Coupling Constants Of Mesons Research Articles

Hadron production in non-linear relativistic mean field models

By using a parametrization of the non-linear Walecka model which takes into account the binding energy of different hyperons, we present a study of particle production yields measured in central Au–Au collision at RHIC. Two sets of different hyperon–meson coupling constants are employed in obtaining the hadron production and chemical freeze-out parameters. These quantities show a weak dependence on the used hyperon–meson couplings. Results are in good overall accordance with experimental data. We have found that the repulsion among the baryons is quite small and, through a preliminary analysis of the effective mesonic masses, we suggest a way to improve the fittings.

A practical guide to unravel time-like transition form factors

A method to determine masses, widths and coupling constants of vector mesons, like $ \phi$ (1020) , $ \omega$ (782) and $ \rho^{0}_{}$ (770) recurrences is defined. Starting from data on decay rates and cross-sections for the processes: $ \phi$ → M I $ \gamma$ , $ \phi$ → M I e + e - and e + e - → M I $ \phi$ , where MI is a pseudoscalar or scalar meson with isospin I = 0, 1 , the time-like transition form factors, which describe the vertex $ \phi$ $ \gamma$ M I , are parameterized using a vector-meson-propagators description in the low-energy region ( < 3-4 GeV), the quark-counting rule prescription for the high-energy behavior, and the analyticity imposed by means of the dispersion relations.

Faddeev calculation of the pentaquarkΘ+in the Nambu–Jona-Lasinio model-based diquark picture

A Bethe-Salpeter-Faddeev (BSF) calculation is performed for the pentaquark $$\Theta^+$$ in the diquark picture of Jaffe and Wilczek in which $$\Theta^+$$ is a diquark-diquark-$${\bar s}$$ three-body system. Nambu-Jona-Lasinio (NJL) model is used to calculate the lowest order diagrams in the two-body scatterings of $${\bar s}D$$ and $D D$. With the use of coupling constants determined from the meson sector, we find that $${\bar s}D$$ interaction is attractive in s-wave while $DD$ interaction is repulsive in p-wave. With only the lowest three-body channel considered, we do not find a bound $$ \frac 12^+$$ pentaquark state. Instead, a bound pentaquark $$\Theta^+$$ with $$ \frac 12^-$$ is obtained with a unphysically strong vector mesonic coupling constants.

CONSTRAINTS ON THE HYPERON-SIGMA MESON COUPLING BY GW OBSERVATIONS

The next generation of gravitational wave observatories are promissing candidates to make the first detections. Once the detection occurs the GW characteristics permit to extract some information about the gravitational wave source. In the present work we focus on waves produced by neutron stars which can give stringent constraints on the nuclear matter equation of state. The microscopic description is based on a nonlinear field-theoretical model in order to construct such an equation of state. The model has free parameters, which from actual knowledge may not be pinned down by direct nuclear matter experiments. An important example is the hyperon-sigma meson coupling constant, currently determined by the spin-isospin SU(6) scheme. The coupling constant is of significant relevance for the structure of the equation of state, controlling its rigidity and, consequently, the properties of neutron stars and gravitational wave signals. We show, in this work, how one can constrain the hyperon-sigma meson coupling constant assuming the detection of a gravitational wave.

Meson coupling constants at high mass and large [formula omitted

Quark–hadron duality implies that a process described in terms of quark loops should be the hadronic amplitude when averaged over a sufficient number of states. Ambiguities associated with the notion of quark–hadron duality can be made arbitrarily small for highly excited mesons at large N c . QCD is expected to form a string like description at large N c yielding an exponentially increasing Hagedorn spectrum for high mass. It is shown that in order to reconcile quantum–hadron duality with a Hagedorn spectrum, the magnitude of individual coupling constants between high-lying mesons in a typical decay process must be characteristically larger than the average of the coupling constants to mesons with nearby masses. The ratio of the square of the average coupling to the average of the coupling squared (where the average is over mesons with nearby masses) drops exponentially with the mass of the meson. Scenarios are discussed by which such a high precision cancellation can occur.

Meson mixing in pion superfluid

We investigate meson mixing and meson coupling constants in pion superfluid in the framework of two flavor NJL model at finite isospin density. The mixing strength develops fast with increasing isospin chemical potential, and the coupling constants in normal phase and in the pion superfluid phase behave very differently.

Nucleon Meson Form Factors and Coupling Constants

The nucleon-nucleon (NN) interaction has been an object of active study for over fifty years. In the past decade high precision potentials based on one boson exchange (OBE) were developed: Argonne 18, Nijmegen '93, CD Bonn, etc. Unfortunately they are highly parametrized (≈ 40 parameters) and less theoretically sound than their predecessors: Bonn B, Nijmegen '78, Paris, etc. Historically OBE potentials parametrize the coupling constants/form factors of an effective Lagrangian. We have calculated these form factors using quark model simple harmonic oscillator wave functions and the 3P0 model of hadronic decays. We present preliminary results for phase shifts of a toy nuclear interaction model, pion (π) and scalar/iso- scalar (σ) exchange. Prospects for future work, including self-consistently extending this work to non-zero strangeness hadrons, are discussed.

Scalar form factor of the nucleon and nucleon-scalar meson coupling constant in QCD

Scalar form factor of the nucleon is calculated in the framework of light-cone QCD sum rules, using the most general form of the baryon current. Using the result on scalar form factor of the nucleon, the nucleon-scalar $\ensuremath{\sigma}$ and ${a}_{0}$ meson coupling constants are estimated. Our results on these couplings are in good agreement with the prediction of the external-field QCD sum rules method.

A Faddeev Calculation for Pentaquark Θ+in Diquark Picture with Nambu-Jona-Lasinio Type Interaction

A Bethe-Salpeter-Faddeev (BSF) calculation is performed for the pentaquark Θ+ in the diquark picture of Jaffe and Wilczek in which Θ+ is a diquark-diquark-\bars three-body system. Nambu-Jona-Lasinio (NJL) model is used to calculate the lowest order diagrams in the two-body scatterings of \barsD and DD. With the use of coupling constants determined from the meson sector, we find that \barsD interaction is attractive while DD interaction is repulsive. However, we cannot find a bound ½+ pentaquark state. Instead, a bound pentaquark Θ+ in ½- channel is obtained with unphysically strong vector mesonic coupling constants.

Nucleon–meson coupling constants and form factors in the quark model

Abstract We demonstrate the calculation of the coupling constants and form factors required by effective hadron Lagrangians using the quark model. These relations follow from equating expressions for strong transition amplitudes in the two approaches. As examples we derive the NNm nucleon–meson coupling constants and form factors for m = π , η , η ′ , σ , a 0 , ω and ρ, using harmonic oscillator quark model meson and baryon wavefunctions and the 3P0 decay model; these results are relevant to quark-based descriptions of the NN force. This technique should be useful in the application of effective Lagrangians to processes in which the lack of data precludes the direct determination of coupling constants and form factors from experiment.

Charge and parity projected relativistic mean field model with pion for finite nuclei

We construct a new relativistic mean field model by explicitly introducing a \ensuremath{\pi}-meson mean field with charge number and parity projection. We call this model the charge and parity projected relativistic mean field (CPPRMF) model. We take the chiral \ensuremath{\sigma} model Lagrangian for the construction of finite nuclei. We apply this framework first for the $^{4}\mathrm{He}$ nucleus as a pilot case and study the role of the \ensuremath{\pi}-meson field on the structure of nuclei. We demonstrate that it is essential to solve the mean field equation with the variation introduced after the projection in order to take the pionic correlations into account explicitly. We study the ground-state properties of $^{4}\mathrm{He}$ by varying several parameters, such as the \ensuremath{\sigma}-meson mass and the \ensuremath{\omega}-meson coupling constant. We are able to construct a good ground state for $^{4}\mathrm{He}$. A depression appears in the central region of the density distribution, and the second maximum and the position of the dip in the form factor of $^{4}\mathrm{He}$ are naturally obtained in the CPPRMF model.

Propagators of light scalar mesons

For the first time, as far as we know, in field theory are found explicit forms of propagators satisfying the K\"allen-Lehmann representation. To be exact, it is shown that scalar meson propagators, taking into account a virtual intermediate state contribution to the resonance self-energy, satisfy the K\"allen-Lehmann representation in the wide domain of coupling constants of the light scalar mesons with the two-particle states. It is proposed to use these propagators in routine fitting data about light scalar mesons to reveal physics underlying the light scalar mesons.

Chemical equilibration in relativistic heavy ion collisions

In the hadronic sector of relativistic heavy ion physics, the ρ ⇆ 2 π reaction is the strongest one, strong enough to equilibrate the ρ with the pions throughout the region from chemical freezeout to thermal freezeout when free-particle interactions (with no medium-dependent effects) are employed. Above the chiral restoration temperature, only ρ's and π's are present, in that the chirally restored A 1 is equivalent to the ρ and the mesons have an SU(4) symmetry, with no dependence on isospin and negligible dependence on spin. In the same sense the σ and π are “equivalent” scalars. Thus the chirally restored ρ ⇆ 2 π exhaust the interspecies transitions. We evaluate this reaction at T c and find it to be much larger than below T c , certainly strong enough to equilibrate the chirally restored mesons just above T c . When emitted just below T c the mesons remain in the T c + ε freezeout distribution, at least in the chiral limit because of the Harada–Yamawaki “vector manifestation” that requires that mesonic coupling constants go to zero (in the chiral limit) as T goes to T c from below. Our estimates in the chiral limit give deviations in some particle ratios from the standard scenario (of equilibrium in the hadronic sector just below T c ) of about double those indicated experimentally. This may be due to the neglect of explicit chiral symmetry breaking in our estimates. We also show that the instanton molecules present above T c are the giant multipole vibrations found by Asakawa, Hatsuda and Nakahara and of Wetzorke et al. in lattice gauge calculations. Thus, the matter formed by RHIC can equivalently be called: chirally restored mesons, instanton molecules, or giant collective vibrations. It is a strongly interacting liquid.

Parity non-conservation in proton-proton elastic scattering

The parity-non-conserving longitudinal asymmetry in proton-proton (p p) elastic scattering is calculated in the lab energy range 0-350 MeV using contemporary, realistic strong-interaction potentials combined with a weak-interaction potential comprised of $\rho$ - and $\omega$ -meson exchanges as exemplified by the DDH model. Values for the $\rho$ - and $\omega$ -meson coupling constants, $h^{pp}_\rho$ and $h^{pp}_\omega$ , are determined from comparison with the measured asymmetries at 13.6 MeV, 45 MeV, and 221 MeV.

Combined effect of coherentZexchange and the hyperfine interaction in the atomic parity-nonconserving interaction

The nuclear spin-dependent parity nonconserving (PNC) interaction arising from a combination of the hyperfine interaction and the coherent, spin-independent, PNC interaction from Z exchange is evaluated using many-body perturbation theory. For the 6s-7s transition in 133Cs, we obtain a result that is about 40% smaller than that found previously by Bouchiat and Piketty [Phys. Lett. B 269, 195 (1991)]. Applying this result to 133Cs, leads to an increase in the experimental value of nuclear anapole moment and exacerbates differences between constraints on PNC meson coupling constants obtained from the Cs anapole moment and those obtained from other nuclear parity violating experiments. Nuclear spin-dependent PNC dipole matrix elements, including contributions from the combined weak-hyperfine interaction, are also given for the 7s-8s transition in 211Fr and for transitions between ground-state hyperfine levels in K, Rb, Cs, Ba+, Au, Tl, Fr, and Ra+.

The F/D ratio and Messon-Baryon couplings from QCD sum rules

Coupling constants of the pseudoscalar mesons to the octet baryons are computed in the QCD sum rule approach. The πNN, ηNN, πξξ, ηξξ, πΣΣ, ηΣΣ as well as πΓΣ coulings are studied. Determining the pertinent. Diract structure in the correlation function, we analyze the couplings in the SU(3) limit. We find the F/D ratio to be ∼0.6 − 0.8 that is consistent with the SU(6) value. We also estimate the SU(3) breaking effect using a projected correlation function method.

NN interaction derived from the Nambu–Jona-Lasinio model

The nucleon–nucleon potential is calculated within the Nambu–Jona-Lasinio (NJL) model. The effect of the quark–meson coupling constant, g, on the energy per baryon in quark matter, medium quark mass, medium pion and sigma meson masses and finally on the nucleon–nucleon potential is investigated. It is found that the potential obtained is attractive and the attraction raises with increasing coupling constant g, due to the increases in the scalar interaction. The medium and long range parts of the potential are well reproduced with g=4.6, where a better agreement with the phenomenological Paris potential is obtained. When the short range part is added to the NJL potential, through the one gluon exchange potential, the potential obtained exhibits all the qualitative features of the distance-dependence of the nucleon–nucleon interaction viz., a repulsive soft core followed by an attractive part at the right positions.

Pseudovector vs pseudoscalar coupling in one-boson exchangeNNpotentials

We examine the effects of pseudoscalar and pseudovector coupling of the pi and eta mesons in one-boson exchange models of the NN interaction using two approaches: time-ordered perturbation theory unitarized with the relativistic Lippmann-Schwinger equation, and a reduced Bethe-Salpeter equation approach using the Thompson equation. Contact terms in the one-boson exchange amplitudes in time-ordered perturbation theory lead naturally to the introduction of s-channel nucleonic cutoffs for the interaction, which strongly suppresses the far off-shell behavior of the amplitudes in both approaches. Differences between the resulting NN predictions of the various models are found to be small, and particularly so when coupling constants of the other mesons are readjusted within reasonable limits.

Heavy-light chiral quark model

We present a new chiral quark model for mesons involving a heavy and a light (anti-) quark. The model relates various combinations of a quark - meson coupling constant and loop integrals to physical quantities. Then, some quantities may be predicted and some used as input. The extension from other similar models is that the present model includes the lowest order gluon condensate of the order (300 MeV)^4 determined by the mass splitting of the 0^- and the 1^- heavy meson states. Within the model, we find a reasonable description of parameters such as the decay constants f_B and f_D, the Isgur-Wise function and the axial vector coupling g_A in chiral perturbation theory for light and heavy mesons.

Electromagnetic Transition Form Factors and Dilepton Decay Rates of Nucleon Resonances

Relativistic, kinematically complete phenomenological expressions for the dilepton decay rates of nucleon resonances with arbitrary spin and parity are derived in terms of the magnetic, electric, and Coulomb transition form factors. The dilepton decay rates of the nucleon resonances with masses below 2 GeV are estimated using the extended vector meson dominance (VMD) model for the transition form factors. The model provides a unified description of the photo- and electroproduction data, γ(γ*)N→N*, the vector meson decays, N*→Nϕ(ω), and the dilepton decays, N*→Nℓ+ℓ−. The constraints on the transition form factors from the quark counting rules are taken into account. The parameters of the model are fixed by fitting the available photo- and electroproduction data and using results of the multichannel partial-wave analysis of the π N scattering. Where experimental data are not available, predictions of the non-relativistic quark models are used as an input. The vector meson coupling constants of the magnetic, electric, and Coulomb types are determined. The dilepton widths and the dilepton spectra from decays of nucleon resonances with masses below 2 GeV are calculated.