The Multichannel Quark Model

TL;DR

This paper presents a non-relativistic multichannel quark model that unifies meson-meson scattering with meson spectroscopy, extending the naive quark model's applicability and providing a detailed method for solving the complex equations involved.

Contribution

It introduces techniques to solve multichannel quark equations, demonstrating how the model unifies scattering and spectroscopy, and extends the naive quark model to include resonance interactions.

Findings

Reproduces standard quark model spectroscopy in certain limits

Shows resonance masses are lowered by two-meson couplings

Alters line-shapes and energy dependence of wide resonances

Abstract

We discuss the non-relativistic multichannel quark model and describe the techniques developed to solve the resulting equations. We then investigate some simple solutions to demonstrate how the model unifies meson-meson scattering with meson spectroscopy, thereby greatly extending the domain of applicability of the naive quark model. In the limits of narrow resonance widths and no quark exchange, it reproduces the standard quark model spectroscopy and Breit-Wigner phase description. Outside those limits s-channel resonance masses are lowered by their two-meson couplings, the line-shapes of wide resonances are significantly altered, and the equivalent Breit-Wigner masses and widths show an energy dependence. Because meson-meson interactions are due to coherent s-channel resonance production and t-channel quark exchange (though other interactions can readily be added), the multichannel equations model experimental resonance production and decay in a way that the usual eigenvalue equations cannot.