Decaying hadrons within constituent-quark models

TL;DR

This paper develops a relativistically invariant coupled-channel formalism incorporating mesonic degrees of freedom into constituent-quark models, enabling the description of hadron decays and resonance phenomena more realistically.

Contribution

It introduces a novel formalism based on point-form relativistic quantum mechanics that couples quark states with mesons, allowing for decay processes in constituent-quark models.

Findings

Formalism reduces to a hadronic eigenvalue problem with meson loops.

Form factors at meson-hadron vertices incorporate quark substructure.

Approach enables comparison of dressed quark model states with experimental data.

Abstract

Within conventional constituent-quark models hadrons come out as stable bound states of the valence (anti)quarks. Thereby the resonance character of hadronic excitations is completely ignored. A more realistic description of hadron spectra can be achieved by including explicit mesonic degrees of freedom, which couple directly to the constituent quarks. We will present a coupled-channel formalism that describes such hybrid systems in a relativistically invariant way and allows for the decay of excited hadrons. The formalism is based on the point-form of relativistic quantum mechanics. If the confining forces between the (anti)quarks are described by instantaneous interactions it can be formally shown that the mass-eigenvalue problem for a system that consists of dynamical (anti)quarks and mesons reduces to a hadronic eigenvalue problem in which the eigenstates of the pure confinement problem (bare hadrons) are coupled via meson loops. The only point where the quark substructure enters are form factors at the meson-(bare) hadron vertices. The physical picture that emerges resembles the kind of hadronic resonance model that has been developed by Sato and Lee and is now heavily used at the Excited Baryon Analysis Center (EBAC) to fix $N^\ast$ properties. Our approach, however, is in a certain sense inverse to the one of Sato and Lee. Whereas they want to undress physical resonances to end up with bare quantities, we rather want to dress the bound-states resulting from a pure constituent quark model to end up with quantities that can be directly compared with experiment. The way how our approach works will be exemplified by means of a simple quark-antiquark-meson system.