Pseudoscalar and vector mesons as q\bar{q} bound states

Two-body bound states such as mesons are described by solutions of the Bethe-Salpeter equation. We discuss recent results for the pseudoscalar and vector meson masses and leptonic decay constants, ranging from pions up to c\bar{c} bound states. Our results are in good agreement with data. Essential in these calculation is a momentum-dependent quark mass function, which evolves from a constituent-quark mass in the infrared region to a current-quark mass in the perturbative region. In addition to the mass spectrum, we review the electromagnetic form factors of the light mesons. Electromagnetic current conservation is manifest and the influence of intermediate vector mesons is incorporated self-consistently. The results for the pion form factor are in excellent agreement with experiment.Comment: 8 pages, 6 .eps figures, contribution to the proceedings of the first meeting of the APS Topical Group on Hadron Physics, Fermilab, Oct. 200

Aspects of the confinement mechanism in Coulomb-gauge QCD

Phenomenological consequences of the infrared singular, instantaneous part of the gluon propagator in Coulomb gauge are investigated. The corresponding quark Dyson-Schwinger equation is solved, neglecting retardation and transverse gluons and regulating the resulting infrared singularities. While the quark propagator vanishes as the infrared regulator goes to zero, the frequency integral over the quark propagator stays finite and well-defined. Solutions of the homogeneous Bethe-Salpeter equation for the pseudoscalar and vector mesons as well as for scalar and axial-vector diquarks are obtained. In the limit of a vanishing infrared regulator the diquark masses diverge, while meson properties and diquark radii remain finite and well-defined. These features are interpreted with respect to the resulting aspects of confinement for colored quark-quark correlations.Comment: 4 pages, 6 figure

Solving the Bethe-Salpeter equation for a pseudoscalar meson in Minkowski space

A new method of solution of the Bethe-Salpeter equation for a pseudoscalar quark-antiquark bound state is proposed. With the help of an integral representation, the results are directly obtained in Minkowski space. Dressing of Green's functions is naturally taken into account, thus providing the possible inclusion of a running coupling constant as well as quark propagators. First numerical results are presented for a simplified ladder approximation

Covariant calculation of mesonic baryon decays

We present covariant predictions for pi and eta decay modes of N and Delta resonances from relativistic constituent-quark models based on one-gluon-exchange and Goldstone-boson-exchange dynamics. The results are calculated within the point-form approach to Poincare-invariant relativistic quantum mechanics applying a spectator-model decay operator. The direct predictions of the constituent-quark models for covariant pi and eta decay widths show a behaviour completely different from previous ones calculated in nonrelativistic or so-called semirelativistic approaches. It is found that the present theoretical results agree with experiment only in a few cases but otherwise always remain smaller than the experimental data (as compiled by the Particle Data Group). Possible reasons for this behaviour are discussed with regard to the quality of both the quark-model wave functions and the mesonic decay operator.Comment: 10 pages, 2 figures, accepted for publication in Phys. Rev.

Schwinger functions and light-quark bound states

We examine the applicability and viability of methods to obtain knowledge about bound-states from information provided solely in Euclidean space. Rudimentary methods can be adequate if one only requires information about the ground and first excited state and assumptions made about analytic properties are valid. However, to obtain information from Schwinger functions about higher mass states, something more sophisticated is necessary. A method based on the correlator matrix can be dependable when operators are carefully tuned and errors are small. This method is nevertheless not competitive when an unambiguous analytic continuation of even a single Schwinger function to complex momenta is available.Comment: 27 pages, 14 figure

Extended Goldstone-Boson-Exchange Constituent Quark Model

We present an extension of the Goldstone-boson-exchange constituent quark model including additional interactions beyond the ones used hitherto. For the hyperfine interaction between the constituent quarks we assume pseudoscalar, vector, and scalar meson exchanges and consider all relevant force components produced by these types of exchanges. The resulting model, which corresponds to a relativistic Poincare-invariant Hamiltonian (or equivalently mass operator), provides a unified framework for a covariant description of all light and strange baryons. The ground states and resonances up to an excitation energy of about 2 GeV are reproduced in fair agreement with phenomenology, with the exception of the first excitations above the Lambda and Xi ground states.Comment: 11 pages, 4 figures, 3 tables; substantial revisions, additional author, bibliography extended and update

Spectator-model operators in point-form relativistic quantum mechanics

We address the construction of transition operators for electromagnetic, weak, and hadronic reactions of relativistic few-quark systems along the spectator model. While the problem is of relevance for all forms of relativistic quantum mechanics, we specifically adhere to the point form, since it preserves the spectator character of the corresponding transition operators in any reference frame. The conditions imposed on the construction of point-form spectator-model operators are discussed and their implications are exemplified for mesonic decays of baryon resonances within a relativistic constituent quark model.Comment: 10 pages, 4 figures, updated version accepted for publication in Europ. Phys. J.

Vector mesons in a relativistic point-form approach

We apply the point form of relativistic quantum mechanics to develop a Poincare invariant coupled-channel formalism for two-particle systems interacting via one-particle exchange. This approach takes the exchange particle explicitly into account and leads to a generalized eigenvalue equation for the Bakamjian-Thomas type mass operator of the system. The coupling of the exchange particle is derived from quantum field theory. As an illustrative example we consider vector mesons within the chiral constituent quark model in which the hyperfine interaction between the confined quark-antiquark pair is generated by Goldstone-boson exchange. We study the effect of retardation in the Goldstone-boson exchange by comparing with the commonly used instantaneous approximation. As a nice physical feature we find that the problem of a too large $\rho$-$\omega$ splitting can nearly be avoided by taking the dynamics of the exchange meson explicitly into account.Comment: 14 pages, 1 figur

Nucleon electromagnetic form factors

Elastic electromagnetic nucleon form factors have long provided vital information about the structure and composition of these most basic elements of nuclear physics. The form factors are a measurable and physical manifestation of the nature of the nucleons' constituents and the dynamics that binds them together. Accurate form factor data obtained in recent years using modern experimental facilities has spurred a significant reevaluation of the nucleon and pictures of its structure; e.g., the role of quark orbital angular momentum, the scale at which perturbative QCD effects should become evident, the strangeness content, and meson-cloud effects. We provide a succinct survey of the experimental studies and theoretical interpretation of nucleon electromagnetic form factors.Comment: Topical review invited by Journal of Physics G: Nuclear and Particle Physics; 34 pages (contents listed on page 34), 11 figure