Constant-cutoff approach to meson-hyperon couplings

The kaon coupling constants at hyperon-nucleon vertices and the pion coupling constants at hyperon-hyperon vertices are calculated in the framework of the constant-cutoff approach to the CHK bound-state model of hyperons, where the postive-parity hyperons such as Λ, Σ, and ∑^*=∑(1385) are theP-wave bound states of an antikaon and theSU(2) Skyrme soliton, while Λ^* is theS-wave bound state. Meson coupling constants are defined as matrix elements of the meson-source terms between two single-baryon states following the method developed for resolving the Yukawa coupling problem in theSU(2) Skyrme soliton model. The magnitudes of the meson coupling constants are found to be close to those obtained using the complete Skyrme model and the phenomenological values.     

Viscous generalized Chaplygin gas as a unified dark fluid: including perturbation of bulk viscosity

In this article, the three-point QCD sum rules are used to compute the strong coupling constants of vertices containing the strange bottomed (charmed) mesons with the pion. The coupling constants are calculated when both the bottom (charm) and the pion states are off-shell. A comparison of the obtained results of the coupling constants with existing predictions is also made.     

Sensitivity of pion production to the nuclear EOS and to the delta's coupling constant

A relativistic baryon-meson mean field theory (including delta resonances) is used to study the dependence of pion production in heavy ion collisions on the nuclear equation of state and on the delta-meson coupling constants. For fixed ground state equations of state, the pion yields depend sensitively on the value of the delta-meson coupling constants.     

Numerical solution of the spinor Bethe-Salpeter equation and the goldstein problem

The spinor Bethe-Salpeter equation describing bound states of a fermion-antifermion pair with massless-boson exchange reduces to a single (uncoupled) partial differential equation for special combinations of the fermion-boson couplings. For spinless bound states with positive or negative parity this equation is a generalization to nonvanishing bound-state masses of the equations studied by Kummer and Goldstein, respectively. In the tight-binding limit the Kummer equation has a discrete spectrum, in contrast to the Goldstein equation, while for loose binding only the generalized Goldstein equation has a nonrelativistic limit. For intermediate binding energies the equations are solved numerically. The generalized Kummer equation is shown to possess a discrete spectrum of coupling constants for all bound-state masses. For the generalized Goldstein equation a discrete spectrum of coupling constants is found only if the binding energy is smaller than a critical value.     

Meson Cloud Effect on △(1232) Resonance Transition Properties with a Relativistic Quark Model Approach

Based on a relativistic quark model approach, the transition properties of the first nucleon resonance △(1232), and the coupling constants gπNN, g△πN are investigated. Tvo different vays to remove the center of mass motion are considered. The results of the relativistic approaches with and without center ofmass correction are compared with those of nonrelativistic constituent quark model. Moreover, pion meson cloud effect on these calculated observables is explicitly addressed. Better results are obtained by taking the pion meson cloud into account.     

Meson Cloud Effect on Δ(1232) Resonance Transition Properties with a Relativistic Quark Model Approach

Based on a relativistic quark model approach, the transition properties of the first nucleon resonance Δ(1232), and the coupling constants g_πNN, g_ΔπN are investigated. Two different ways to remove the center of mass motion are considered. The results of the relativistic approaches with and without center of mass correction are compared with those of nonrelativistic constituent quark model. Moreover, pion meson cloud effect on these calculated observables is explicitly addressed. Better results are obtained by taking the pion meson cloud into account.     

The πNN bound-state problem

Bound-state solutions for the system composed of a pion and two nucleons are studied, and it is shown that their existence is essentially determined by the range of the πN interaction in momentum space. The relativistic Faddeev equations are solved to search for bound-state solutions of a negative pion and two neutrons, using the newly constructed πN separable potentials that reproduce the phase shift of the P₃₃ channel from 0 to 350 MeV, and realistic NN interactions such as the Reid soft-core, Paris, and Malfliet-Tjon potentials. It is found that bound-state solutions are possible for some of the πN interactions that have very long range in momentum space.     

Generalized Parton Distributions of the Pion on the Transverse Lattice

The quark-generalized parton distributions of the pion are calculated from light-cone wavefunctions in transverse lattice gauge theory at large N_c. The pion effective size is found to decrease with increasing momentum transfer. An analytic ansatz, consistent with finite bound-state light-cone energy conditions, is given for the light-cone momentum dependence of the wavefunctions. This leads to simple, universal predictions for the behaviour of the distributions near the endpoints, complementing numerical DLCQ data.     

Hamiltonian approach to the bound-state problem in QCD2

Bosonization of two-dimensional QCD in the large-N _C limit is performed within the Hamiltonian approach in the Coulomb gauge. A generalized Bogolyubov transformation is applied to diagonalize the Hamiltonian in the bosonic sector of the theory, and the composite operators creating (annihilating) bosons are obtained in terms of dressed quark operators. The bound-state equation is reconstructed as the result of the generalized Bogolyubov transformation, and the form of its massless solution, a chiral pion, is found explicitly. The chiral properties of the theory are discussed.     

Pion Coupling to Nuclei

The concept of the pion-nucleus coupling constants is discussed. Methods of their determination are reviewed. These include: forward dispersion relations, extrapolation of differential cross sections to the poles in the angular variable, analysis of data on electromagnetic form factors with the use of the PCAC and CVC hypotheses, pion photoproduction at threshold and low-ernergy theorems. Our present knowledge of the pion coupling to the He, Li, Be, C, N and O nuclei is summarized.     

Single-pion production and the structure of the weak neutral current

We investigate the restrictions on the structure of the weak neutral current imposed by single pion production cross sections on single nucleons. A general vector (V), axial-vector (A) neutral current with |ΔI|?1 is assumed, where the isovector V,A neutral currents are the neutral members of the isotriplets containing the charged weak currents. From neutrino cross sections alone we derive bounds for the neutral current coupling constants. These bounds supplement the known constraints from inclusive scattering in a very useful way. More specific assumptions about the isoscalar neutral current are also considered. We discuss the resulting bounds using the existing neutrino data. Finally, it is shown that with the advent of antineutrino data for single pion production the neutral current coupling constants will be determined uniquely.     

Regarding the Distribution of Glue in the Pion

Understanding why the scale of emergent hadron mass is obvious in the proton but hidden in the pion may rest on mapping the distribution functions(DFs) of all partons within the pion and comparing them with those in the proton;and since glue provides binding in quantum chromodynamics,the glue DF could play a special role.Producing reliable predictions for the proton's DFs is difficult because the proton is a three-valence-body bound-state problem.As sketched herein,the situation for the pion,a two-valence-body problem,is much better,with continuum and lattice predictions for the valence-quark and glue DFs in agreement.This beginning of theory alignment is timely because experimental facilities now either in operation or planning promise to realize the longstanding goal of providing pion targets,thereby enabling precision experimental tests of rigorous theory predictions concerning Nature's most fundamental Nambu-Goldstone bosons.     

Drawing insights from pion parton distributions

A symmetry-preserving continuum approach to the two valence-body bound-state problem is used to calculate the valence,glue and sea distributions within the pion;unifying them with,inter alia,electromagnetic pion elastic and transition form factors.The analysis reveals the following momentum fractions at the scale ζ2:=2GeV:〈xvalence〉=0.48(3),〈xglue〉=0.41(2),〈xsea〉=0.11(2);and despite hardening induced by the emergent phenomenon of dynamical chiral symmetry breaking,the valence-quark distribution function,q^π(x),exhibits the x≈1 behaviour predicted by quantum chromodynamics(QCD).After evolution to ζ=5.2 GeV,the prediction for q^π(x)matches that obtained using lattice-regularised QCD.This confluence should both stimulate improved analyses of existing data and aid in planning efforts to obtain new data on the pion distribution functions.     

Pionic disintegration of the deuteron

Pionic disintegration of the deuteron between threshold and the 3,3 resonance region is described by a model containing one- and two-body absorption. The two-body absorption mechanism is due to pion and ?-meson rescattering calculated from phenomenological Lagrangians. The role of the ?-meson is crucial in reducing the cross section due to pion exchange. The role of the mass distribution of the ρ-meson, hadronic form factors and final state interactions are investigated. Good agreement with empirical results for the total cross section is obtained with a set of currently accepted values for the meson-nucleon coupling constants and the ρ-mass distribution.     

Elastic neutrino proton scattering and the structure of the neutral current

Optimal constraints on the structure of a general V, A hadronic neutral current are derived from neutrino proton scattering and compared with corresponding results from inclusive neutrino scattering and single pion production by neutrinos. For an arbitrary axial component of the neutral current, restrictions for the vector coupling constants are obtained. It is shown that the most general neutral current which can be related to charged weak and electromagnetic currents accounts for all existing data on neutrino hadron scattering. The neutral current coupling constants are determined for the pure isovector model, the Salam-Weinberg model and the bottom-quark model. All three models lead to practically the same isovector couplings but they differ in the strength of the isoscalar current.     

A Combined Study of the Pion’s Static Properties and form Factors

We study consistently the pion’s static observables and the elastic and γ* γ → π ⁰ transition form factors within a light-front model. Consistency requires that all calculations are performed within a given model with the same and single adjusted length or mass-scale parameter of the associated pion bound-state wave function. Our results agree well with all extent data including recent Belle data on the γ* γ → π ⁰ form factor at large q ², yet the BaBar data on this transition form factor resists a sensible comparison. We relax the initial constraint on the bound-state wave function and show the BaBar data can partially be accommodated. This, however, comes at the cost of a hard elastic form factor not in agreement with experiment. Moreover, the pion charge radius is about 40 % smaller than its experimentally determined value. It is argued that a decreasing charge radius produces an ever harder form factor with a bound-state amplitude difficultly reconcilable with soft QCD. We also discuss why vector dominance type models for the photon-quark vertex, based on analyticity and crossing symmetry, are unlikely to reproduce the litigious transition form factor data.     

Relation between the charged and neutral pion–nucleon coupling constants in the Yukawa model

In the Yukawa-model framework for NN forces, a simple relation between the charged and neutral pion–nucleon coupling constants is derived. The relation implies that the charged pion–nucleon constant is larger than the neutral one since the np interaction is stronger than the pp interaction. The derived value of the charged pion–nucleon constant shows a very good agreement with one of the recent measurements. In relative units, the splitting between the charged and neutral pion–nucleon constants is predicted to be practically the same as that between the charged and neutral pion masses. The charge dependence of the NN scattering length arising from the mass difference between the charged and neutral pions is also analyzed.     

The study of the binding energy of nuclear matter in the relativistic σ− ω− π model with Δ isobar degree of freedom

The relativistic σ?ω?π model is proposed and used to calculate the binding energy of relativistic nuclear matter. By coupling Δ isobar to the σ meson, the zero-point fluctuation energy of the Δ isobar in the one loop approximation is derived. We calculate the effective mass of nucleon and Δ isobar, exchange and correlation energies, pressure and incompressibility of nuclear matter. The density dependence correction to σNN ωNN coupling constants is a very important mechanism to saturate the binding energy. The pion propagator is nuclear matter is constructed by the relativistic particle-hole, delta-hole and short-range correlation. The pion dispersion relation is calculated we find it’s very sensitive to the effective mass of nucleon and Δ isobar.     

Chiral symmetry restoration and parity mixing

We derive the expressions of the vector and axial current from a chiral Lagrangian restricted to nucleons and pions. They display mixing terms between the axial and vector currents. We study the modifications in the nuclear medium of the coupling constants of the axial current, namely the pion decay constant and the nucleonic axial one due to the requirements of chiral symmetry. We express the renormalizations in terms of the local scalar pion density. The latter also governs the quark condensate evolution and we discuss the link between this evolution and the renormalizations. In the case of the nucleon axial coupling constant this renormalization corresponds to a new type of pion exchange currents, with two exchanged pions. We give an estimate for the resulting quenching. Although moderate it helps explaining the quenching experimentally observed.