensed matter physics. Since it is not possible to cover all the domains he investigated in a single volume, we have selected only a limited number of topics. We have tried, when possible, to present a juxtaposition of articles written by his former students or colleagues with others written instead by younger researchers whose work is inspired by important concepts originating from the work of Jacques Friedel, but who may have never met him.
Huffman, John W.; Smith, Valerie J.; Padgett, Lea W.
2008-01-01
The Friedel-Crafts acylation of N-p-toluenesulfonylpyrrole under Friedel-Crafts conditions has been reinvestigated. Evidence is presented in support of the hypothesis that when AlCl3 is used as the Lewis acid, acylation proceeds via reaction of an organoaluminum intermediate with the acyl halide. This leads to the production of the 3-acyl derivative as the major product. With weaker Lewis acids (EtAlCl2, Et2AlCl) or less than one equivalent of AlCl3 the relative amount of 2-acyl product is increased. A mechanistic rationalization is presented to explain these data. PMID:19247425
Friedel-Crafts Alkylation Using Elemental Aluminum Catalyst: An Undergraduate Laboratory Experiment.
ERIC Educational Resources Information Center
Meeks, B. Spencer; Lucas, Anita R.
1989-01-01
Provides methodology for carrying out the synthesis of sec-butyltoluene by the Friedel-Crafts alkylation of toluene. Suggests using simple elemental aluminum as the catalyst in place of AlCl3 or amalgamated aluminum. Notes satisfactory results for both macro- and microscale operations. (MVL)
The longevity of Jacques Friedel's model of the virtual bound state
NASA Astrophysics Data System (ADS)
Levy, Peter M.; Fert, Albert
2016-03-01
We illustrate the continuing pertinence of Friedel's model of the virtual bound state to describe electron scattering in metals. This model has been applied to such disparate studies as the chirality of spin interactions in metals, and the spin Hall effect caused by scattering from impurities with spin-orbit coupling. xml:lang="fr"
Deciphering DNA-based asymmetric catalysis through intramolecular Friedel-Crafts alkylations.
Park, Soyoung; Ikehata, Keiichi; Watabe, Ryo; Hidaka, Yuta; Rajendran, Arivazhagan; Sugiyama, Hiroshi
2012-10-28
We describe asymmetric intramolecular Friedel-Crafts alkylations with a DNA-based hybrid catalyst and propose a plausible binding model. This study shows promise for studying relationships between the helical chirality of DNA and enantioselectivity of the chemical reaction. PMID:22986468
Zhang, J.-Z.; Dyson, A.; Ridley, B. K.
2015-01-14
Using the dielectric continuum (DC) and three-dimensional phonon (3DP) models, energy relaxation (ER) of the hot electrons in the quasi-two-dimensional channel of lattice-matched InAlN/AlN/GaN heterostructures is studied theoretically, taking into account non-equilibrium polar optical phonons, electron degeneracy, and screening from the mobile electrons. The electron power dissipation (PD) and ER time due to both half-space and interface phonons are calculated as functions of the electron temperature T{sub e} using a variety of phonon lifetime values from experiment, and then compared with those evaluated by the 3DP model. Thereby, particular attention is paid to examination of the 3DP model to use for the hot-electron relaxation study. The 3DP model yields very close results to the DC model: With no hot phonons or screening, the power loss calculated from the 3DP model is 5% smaller than the DC power dissipation, whereas slightly larger 3DP power loss (by less than 4% with a phonon lifetime from 0.1 to 1 ps) is obtained throughout the electron temperature range from room temperature to 2500 K after including both the hot-phonon effect (HPE) and screening. Very close results are obtained also for ER time with the two phonon models (within a 5% of deviation). However, the 3DP model is found to underestimate the HPE by 9%. The Mori-Ando sum rule is restored by which it is proved that the PD values obtained from the DC and 3DP models are in general different in the spontaneous phonon emission process, except when scattering with interface phonons is sufficiently weak, or when the degenerate modes condition is imposed, which is also consistent with Register's scattering rate sum rule. The discrepancy between the DC and 3DP results is found to be caused by how much the high-energy interface phonons contribute to the ER: their contribution is enhanced in the spontaneous emission process but is dramatically reduced after including the HPE. Our calculation with both
Yi, Qiru; Li, Gang; Zhang, Jie; Luo, Sheng Nian; Fan, Duan; Gao, Zhenhua; Wang, Yanping; Gao, Guanfeng; Jiang, Shiping; Jiang, Xiaoming
2015-07-01
The characteristics of Friedel pairs in diffraction contrast tomography (DCT) are studied in the condition that the rotation axis of the sample is not exactly perpendicular to the incident X-ray direction. For the rotation axis approximately aligned along the vertical direction, the Friedel pairs close to the horizontal plane are insensitive to the non-perpendicularity of the rotation axis, and can be used to refine the sample-to-detector distance and X-ray energy, while the Friedel pairs close to the vertical direction are sensitive to the non-perpendicularity of the rotation axis, and can be used to determine the rotation axis orientation. The correct matching proportion of Friedel pairs decreases with increasing non-perpendicularity of the rotation axis. A method of data processing considering rotation axis misalignment is proposed, which significantly increases the correct matching and indexing proportions of the diffraction spots. A pure aluminium polycrystalline sample is investigated using DCT at beamline 4W1A of Beijing Synchrotron Radiation Facility. Based on the analysis of Friedel pairs, the sample-to-detector distance and X-ray energy are refined to be 8.67 mm and 20.04 keV, respectively. The non-perpendicular angle of the rotation axis is calculated to be 0.10°. With these refined geometric parameters, the matching proportion of the spatial position of diffraction spots is 90.62%. Three-dimensional reconstruction of the sample with 13 grains is realised using the algebraic reconstruction technique. It is demonstrated that the precise correction of the orientation of the sample rotation axis is effective in DCT suffering from rotation axis misalignment, and the higher accuracy in determining the rotation axis is expected to improve the reconstruction precision of grains. PMID:26134812
ERIC Educational Resources Information Center
Pong, Wai Yan
2007-01-01
We begin by answering the question, "Which natural numbers are sums of consecutive integers?" We then go on to explore the set of lengths (numbers of summands) in the decompositions of an integer as such sums.
Ghahramany, N.; Khosravi, R.
2009-07-01
We investigate the rare semileptonic decays B{sub s}{yields}[f{sub 0}(980),K{sub 0}*(1430)]l{sup +}l{sup -}, (l=e, {mu}, {tau}), and B{sub s}{yields}[f{sub 0}(980),K{sub 0}*(1430)]{nu}{nu} in the framework of the three-point QCD sum rules. These decays are important to study because the f{sub 0}(980) and K{sub 0}*(1430) are the scalar mesons with total spin 0 and even parity and the quark content of them are still controversial in high energy physics. These rare decays occur at loop level by electroweak penguin and weak box diagrams in the standard model via the flavor changing neutral current transitions of b{yields}d, s, and not allowed by tree level. Considering the effective contributions of the nonperturbative parts of the correlation function, we calculate the relevant form factors of these transitions. The branching fractions and longitudinal lepton polarization asymmetry are also investigated.
Experimental study of isovector spin sum rules
Alexandre Deur; Peter Bosted; Volker Burkert; Donald Crabb; Kahanawita Dharmawardane; Gail Dodge; Tony Forest; Keith Griffioen; Sebastian Kuhn; Ralph Minehart; Yelena Prok
2008-02-04
We present the Bjorken integral extracted from Jefferson Lab experiment EG1b for $0.05<2.92$ GeV$^2$. The integral is fit to extract the twist-4 element $f_{2}^{p-n}$ which is large and negative. Systematic studies of this higher twist analysis establish its legitimacy at $Q^{2}$ around 1 GeV$^{2}$. We also extracted the isovector part of the generalized forward spin polarizability $\\gamma_{0}$. Although this quantity provides a robust test of Chiral Perturbation Theory, our data disagree with the calculations.
ERIC Educational Resources Information Center
Shi, Yixun
2010-01-01
Starting with an interesting number game sometimes used by school teachers to demonstrate the factorization of integers, "sum-difference numbers" are defined. A positive integer n is a "sum-difference number" if there exist positive integers "x, y, w, z" such that n = xy = wz and x ? y = w + z. This paper characterizes all sum-difference numbers…
Holler, Michel; Allenbach, Nicolas; Sonet, Jordan; Nierengarten, Jean-François
2012-03-01
Systematic investigations of the cyclooligomerization of 1,4-disubstituted hydroquinone derivatives under Friedel-Crafts conditions have been carried out to demonstrate that the formation of pillar[5]arenes occurs under thermodynamic control. PMID:22159430
NASA Astrophysics Data System (ADS)
Fu, Hai-Bing; Wu, Xing-Gang; Ma, Yang; Cheng, Wei; Zhong, Tao
2016-08-01
We present a detailed calculation on the B\\to {K}* transition form factors (TFFs), {A}{0,1,2}, V and {T}{1,2,3}, within the QCD light-cone sum rules (LCSRs). To suppress the contributions from high-twist light-cone distribution amplitudes, we adopt a right-handed chiral correlator to do the LCSR calculation. In the resultant LCSRs for the TFFs, the transverse leading-twist distribution amplitude {φ }2;{K*}\\perp provides over 90% contribution, thus those TFFs provide good platforms for testing the property of {φ }2;{K*}\\perp . We suggest a model for {φ }2;{K*}\\perp , in which two parameters {B}2;{K*}\\perp and {C}2;{K*}\\perp dominantly control its longitudinal distribution. With a proper choice of {B}2;{K*}\\perp and {C}2;{K*}\\perp , our predictions on B\\to {K}* TFFs are consistent with those of lattice QCD predictions. As an application, we also calculate the branching fraction of the B-meson rare decay B\\to {K}*{μ }+{μ }-. The predicted differential branching fraction {{d}}{B}/{{d}}{q}2(B\\to {K}*{μ }+{μ }-) is consistent with the LHCb and Belle measurements within errors. After integrating over the allowable q 2-region, we get the branching fraction, {B}(B\\to {K}*{μ }+{μ }-)=≤ft({1.088}-0.205+0.261\\right)× {10}-6, where the errors are squared average of the mentioned error sources. When the precision of experimental measurements or the other source of theoretical uncertainties for this process have been further improved in the future, we may get a definite conclusion on the behavior of {φ }2;{K*}\\perp .
Jiang, Yonghai; Yang, Yu; Qian, Guangren; Hou, Hetian; Xi, Beidou; Xu, Yunfeng
2015-01-01
This research paper investigated a novel absorbent of calcium aluminate-rich cementitious materials (Friedel's salt adsorbent, FA) for aqueous hexavalent chromium (VI) removal. The adsorption kinetics showed that the maximum adsorption capacities of FA were 3.36, 14.66, and 26.17 mg/g when the initial Cr(VI) concentration was 10, 50, and 100 mg/L, respectively. The adsorption fitted with the pseudo-second-order kinetic model, suggesting the important roles of intercalation in the adsorption process with increasing Cr(VI) concentrations. This Friedel's salt adsorbent is suggested as an adaptive and effective adsorbent for Cr(VI) removal in contaminated groundwater. PMID:25798557
Naphthalene-based calixarenes: unusual regiochemistry of a Friedel-Crafts alkylation.
Shorthill, B J; Glass, T E
2001-02-22
[reaction: see text] In the pursuit of naphthalene-based calixarenes, a Friedel-Crafts alkylation with unusual regiochemistry was observed. Treatment of carbinol 14 with catalytic triflic acid was expected to produce calixarenes of the class represented by 16. Instead, the major product was cyclic trimer 15, in which alkylation of each naphthalene ring occurred at the electronically deactivated position. The structure of compound 15 was assigned by 2-D NMR studies. PMID:11178829
Lewis Acid Catalyzed Friedel-Crafts Alkylation of Alkenes with Trifluoropyruvates.
Xiang, Bin; Xu, Teng-Fei; Wu, Liang; Liu, Ren-Rong; Gao, Jian-Rong; Jia, Yi-Xia
2016-05-01
A Friedel-Crafts alkylation reaction of styrenes with trifluoropyruvates has been developed, which delivered allylic alcohols in excellent yields (up to 98%) using the Ni(ClO4)2·6H2O/bipyridine complex as a catalyst. The asymmetric reaction was catalyzed by the chiral Cu(OTf)2/bisoxazoline complex to afford the corresponding chiral allylic alcohols bearing trifluoromethylated quaternary stereogenic centers in moderate enantioselectivities (up to 75% ee). PMID:27028539
Griffiths, Kieran; Kumar, Prashant; Akien, Geoffrey R; Chilton, Nicholas F; Abdul-Sada, Alaa; Tizzard, Graham J; Coles, Simon J; Kostakis, George E
2016-06-14
A series of custom-designed, high yield, isoskeletal tetranuclear Zn/4f coordination clusters showing high efficiency as catalysts with low catalytic loadings in Friedel-Crafts alkylation are described for the first time. The possibility of altering the 4f centers in these catalysts without altering the core topology allows us to further confirm their stability via EPR and NMR, as well to gain insights into the plausible reaction mechanism, showcasing the usefulness of these bimetallic systems as catalysts. PMID:27248829
Aydin, C.; Yilmaz, A. H.; Bayar, M.
2010-05-01
We recalculated the coupling constants of {rho}({omega}){yields}{eta}{gamma} and {eta}{sup '{yields}{rho}}({omega}){gamma} decays especially with loop contributions in the case of axial-vector coupling in the method of QCD sum rules for dimension d=6. A comparison of our prediction on the coupling constants with the result obtained from analysis of the experimental data and calculations done before is performed.
NASA Astrophysics Data System (ADS)
Monien, H.
2010-04-01
Gaussian quadrature is a well-known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums has found some new interest. In this paper we apply these ideas to infinite sums in general and give an explicit construction for the weights and abscissae of Gaussian formulas. The abscissae of the Gaussian summation have a very interesting asymptotic distribution function with a kink singularity. We apply the Gaussian summation technique to two problems which have been discussed in the literature. We find that the Gaussian summation has a very rapid convergence rate for the Hardy-Littlewood sum for a large range of parameters.
Nakamura, Shuichi; Matsuda, Nazumi; Ohara, Mutsuyo
2016-07-01
Organocatalytic enantioselective aza-Friedel-Crafts reactions of cyclic ketimines with pyrroles or indoles were catalyzed by imidazoline/phosphoric acid catalysts. The reaction was applied to various 3H-indol-3-ones to afford products in excellent yields and enantioselectivities. The chiral catalysts can be recovered by a single separation step using column chromatography and are reusable without further purification. Based on the experimental investigations, a possible transition state has been proposed to explain the origin of the asymmetric induction. PMID:27124556
Structure-property correlation study through sum-over-state approach
NASA Astrophysics Data System (ADS)
Nandi, P. K.; Hatua, K.; Bansh, A. K.; Panja, N.; Ghanty, T. K.
2015-01-01
The use of Thomas Kuhn (TK) sum rule in the expanded sum-over-state (SOS) expression of hyperpolarizabilities leads to various relationships between different order of polarizabilities and ground state dipole moment etc.
Summing pressure compensation control
Myers, H.A.
1988-04-26
This patent describes a summing pressure compensator control for hydraulic loads with at least one of the hydraulic loads being a variable displacement motor having servo means for controlling the displacement thereof, first hydraulic means responsive to the supply of fluid to the variable displacement motor to provide a first pressure signal, second hydraulic means responsive to the supply of fluid to a second hydraulic load to provide a second pressure signal, summing means for receiving the first and second pressure signals and providing a control signal proportional to the sum of the first and second pressure signals, the control signal being applied to the servo means to increase the displacement of the variable displacement motor.
NASA Technical Reports Server (NTRS)
Robertson, G.
1982-01-01
Calibration was performed on the shuttle upper atmosphere mass spectrometer (SUMS). The results of the calibration and the as run test procedures are presented. The output data is described, and engineering data conversion factors, tables and curves, and calibration on instrument gauges are included. Static calibration results which include: instrument sensitive versus external pressure for N2 and O2, data from each scan of calibration, data plots from N2 and O2, and sensitivity of SUMS at inlet for N2 and O2, and ratios of 14/28 for nitrogen and 16/32 for oxygen are given.
Probability density functions of the average and difference intensities of Friedel opposites.
Shmueli, U; Flack, H D
2010-11-01
Trigonometric series for the average (A) and difference (D) intensities of Friedel opposites were carefully rederived and were normalized to minimize their dependence on sin(theta)/lambda. Probability density functions (hereafter p.d.f.s) of these series were then derived by the Fourier method [Shmueli, Weiss, Kiefer & Wilson (1984). Acta Cryst. A40, 651-660] and their expressions, which admit any chemical composition of the unit-cell contents, were obtained for the space group P1. Histograms of A and D were then calculated for an assumed random-structure model and for 3135 Friedel pairs of a published solved crystal structure, and were compared with the p.d.f.s after the latter were scaled up to the histograms. Good agreement was obtained for the random-structure model and a qualitative one for the published solved structure. The results indicate that the residual discrepancy is mainly due to the presumed statistical independence of the p.d.f.'s characteristic function on the contributions of the interatomic vectors. PMID:20962376
NASA Astrophysics Data System (ADS)
Desgranges, Caroline; Huber, Landon; Delhommelle, Jerome
2016-07-01
We determine the impact of the Friedel oscillations on the phase behavior, critical properties, and thermodynamic contours in films [two dimensions (2 D )] and bulk phases [three dimensions (3 D )]. Using expanded Wang-Landau simulations, we calculate the grand-canonical partition function and, in turn, the thermodynamic properties of systems modeled with a linear combination of the Lennard-Jones and Dzugutov potentials, weighted by a parameter X (0
Environmentally benign Friedel-Crafts benzylation over nano-TiO2/SO4 2-
NASA Astrophysics Data System (ADS)
Devi, Kalathiparambil RPS; Sreeja, Puthenveetil B.; Sugunan, Sankaran
2013-05-01
During the past decade, much attention has been paid to the replacement of homogeneous catalysts by solid acid catalysts. Friedel-Crafts benzylation of toluene with benzyl chloride (BC) in liquid phase was carried out over highly active, nano-crystalline sulfated titania systems. These catalysts were prepared using the sol gel method. Modification was done by loading 3% of transition metal oxides over sulfated titania. Reaction parameters such as catalyst mass, molar ratio, temperature, and time have been studied. More than 80% conversion of benzyl chloride and 100% selectivity are shown by all the catalysts under optimum conditions. Catalytic activity is correlated with Lewis acidity obtained from perylene adsorption studies. The reaction appears to proceed by an electrophile, which involves the reaction of BC with the acidic titania catalyst. The catalyst was regenerated and reused up to four reaction cycles with equal efficiency as in the first run. The prepared systems are environmentally friendly and are easy to handle.
Pecchioli, Tommaso; Muthyala, Manoj Kumar; Haag, Rainer; Christmann, Mathias
2015-01-01
The first immobilization of a MacMillan's first generation organocatalyst onto dendritic support is described. A modified tyrosine-based imidazolidin-4-one was grafted to a soluble high-loading hyperbranched polyglycerol via a copper-catalyzed alkyne-azide cycloaddition (CuAAC) reaction and readily purified by dialysis. The efficiency of differently functionalized multivalent organocatalysts 4a-c was tested in the asymmetric Friedel-Crafts alkylation of N-methylpyrrole with α,β-unsaturated aldehydes. A variety of substituted enals was investigated to explore the activity of the catalytic system which was also compared with monovalent analogues. The catalyst 4b showed excellent turnover rates and no loss of activity due to immobilization, albeit moderate enantioselectivities were observed. Moreover, easy recovery by selective precipitation allowed the reuse of the catalyst for three cycles. PMID:26150897
Friedel's salt formation in sulfoaluminate cements: A combined XRD and {sup 27}Al MAS NMR study
Paul, G.; Boccaleri, E.; Buzzi, L.; Canonico, F.; Gastaldi, D.
2015-01-15
Four different binders based on calcium sulfoaluminate cements have been submitted to accelerated chlorination through ionic exchange on hydrated pastes, in order to investigate their ability to chemically bind chloride ions that might reduce chloride penetration. The composition of hydrated cements before and after the treatment was evaluated by means of an X-Ray Diffraction–{sup 27}Al Magic Angle Spinning Nuclear Magnetic Resonance Spectroscopy combined study, allowing to take into account even partially amorphous phases and to make quantitative assumption on the relative abundance of the different aluminium-containing phases. It was found that low SO{sub 3} Sulfoaluminate–Portland ternary systems are the most effective in binding chloride ions and the active role played by different members of the AFm family in chloride uptake was confirmed. Moreover, a peculiar behavior related to the formation of Friedel's salt in different pH conditions was also established for the different cements.
Strong Quantum Size Effects in Pb(111) Thin Films Mediated by Anomalous Friedel Oscillations
Jia, Yu; Wu, Biao; Li, Chong; Eguiluz, Adolfo G; Weitering, Hanno; Zhang, Zhenyu
2010-01-01
Using first-principles calculations within density functional theory, we study Friedel oscillations (FOs) in the electron density at different metal surfaces and their influence on the lattice relaxation and stability of ultrathin metal films.We show that the FOs at the Pb(111) surface decay as 1=x with the distance x from the surface, different from the conventional 1=x2 power law at other metal surfaces. The underlying physical reason for this striking difference is tied to the strong nesting of the two different Fermi sheets along the Pb(111) direction. The interference of the strong FOs emanating from the two surfaces of a Pb(111) film, in turn, not only results in superoscillatory interlayer relaxations around the center of the film, but also determines its stability in the quantum regime. As a simple and generic picture, the present findings also explain why quantum size effects are exceptionally robust in Pb(111) films.
Friedel oscillations in graphene-based systems probed by Scanning Tunneling Microscopy
NASA Astrophysics Data System (ADS)
Mallet, Pierre; Brihuega, Iván; Cherkez, Vladimir; Gómez-Rodríguez, Jose Marìa; Veuillen, Jean-Yves
2016-03-01
For the last 25 years, scientists have demonstrated the capabilities of Scanning Tunneling Microscopy (STM) to visualize in real space the response of a two-dimensional electron gas to atomic-scale impurities. The analysis of the Friedel oscillations surrounding the impurities yields valuable information regarding the elastic scattering properties, the band structure, the doping level and the symmetry of the electronic states in the two-dimensional host system. We will address in this article the use of this technique for probing the electronic properties of graphene, the star two-dimensional compound of the last decade. In particular, we will emphasize how this technique can be pushed up to unravel the electronic pseudospin, a distinctive degree of freedom of graphene's Dirac fermions. xml:lang="fr"
Counting Triangles to Sum Squares
ERIC Educational Resources Information Center
DeMaio, Joe
2012-01-01
Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.
Darmann, Andreas; Nicosia, Gaia; Pferschy, Ulrich; Schauer, Joachim
2014-01-01
In this work we address a game theoretic variant of the Subset Sum problem, in which two decision makers (agents/players) compete for the usage of a common resource represented by a knapsack capacity. Each agent owns a set of integer weighted items and wants to maximize the total weight of its own items included in the knapsack. The solution is built as follows: Each agent, in turn, selects one of its items (not previously selected) and includes it in the knapsack if there is enough capacity. The process ends when the remaining capacity is too small for including any item left. We look at the problem from a single agent point of view and show that finding an optimal sequence of items to select is an NP-hard problem. Therefore we propose two natural heuristic strategies and analyze their worst-case performance when (1) the opponent is able to play optimally and (2) the opponent adopts a greedy strategy. From a centralized perspective we observe that some known results on the approximation of the classical Subset Sum can be effectively adapted to the multi-agent version of the problem. PMID:25844012
ERIC Educational Resources Information Center
DeTemple, Duane
2010-01-01
Purely combinatorial proofs are given for the sum of squares formula, 1[superscript 2] + 2[superscript 2] + ... + n[superscript 2] = n(n + 1) (2n + 1) / 6, and the sum of sums of squares formula, 1[superscript 2] + (1[superscript 2] + 2[superscript 2]) + ... + (1[superscript 2] + 2[superscript 2] + ... + n[superscript 2]) = n(n + 1)[superscript 2]…
Anisotropic density fluctuations, plasmons, and Friedel oscillations in nodal line semimetal
NASA Astrophysics Data System (ADS)
Rhim, Jun-Won; Kim, Yong Baek
2016-04-01
Motivated by recent experimental efforts on three-dimensional semimetals, we investigate the static and dynamic density response of the nodal line semimetal by computing the polarizability for both undoped and doped cases. The nodal line semimetal in the absence of doping is characterized by a ring-shape zero energy contour in momentum space, which may be considered as a collection of Dirac points. In the doped case, the Fermi surface has a torus shape and two independent processes of the momentum transfer contribute to the singular features of the polarizability even though we only have a single Fermi surface. In the static limit, there exist two independent singularities in the second derivative of the static polarizability. This results in the highly anisotropic Friedel oscillations which show the angle-dependent algebraic power law and the beat phenomena in the oscillatory electron density near a charged impurity. Furthermore, the dynamical polarizability has two singular lines along {\\hslash }ω =γ p and {\\hslash }ω =γ p{sin}η , where η is the angle between the external momentum {p} and the plane where the nodal ring lies. From the dynamical polarizability, we obtain the plasmon modes in the doped case, which show anisotropic dispersions and angle-dependent plasma frequencies. Qualitative differences between the low and high doping regimes are discussed in light of future experiments.
Friedel oscillation near a van Hove singularity in two-dimensional Dirac materials
NASA Astrophysics Data System (ADS)
Lu, Chi-Ken
2016-02-01
We consider Friedel oscillation in the two-dimensional Dirac materials when the Fermi level is near the van Hove singularity. Twisted graphene bilayer and the surface state of topological crystalline insulator are the representative materials which show low-energy saddle points that are feasible to probe by gating. We approximate the Fermi surface near saddle point with a hyperbola and calculate the static Lindhard response function. Employing a theorem of Lighthill, the induced charge density δ n due to an impurity is obtained and the algebraic decay of δ n is determined by the singularity of the static response function. Although a hyperbolic Fermi surface is rather different from a circular one, the static Lindhard response function in the present case shows a singularity similar with the response function associated with circular Fermi surface, which leads to the δ n\\propto {{R}-2} at large distance R. The dependences of charge density on the Fermi energy are different. Consequently, it is possible to observe in twisted graphene bilayer the evolution that δ n\\propto {{R}-3} near Dirac point changes to δ n\\propto {{R}-2} above the saddle point. Measurements using scanning tunnelling microscopy around the impurity sites could verify the prediction.
Test kit/spectrometer for the analysis of petroleum substances using Friedel-Crafts colorimetry
NASA Astrophysics Data System (ADS)
Hanby, John D.; Hewitt, Alan D.; Lory, Ernest E.
2001-02-01
12 Laboratory and field results of the testing of a new, visible-range spectrometry utilizing the robust signals produced by Friedel-Crafts reaction compounds demonstrate the utility of a rapid, portable, and sensitive method of on-site analysis for petroleum substances in soil and water samples. Preliminary testing of the kits and spectrometer was performed at the U.S. Army Cold Regions Research and Engineering Laboratory (CRREL) in Hanover, NH. Specific field protocols for the sampling and handling of soils for gasoline range organics and diesel range organics were established for the field sampling, which was conducted at the U.S. Navy Facilities Engineering Service Center in Port Hueneme, CA. Co-located soil samples were collected and either split or homogenized for subsequent partitioning to provide samples for the on-site analysis by the field kit/spectrometer technology and for later analysis by off- site reference laboratories. Test kit colorimetric results are by visual and spectrometric methods, and are compared with reference laboratory results and CRREL analyses.
Friedel oscillation near a van Hove singularity in two-dimensional Dirac materials.
Lu, Chi-Ken
2016-02-17
We consider Friedel oscillation in the two-dimensional Dirac materials when the Fermi level is near the van Hove singularity. Twisted graphene bilayer and the surface state of topological crystalline insulator are the representative materials which show low-energy saddle points that are feasible to probe by gating. We approximate the Fermi surface near saddle point with a hyperbola and calculate the static Lindhard response function. Employing a theorem of Lighthill, the induced charge density [Formula: see text] due to an impurity is obtained and the algebraic decay of [Formula: see text] is determined by the singularity of the static response function. Although a hyperbolic Fermi surface is rather different from a circular one, the static Lindhard response function in the present case shows a singularity similar with the response function associated with circular Fermi surface, which leads to the [Formula: see text] at large distance R. The dependences of charge density on the Fermi energy are different. Consequently, it is possible to observe in twisted graphene bilayer the evolution that [Formula: see text] near Dirac point changes to [Formula: see text] above the saddle point. Measurements using scanning tunnelling microscopy around the impurity sites could verify the prediction. PMID:26795372
On exponential sums of digital sums related to Gelfond's theorem
NASA Astrophysics Data System (ADS)
Okada, Tatsuya; Kobayashi, Zenji; Sekiguchi, Takeshi; Shiota, Yasunobu
2008-01-01
In this paper, we first give explicit formulas of exponential sums of sum of digits related to Gelfond's theorem. As an application of these formulas, we obtain a simple expression of Newman-Coquet type summation formula related to the number of binary digits in a multiple of a prime number.
NASA Astrophysics Data System (ADS)
Bréchet, Yves
2016-03-01
Jacques Friedel's contribution to the theory of plasticity is described, as well as the more recent developments it inspired. It involves the microscopic properties of dislocations as well as macroscopic effects. The evolution of fundamental metallurgy toward numerical metallurgy is discussed, and Friedel's point of view on numerical methods is analyzed.
Fisher, D.; Melamed, E.
1995-07-01
NThis report is a transcript of an interview with Hymer L. Friedell by representatives of the US DOE Office of Human Radiation Experiments. Dr. Friedell was selected for this interview because of his participation in the early stages of the medical use of radioisotopes, his important role in the Manhattan Engineer District Medical Division, and his distinguished medical career and his involvement in the distribution of isotopes and the approval for their use in humans. After a brief biographical sketch Dr. Friedell discusses his remembrances on a wide range of subjects. Topics discussed include pre-war radiation therapy, information provided to patients, the Army Medical Corps and the Manhattan Project, his work at the Chicago Metallurgical Laboratory, inspection visits of Manhattan Project facilities and proposed sites, Plutonium injection studies, and actions of the AEC Isotope Distribution Committee.
Ranjbar, Sara; Riente, Paola; Rodríguez-Escrich, Carles; Yadav, Jagjit; Ramineni, Kishore; Pericàs, Miquel A
2016-04-01
Heterogenized versions of the second-generation MacMillan imidazolidin-4-one are described for the first time. This versatile organocatalyst has been supported on 1% DVB Merrifield resin and Fe3O4 magnetic nanoparticles through a copper-catalyzed alkyne-azide cycloaddition (CuAAC) reaction. The resulting catalytic materials have been successfully applied to the asymmetric Friedel-Crafts alkylation of indoles with α,β-unsaturated aldehydes. While both catalytic systems can be easily recovered and admit repeated recycling, the polystyrene-based catalyst shows higher stability and provides better stereoselectivities. PMID:27010999
Doan, Tan L H; Dao, Thong Q; Tran, Hai N; Tran, Phuong H; Le, Thach N
2016-05-01
A zirconium-based metal-organic framework, an effective heterogeneous catalyst, has been developed for the Friedel-Crafts benzoylation of aromatic compounds under microwave irradiation. Constructed by a Zr(iv) cluster and a linker 1,4-bis(2-[4-carboxyphenyl]ethynyl)benzene (H2CPEB), the MOF, possessing large pores and high chemical stability, was appropriate for the enhancement of Lewis acid activity under microwave irradiation. The reaction studies demonstrated that the material could give high yields for a few minutes and maintain its reactivity and structure over several cycles. PMID:27064371
Liu, Yongmei; Meng, Guangrong; Liu, Ruzhang; Szostak, Michal
2016-05-21
Highly chemoselective Friedel-Crafts acylation with twisted amides under mild conditions is reported for the first time. The reaction shows high functional group tolerance, obviating the need for preformed sensitive organometallic reagents and expensive transition metal catalysts. The high reactivity of amides is switched on by ground-state steric distortion to disrupt the amide bond nN→πCO* resonance as a critical design feature. Conceptually, this new acid-promoted mechanism of twisted amides provides direct access to bench-stable acylating reagents under mild, metal-free conditions. PMID:27139813
Bao, Xiaoze; Wang, Baomin; Cui, Longchen; Zhu, Guodong; He, Yuli; Qu, Jingping; Song, Yuming
2015-11-01
A highly efficient and practical one-pot sequential process, consisting of an organocatalytic enantioselective Friedel-Crafts-type addition of 4-nonsubstituted pyrazolones to isatin-derived N-Boc ketimines and a subsequent diastereoselective fluorination of the pyrazolone moiety, is developed. This reaction sequence delivers novel oxindole-pyrazolone adducts featuring vicinal tetrasubstituted stereocenters with a 0.5 mol % catalyst loading in high yield with excellent enantio- and diastereocontrol. Notably, chloro, bromo, and thioether functionalities can be readily incorporated, rendering a broad diversity of the product. PMID:26473513
NASA Astrophysics Data System (ADS)
Ammar, Muhammad; Jiang, Sai; Ji, Shengfu
2016-01-01
A new strategy has been developed for the encapsulation of the phosphotungstic heteropoly acid (H3PW12O40 denoted as PTA) into zeolite imidazolate framework (ZIF-67) cage and the PTA@ZIF-67(ec) catalysts with different PTA content were prepared. The structure of the catalysts was characterized by XRD, BET, SEM, FT-IR, ICP-AES and TG. The catalytic activity and recovery properties of the catalysts for the Friedel-Crafts acylation of anisole with benzoyl chloride were evaluated. The results showed that 14.6-31.7 wt% PTA were encapsulated in the ZIF-67 cage. The PTA@ZIF-67(ec) catalysts had good catalytic activity for Friedel-Crafts acylation. The conversion of anisole can reach ~100% and the selectivity of the production can reach ~94% over 26.5 wt% PTA@ZIF-67(ec) catalyst under the reaction condition of 120 °C and 6 h. After reaction, the catalyst can be easily separated from the reaction mixture by the centrifugation. The recovered catalyst can be reused five times and the selectivity can be kept over 90%.
Compressibility sum rule for the two-dimensional electron gas.
Das, M P; Golden, K I; Green, F
2001-07-01
The authors establish formulas for the isothermal compressibility and long-wavelength static density-density response function of a weakly correlated two-dimensional electron gas in the 1
ERIC Educational Resources Information Center
Dintzner, Matthew R.; Maresh, Justin J.; Kinzie, Charles R.; Arena, Anthony F.; Speltz, Thomas
2012-01-01
Students in the undergraduate organic laboratory synthesize tetrahydro-2-(4-nitrophenyl)-4-phenyl-2"H"-pyran via the Montmorillonite K10 clay-catalyzed reaction of p-nitrobenzaldehye with methanol, 3-buten-1-ol, and benzene. The synthesis comprises an environmentally friendly tandem Prins-Friedel-Crafts-type multicomponent reaction (MCR) and sets…
ERIC Educational Resources Information Center
Fay, Temple H.
1997-01-01
Presents an exercise suitable for beginning calculus students that may give insight into series representations and allow students to see some elementary application of these representations. The Fourier series is used to approximate by taking sums of trigonometric functions of the form sin(ns) and cos(nx) for n is greater than or = zero. (PVD)
Direct Sum Decomposition of Groups
ERIC Educational Resources Information Center
Thaheem, A. B.
2005-01-01
Direct sum decomposition of Abelian groups appears in almost all textbooks on algebra for undergraduate students. This concept plays an important role in group theory. One simple example of this decomposition is obtained by using the kernel and range of a projection map on an Abelian group. The aim in this pedagogical note is to establish a direct…
Burke, Sarah J.; Mehta, Sharan K.; Appenteng, Roselyn
2015-01-01
Due to the profound extent to which natural products inspire medicinal chemists in drug discovery, there is demand for innovative syntheses of these often complex materials. This article describes the synthesis of tricarbocyclic natural product architectures through an extension of the enantioselective Birch-Cope sequence with intramolecular Friedel-Crafts alkylation reactions. Additionally, palladium-catalyzed enol silane cycloalkenylation of the tricarbocyclic structures afforded the challenging bicyclo[3.2.1]octane C/D ring system found in the gibberellins and the ent-kauranes, two natural products with diverse medicinal value. In the case of the ent-kaurane derivative, an unprecedented alkene rearrangement converted four alkene isomers to one final product. PMID:25598198
Hossini, Issam; Harrad, Mohamed Anoir; Ait Ali, Mustapha; El Firdoussi, Larbi; Karim, Abdallah; Valerga, Pedro; Puerta, M Carmen
2011-01-01
Friedel-Craft acylation at 100 °C of 2,5,9,9-tetramethyl-6,7,8,9-tetrahydro-5H-benzocycloheptene [ar-himachalene], a sesquiterpenic hydrocarbon obtained by catalytic dehydrogenation of α-, β- and γ-himachalenes, produces a mixture of two compounds: (3,5,5,9-tetramethyl-6,7,8,9-tetrahydro-5H-benzocyclohepten-2-yl)-ethanone (2, in 69% yield), with a conserved reactant backbone, and 3, with a different skeleton, in 21% yield. The crystal structure of 3 reveals it to be 1-(8-ethyl-8-hydroperoxy-3,5,5-trimethyl-5,6,7,8-tetrahydronaphthalen-2-yl)-ethanone. In this compound O-H…O bonds form dimers. These hydrogen-bonds, in conjunction with weaker C-H…O interactions, form a more extended supramolecular arrangement in the crystal. PMID:21760570
Wang, Wentao; Liu, Xiaohua; Cao, Weidi; Wang, Jun; Lin, Lili; Feng, Xiaoming
2010-02-01
A highly enantioselective Friedel-Crafts (F-C) alkylation of indoles and pyrrole with chalcone derivatives catalyzed by a chiral N,N'-dioxide-Sc(OTf)(3) complex has been developed that tolerates a wide range of substrates. The reaction proceeds in moderate to excellent yields and high enantioselectivities (85-92 % enantiomeric excess) using 2 mol % (for indole) or 0.5 mol % (for pyrrole) catalyst loading, which showed the potential value of the catalyst system. Meanwhile, a strong positive nonlinear effect was observed. On the basis of the experimental results and previous reports, a possible working model is proposed to explain the origin of the activation and asymmetric induction. PMID:20013964
Robust adiabatic sum frequency conversion.
Suchowski, Haim; Prabhudesai, Vaibhav; Oron, Dan; Arie, Ady; Silberberg, Yaron
2009-07-20
We discuss theoretically and demonstrate experimentally the robustness of the adiabatic sum frequency conversion method. This technique, borrowed from an analogous scheme of robust population transfer in atomic physics and nuclear magnetic resonance, enables the achievement of nearly full frequency conversion in a sum frequency generation process for a bandwidth up to two orders of magnitude wider than in conventional conversion schemes. We show that this scheme is robust to variations in the parameters of both the nonlinear crystal and of the incoming light. These include the crystal temperature, the frequency of the incoming field, the pump intensity, the crystal length and the angle of incidence. Also, we show that this extremely broad bandwidth can be tuned to higher or lower central wavelengths by changing either the pump frequency or the crystal temperature. The detailed study of the properties of this converter is done using the Landau-Zener theory dealing with the adiabatic transitions in two level systems. PMID:19654679
Summing Planar Bosonic Open Strings
Bardakci, Korkut
2006-02-16
In earlier work, planar graphs of massless {phi}{sup 3} theory were summed with the help of the light cone world sheet picture and the mean field approximation. In the present article, the same methods are applied to the problem of summing planar bosonic open strings. They find that in the ground state of the system, string boundaries form a condensate on the world sheet, and a new string emerges from this summation. Its slope is always greater than the initial slope, and it remains non-zero even when the initial slope is set equal to zero. If they assume the initial string tends to a field a theory in the zero slope limit, this result provides evidence for string formation in field theory.
NASA Astrophysics Data System (ADS)
Akhrem, Irena S.; Orlinkov, Alexander V.; Vol'pin, Mark E.
1996-10-01
The results of studies on direct functionalisation of activated alkanes and cycloalkanes under the action of 'classical' Friedel-Crafts complexes (viz. equimolar complexes of acyl halides with aluminium halides) and related systems containing smaller or somewhat larger amounts of aluminium halide are surveyed. The studies carried out during the last decade on functionalisation of saturated hydrocarbons devoid of tertiary carbon atoms, by aprotic organic superacids RCOX . 2AlCl3 are summarised. Reactions of alkanes with acylium cations in superacidic media are considered. The published data on the structure of complexes RCOX . AlCl3 and RCOX . 2AlCl3 and on the nature of the active complexes in the reactions of arenes with acylium cations and with complexes RCOX . AlCl3 in both acidic and organic media as well as in the reactions of alkanes with acylium salts in protic superacids and with superacidic complexes RCOX . 2AlCl3 in aprotic solvents are analysed. The prospects for the synthesis of organic compounds from alkanes and cycloalkanes under the action of complexes of acyl halides with aluminium halides are outlined. The bibliography includes 128 references.
Rosana, Michael R; Hunt, Jacob; Ferrari, Anthony; Southworth, Taylor A; Tao, Yuchuan; Stiegman, Albert E; Dudley, Gregory B
2014-08-15
Thermally promoted Friedel-Crafts benzylation of arene solvents has been examined under both conventional convective heating with an oil bath and heating using microwave (MW) energy. Bulk solution temperatures-as measured by internal and external temperature probes and as defined by solvent reflux-were comparable in both sets of experiments. MW-specific rate enhancements were documented under certain conditions and not others. The observed rate enhancements at a given temperature are proposed to arise from selective MW heating of polar solutes, perturbing thermal equilibrium between the solute and bulk solution. Central to MW-specific thermal phenomena is the difference between heat and temperature. Temperature is a measure of the ensemble average kinetic molecular energy of all solution components, but temperature does not provide information about solute-specific energy differences that may arise as a consequence of selective MW heating. Enhanced chemical reactivity of the MW-absorbing solute can be described as a MW-specific "extra-temperature thermal effect", because the measurable solution temperature only captures a portion of the solute kinetic molecular energy. Experimental factors that favor MW-specific rate enhancements are discussed with an eye toward future development of MW-actuated organic reactions, in which the observed thermal reactivity exceeds what is predicted from temperature-based Arrhenius calculations. PMID:25050855
Méndez, Isabel; Rodríguez, Ricardo; Polo, Víctor; Passarelli, Vincenzo; Lahoz, Fernando J; García-Orduña, Pilar; Carmona, Daniel
2016-07-25
By changing the temperature from 283 to 233 K, the S (99 % ee) or R (96 % ee) enantiomer of the Friedel-Crafts (FC) adduct of the reaction between N-methyl-2-methylindole and trans-β-nitrostyrene can be obtained by using (SRh ,RC )-[(η(5) -C5 Me5 )Rh{(R)-Prophos}(H2 O)][SbF6 ]2 as the catalyst precursor. This catalytic system presents two other uncommon features: 1) The ee changes with reaction time showing trends that depend on the reaction temperature and 2) an increase in the catalyst loading results in a decrease in the ee of the S enantiomer. Detection and characterization of the intermediate metal-nitroalkene and metal-aci-nitro complexes, the free aci-nitro compound, and the FC adduct-complex, together with solution NMR measurements, theoretical calculations, and kinetic studies have allowed us to propose two plausible alternative catalytic cycles. On the basis of these cycles, all the above-mentioned observations can be rationalized. In particular, the reversibility of one of the cycles together with the kinetic resolution of the intermediate aci-nitro complexes account for the high ee values achieved in both antipodes. On the other hand, the results of kinetic measurements explain the unusual effect of the increment in catalyst loading. PMID:27345293
NASA Astrophysics Data System (ADS)
Sinha, Urbasi
2011-09-01
This paper is based on work published in [1]. It describes a triple slit experiment using single photons that has been used to provide a bound on one of the most fundamental axioms of quantum mechanics i.e. Born's rule for probabilities [2]. In spite of being one of the most successful theories which describes various natural phenomena, quantum mechanics has enough intricacies and "weirdness" associated with it which makes many physicists believe that it may not be the final theory and hints towards the possibility of more generalized versions. Quantum interference as shown by a double slit diffraction experiment only occurs from pairs of paths. Even in multi-slit versions, interference can only occur between pairs of possibilities and increasing the number of slits does not increase the complexity of the theory that still remains second-order. However, more generalized versions of quantum mechanics may allow for multi-path i.e. higher than second order interference. This experiment also provides a bound on the magnitude of such higher order interference. We have been able to bound the magnitude of three-path interference to less than 10-2 of the expected two-path interference, thus ruling out third and higher order interference and providing a bound on the accuracy of Born's rule.
Fundamentals of Sum-Frequency Spectroscopy
NASA Astrophysics Data System (ADS)
Shen, Y. R.
2016-02-01
1. Historical perspective; 2. Basics of nonlinear optics; 3. Basic theory for surface sum-frequency generation; 4. Experimental considerations; 5. Characterization of bulk materials; 6. Molecular adsorbates at interfaces; 7. Structures and properties of solid surfaces; 8. Interfacial liquid structures; 9. Interfaces of polymers and organic materials; 10. Biomolecules and biological interfaces; 11. Sum-frequency chiral spectroscopy; 12. Miscellaneous topics.
Where Does Latin "Sum" Come From?
ERIC Educational Resources Information Center
Nyman, Martti A.
1977-01-01
The derivation of Latin "sum,""es(s),""est" from Indo-European "esmi,""est,""esti" involves methodological problems. It is claimed here that the development of "sum" from "esmi" is related to the origin of the variation "est-st" (less than"esti"). The study is primarily concerned with this process, but chronological suggestions are also made. (CHK)
Item Response Modeling with Sum Scores
ERIC Educational Resources Information Center
Johnson, Timothy R.
2013-01-01
One of the distinctions between classical test theory and item response theory is that the former focuses on sum scores and their relationship to true scores, whereas the latter concerns item responses and their relationship to latent scores. Although item response theory is often viewed as the richer of the two theories, sum scores are still…
Fouvry, Étienne; Kowalski, Emmanuel; Michel, Philippe
2015-01-01
We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat–Kolchin–Ribet criterion, in a form that is easily applicable in analytic number theory. PMID:25802414
García-García, Carolina; Ortiz-Rojano, Laura; Álvarez, Susana; Álvarez, Rosana; Ribagorda, María; Carreño, M Carmen
2016-05-01
Lewis acid catalyzed Friedel-Crafts alkylation of indoles has been achieved in high yields and selectivities using p-quinols as electrophiles. (S)-Binol-3,3'-(9-anthracenyl)-phosphoric acid was able to catalyze the enantioselective formation of 5-(3-indole)-2-cyclohexenone derivatives. Experimental results and theoretical calculations explained the enantioselectivity based on a transition state where two water molecules act as a tether joining the p-quinol with the phosphoric acid and the NH of indole, thus facilitating the desymmetrization of the prochiral cyclohexadienone framework. PMID:27088217
Reddy, B V Subba; Reddy, Y Vikram; Singarapu, Kiran Kumar
2016-01-21
2-Furylcarbinols undergo a smooth aza-Piancatelli rearrangement followed by Friedel-Crafts alkylation with a bifunctional substrate, (1H-pyrrol-1-yl)aniline, in the presence of 10 mol% In(OTf)3 in acetonitrile at room temperature to afford the corresponding hexahydrobenzo[b]cyclopenta[f]pyrrolo[1,2-d][1,4]diazepin-11(4aH)-one scaffolds in good yields. This method offers significant advantages such as high conversions, mild reaction conditions, short reaction times, and high selectivity. The relative stereochemistry of the product was established by nOe studies. PMID:26646535
Sums-of-Products and Subproblem Independence
NASA Astrophysics Data System (ADS)
Stearns, Richard E.; Hunt, Harry B.
Sums-of-products provide a basis for describing certain computational problems, particularly problems related to constraint satisfaction including SAT, MAX SAT, and #SAT. They also can be used to describe many problems arising from graph theory. By modeling a problem as a sum-of-products problem, the concept of “subproblem independence” takes on a clear meaning. Subproblem independence has immediate computational implications since it can be used to create programs with reduced levels of nesting and programs which exploit memoization. The concept of subproblem independence also extends to quantified sums.
NASA Astrophysics Data System (ADS)
Schuetz, W.; Heuler, P.
1994-03-01
In the first sections, the requirements to be met by hypotheses for fatigue life prediction (including those for the crack initiation and crack propagation phases) are discussed in detail. These requirements are shown to be different for 'scientific' and for 'industrial' fatigue life prediction. Aspects with regard to an assessment of fatigue life prediction hypotheses are discussed. The last section presents the results of a large cooperative program between IABG and several automobile manufacturers, in which Miner's Rule in several versions was assessed against spectrum tests with five different actual automobile components: forged steel stub axle; forged steel stub axle, induction hardened; sheet steel welded rear axle (front wheel drive car); cast aluminum wheel; and welded sheet steel wheel. Since up to 80 components each were available, and two different, but typical, automotive stress-time histories were employed, the assessment was very thorough, avoiding many of the drawbacks of previous assessments. It is shown that damage sums to failure were usually far below 1.0; they also depended on the component in question, the aluminum wheel resulting in the lowest damage sums to failure; the damage sums to failure where always lower for a mild spectrum than for a severe one; and the influence of spectrum variation was predicted best - among the hypotheses tested - by use of a recent proposal of Zenner and Liu.
Energy Science and Technology Software Center (ESTSC)
2015-10-06
This code is a set of global sums to support the paper "Computational Reproducibility for Production Physics Applications" submitted to the Numerical Reproducibility at Exascale (NRE 2015) workshop at the 2015 Supercomputing conference, Nov. 20, 2015
Support activities to maintain SUMS flight readiness
NASA Technical Reports Server (NTRS)
Wright, Willie
1992-01-01
The Shuttle Upper Atmosphere Mass Spectrometer (SUMS), a component experiment of the NASA Orbital Experiments Program (OEX), was flown aboard the shuttle Columbia (OV102) mounted at the forward end of the nose landing gear well with an atmospheric gas inlet system fitted to the lower fuselage (chin panel) surface. The SUMS was designed to provide atmospheric data in flow regimes inaccessible prior to the development of the Space Transportation System (STS). The experiment mission operation began about one hour prior to shuttle de-orbit entry maneuver and continued until reaching 1.6 torr (about 86 km altitude). The SUMS mass spectrometer consists of the spare unit from the Viking mission to Mars. Bendix Aerospace under contract to NASA LaRC incorporated the Viking mass spectrometer, a microprocessor based logic card, a pressurized instrument case, and the University of Texas at Dallas provided a gas inlet system into a configuration suited to interface with the shuttle Columbia. The SUMS experiment underwent static and dynamic calibration as well as vacuum maintenance before and after STS 40 shuttle flight. The SUMS flew a total of 3 times on the space shuttle Columbia. Between flights the SUMS was maintained in flight ready status. The flight data has been analyzed by the NASA LaRC Aerothermodynamics Branch. Flight data spectrum plots and reports are presented in the Appendices to the Final Technical Report for NAS1-17399.
NASA Astrophysics Data System (ADS)
Höppner, Frank
Association rules are rules of the kind "70% of the customers who buy vine and cheese also buy grapes". While the traditional field of application is market basket analysis, association rule mining has been applied to various fields since then, which has led to a number of important modifications and extensions. We discuss the most frequently applied approach that is central to many extensions, the Apriori algorithm, and briefly review some applications to other data types, well-known problems of rule evaluation via support and confidence, and extensions of or alternatives to the standard framework.
Experimental results of the betatron sum resonance
Wang, Y.; Ball, M.; Brabson, B.
1993-06-01
The experimental observations of motion near the betatron sum resonance, {nu}{sub x} + 2{nu}{sub z} = 13, are presented. A fast quadrupole (Panofsky-style ferrite picture-frame magnet with a pulsed power supplier) producing a betatron tune shift of the order of 0.03 at rise time of 1 {mu}s was used. This quadrupole was used to produce betatron tunes which jumped past and then crossed back through a betatron sum resonance line. The beam response as function of initial betatron amplitudes were recorded turn by turn. The correlated growth of the action variables, J{sub x} and J{sub z}, was observed. The phase space plots in the resonance frame reveal the features of particle motion near the nonlinear sum resonance region.