H.R. Petry

Relativistic quark models of baryons with instantaneous forces

Abstract:This is the first of a series of three papers treating light baryon resonances (up to 3 GeV) within a relativistically covariant quark model based on the three-fermion Bethe-Salpeter equation with instantaneous two- and three-body forces. In this paper we give a unified description of the theoretical background and demonstrate how to solve the Bethe-Salpeter equation by a reduction to the Salpeter equation. The specific new features of our covariant Salpeter model with respect to the usual nonrelativistic quark model are discussed in detail. The purely theoretical results obtained in this paper will be applied numerically to explicit quark models for light baryons in two subsequent papers.

Scalar Mesons in a Relativistic Quark Model with Instanton-Induced Forces

Abstract In a relativistic quark model with linear confinement and an instanton-induced interaction which solves the η-η′ puzzle, scalar mesons are found as almost pure SU(3) flavor states. This suggests a new interpretation of the scalar nonet: We propose that the recently discovered ƒ 0 (1500) is not a glueball but the scalar (mainly) -octet meson for which the K K decay mode is suppressed. The mainly-singlet state is tentatively identified with the ƒ 0 (980) . The isovector and isodoublet states correspond to the a0(1450) and K 0 ∗ (1430) , respectively.

Charmed baryons in a relativistic quark model

Abstract.We calculate mass spectra of charmed baryons within a relativistically covariant quark model based on the Bethe-Salpeter equation in instantaneous approximation. Interactions are given by a linearly rising three-body confinement potential and a flavor-dependent two-body force derived from QCD instanton effects. This model has already been successfully applied to the calculation of light flavor baryon spectra and is now extended to heavy baryons. Within the same framework we compare the results to those obtained with the more conventional one-gluon exchange potential.

A Bethe-Salpeter model for light mesons: spectra and decays

Abstract The spectra and electroweak decay properties of light mesons are analyzed within the framework of the instantaneous Bethe-Salpeter equation. The interaction kernel comprises alternative spin-structures for a parameterization of confinement and a residual quark-anti-quark interaction based on instanton effects. It is shown that only with a vector confinement the parameters can be chosen such as to yield an excellent description of the light pseudoscalar and vector mesons including weak and two photon decays. However it is found that it is not possible to reconcile this with the Regge behavior of higher lying meson states with the same parameter set.The spectra and electroweak decay properties of light mesons are analyzed within the framework of the instantaneous Bethe-Salpeter equation. The interaction kernel comprises alternative spin-structures for a parameterization of confinement and a residual quark-antiquark interaction based on instanton effects. It is shown that only with a vector confinement the parameters can be chosen such as to yield an excellent description of the light pseudoscalar and vector mesons including weak and two photon decays. However it is found that it is not possible to reconcile this with the Regge behavior of higher lying meson states with the same parameter set.

Analysis of the instantaneous Bethe-Salpeter equation for qq bound states

Abstract We investigate the structure of the instantaneous Bethe-Salpeter equation for q q bound states in the general case of unequal quark masses and develop a numerical scheme for the calculation of mass spectra and Bethe-Salpeter amplitudes. In order to appreciate the merits of the various competing models beyond the reproduction of the mass spectra we present explicit formulas to calculate electroweak decays. The results for an explicit quark model will be compared to experimental data in the following paper.We investigate the structure of the instantaneous Bethe-Salpeter equation for \(q\bar{q}\)-bound states in the general case of unequal quark masses and develop a numerical scheme for the calculation of mass spectra and Bethe-Salpeter amplitudes. In order to appreciate the merits of the various competing models beyond the reproduction of the mass spectra we present explicit formulas to calculate electroweak decays. The results for an explicit quark model will be compared to experimental data in a subsequent paper

Instanton effects in the decay of scalar mesons

Abstract We show that instanton effects may play an important role in the decay of scalar mesons into two pseudoscalars. Particularly the branching ratios of two meson decays of the f0(1500), which is considered as a glue-ball candidate, are compatible with an ordinary q q -structure of this resonance and a small positive SU(3) mixing angle, in agreement with a result from a recent calculation of the spectrum with the same instanton-induced force. Predictions for the a0(1450)-branching ratios are made.

The Bethe-Salpeter equation and the dispersion relation technique

Abstract We compare results for two-particle scattering amplitudes and for composite particle wave functions and form factors obtained in the framework of a dispersion relation approach with the corresponding solutions of the BS equation.

Electromagnetic meson form factors in a covariant Salpeter model

We present a covariant formulation of the Salpeter equation for {ital q{bar q}} states in order to calculate bound-state transitions between mesons. The corresponding Bethe-Salpeter amplitudes are reconstructed from equal-time amplitudes which were obtained in a previous paper by solving the Salpeter equation for a confining plus an instanton-induced interaction. This method is applied to calculate electromagnetic form factors and decay widths of low-lying pseudoscalar and vector mesons, including predictions for CEBAF experiments. We also describe the momentum transfer dependence for the processes {pi}{sup 0},{eta},{eta}{sup {prime}}{r_arrow}{gamma}{gamma}{sup *}.

Static observables of relativistic three-fermion systems with instantaneous interactions

Abstract.We show that static properties like the charge radius and the magnetic moment of relativistic three-fermion bound states with instantaneous interactions can be formulated as expectation values with respect to intrinsically defined wave functions. The resulting operators can be given a natural physical interpretation in accordance with relativistic covariance. We also indicate how the formalism may be generalized to arbitrary moments. The method is applied to the computation of static baryon properties with numerical results for the nucleon charge radii and the baryon octet magnetic moments. In addition, we make predictions for the magnetic moments of some selected nucleon resonances and discuss the decomposition of the nucleon magnetic moments in contributions of spin and angular momentum, as well as the evolution of these contributions with decreasing quark mass.

Semileptonic decays of baryons in a relativistic quark model

Abstract.We calculate semileptonic decays of light and heavy baryons in a relativistically covariant constituent quark model. The model is based on the Bethe-Salpeter equation in instantaneous approximation. It generates satisfactory mass spectra for mesons and baryons up to the highest observable energies. Without introducing additional free parameters we compute on this basis helicity amplitudes of electronic and muonic semileptonic decays of baryons. We thus obtain form factor ratios and decay rates in good agreement with experiment.