Meson-hyperon couplings in the bound-state approach to the Skyrme model

Kaon and pion coupling constants to hyperons are calculated in the bound-state approach to strangeness in the Skyrme-soliton model. The pion and kaon coupling constants are properly defined as matrix elements of source terms of the mesons sandwiched between two single-baryon states. Numerical calculation of the coupling constants shows that the bound-state approach well reproduces the empirical values.     

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.     

The goldstone pion in SU(2) lattice QCD at low quark mass: Scaling and finite size effects

Results for the pion sector of an extensive numerical simulation of quenched SU(2) QCD with staggered fermions are presented. A wide range of quark masses, gauge couplings and lattice sizes is investigated. The systematic and statistical errors are carefully analyzed. Finite size effects occurring on small lattices and/or at low quark masses are studied in detail. When they are absent or weak, we find that the pion mass and coupling constant verify approximate scaling behaviour at low quark mass for β ≳ 2.4. We determine the K and π coupling constants to be in the ratio 1.25(5). At β = 2.3, we show that the square pion mass contains a substantial contribution which is non-linear in the quark mass and renders chiral limit extrapolations less reliable.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Taming the pion cloud of the nucleon

We present a light-front determination of the pionic contribution to the nucleon self-energy, Σ(π), to second order in pion-baryon coupling constants that allows the pion-nucleon vertex function to be treated in a model-independent manner constrained by experiment. The pion mass μ dependence of Σ(π) is consistent with chiral perturbation theory results for small values of μ and is also linearly dependent on μ for larger values, in accord with the results of lattice QCD calculations. The derivative of Σ(π) with respect to μ(2) yields the dominant contribution to the pion content, which is consistent with the d[over ˉ]-u[over ˉ] difference observed experimentally in the violation of the Gottfried sum rule.     

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.     

Dispersive treatment of low-energy pion-nucleus forward elastic scattering

The amplitudes for pion-nucleus forward elastic scattering are studied by means of dispersion relations, with emphasis on the low-energy and unphysical regions. The importance of the threshold behaviour of inelastic pion scattering is pointed out, and effective coupling constants, a news-wave parameter and the real part of thep-wave scattering length are determined.     

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.     

On the radiative pion decay

A reanalysis of the radiative pion decay together with the calculation of the radiative corrections within chiral perturbation theory (CHPT) is performed. The amplitude of this decay contains an inner Bremsstrahlung contribution and a structure-dependent part, which are both accessible in experiments. In order to obtain a reliable estimate of the hadronic contributions we combine the CHPT result with a large-N_c expansion and experimental data on other decays, which makes it possible to determine the occurring coupling constants. PACS  13.20.Cz; 12.39.Fe     

Axial polarizability and weak currents in nuclei

The effect of the isobaric excitations on the weak axial coupling constants in nuclei is studied through P.C.A.C. We first establish the Klein-Gordon equation for the virtual pion field in the nucleus; it takes into account pion rescattering. The influence of isobar excitation is contained in the axial polarizability coefficient which is linked to the p-wave π-N scattering volume. The derivation of this equation stresses its analogies with electromagnetism. We give then a basic relation between the axial current and the pionic field. It incorporates the effects of the isobars in the axial polarizability, which leads naturally to an electromagnetic analog. We show that this relation leads in heavy nuclei to a quenching of the axial coupling constant by the Lorentz-Lorenz factor, which may originate from the short range or the Pauli correlations, depending on the range of the π-N forces. Hence this quenching may have a different origin than the existence of short-range correlations and may arise from a Pauli blocking effect. On the other hand, the pseudoscalar coupling constant is found to be strongly suppressed. In finite nuclei, these basic quenchings can be masked by surface effects, the general features of which are studied with the help of a solvable model. This model is further used to obtain the asymptotic pion field which is linked to the effective pion-nucleus coupling constant and can be determined experimentally through π-nucleus dispersion relations. We find that this quantity is quenched, in agreement with recent experimental data.     

Pion and K meson production in the multiperipheral model

A simple multiperipheral model, that utilizes only three parameters, two coupling constants and exponential damping for each momentum transfer is developed and applied to the calculation of inclusive distributions. The pion rapidity and p_⊥² distributions are successfully predicted; as are the energy dependences of strange particle production cross sections. The development of inclusive distributions with increasing energy and possible improvements to the model are discussed.     

Study of the Binding Energy of Relativistic Nuclear Matter in the Relativistic σ-ω-π Model

A relativistic σ-ω-π model is proposed to calculate the binding energy of relativistic nuclear matter. We put emphasis on the relativistic particle-hole, delta-hole excitation of pion propagator in nuclear matter. The renormalization of the nucleon self-energy in nuclear matter is made for the pseudo-vector πNN and πNΔ couplings by introducing corresponding form factor and by dispersion relation. We find that the density dependence correction to meson-NN coupling constants is very important to saturate the binding energy of nuclear matter. The density dependence correction to πNN and πNΔ coupling constants has the effect of softening the EOS of nuclear matter.     

The ϱNN vertex in vector-dominance models

A new πN amplitude analysis and experimental data for the pion form factor have been used in order to determine the $\text{I = J = 1 ππ}\text{N}\text{N}$ partial waves and properties of the ?NN vertices. The results are compared with earlier determinations of ?NN coupling constants from πN and NN scattering and from nucleon for, factor data.