[Paper Review] The Multichannel Quark Model

John Weinstein|ArXiv.org|Jun 19, 1996

Quantum Chromodynamics and Particle Interactions2 references3 citations

TL;DR

This paper introduces a non-relativistic multichannel quark model that unifies meson-meson scattering and meson spectroscopy by solving coupled-channel equations incorporating s-channel resonance production and t-channel quark exchange. It demonstrates that wide resonances exhibit energy-dependent masses and widths, and reproduces standard quark model spectroscopy and Breit-Wigner phase shifts in the narrow-width limit, significantly extending the applicability of the naive quark model to strong interaction dynamics.

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.

Motivation & Objective

• To extend the applicability of the naive quark model beyond static spectroscopy to include meson-meson scattering and resonance production.
• To address the limitations of standard quark models in describing wide resonances and inelastic processes.
• To develop a consistent framework that incorporates both s-channel resonances and t-channel quark exchange as the underlying dynamics.
• To reproduce standard quark model results in the narrow-width limit while capturing non-trivial effects in the broad resonance regime.
• To provide a unified description of resonance production and decay that standard eigenvalue equations cannot achieve.

Proposed method

• Formulates a non-relativistic multichannel Schrödinger-type equation with coupled channels representing meson-meson states.
• Incorporates s-channel resonances as intermediate states and t-channel quark exchange as the dominant interaction mechanism.
• Solves the resulting coupled integral equations numerically using techniques tailored for resonant and inelastic scattering.
• Applies the model to simple systems to demonstrate consistency with standard quark model spectroscopy in the narrow-width limit.
• Uses the formalism to compute energy-dependent resonance masses and widths, capturing effects from two-meson coupling.
• Validates the model by recovering Breit-Wigner phase shifts and spectroscopic states under appropriate approximations.

Experimental results

Research questions

• RQ1 How can the naive quark model be extended to describe both meson spectroscopy and meson-meson scattering within a single framework?
• RQ2 What are the effects of two-meson coupling on the masses and widths of resonances in the multichannel quark model?
• RQ3 How does the inclusion of t-channel quark exchange modify the description of resonance production and decay compared to pure s-channel models?
• RQ4 To what extent can the multichannel model reproduce standard quark model spectroscopy and Breit-Wigner phase shifts in the narrow-width limit?
• RQ5 What are the implications of energy-dependent resonance parameters for the interpretation of experimental resonance line-shapes?

Key findings

• The model successfully unifies meson-meson scattering and meson spectroscopy within a single dynamical framework.
• In the limit of narrow resonance widths and no quark exchange, the model reproduces standard quark model spectroscopy and Breit-Wigner phase shifts.
• For wide resonances, the model predicts a lowering of s-channel resonance masses due to coupling to two-meson thresholds.
• The line-shapes of wide resonances are significantly altered compared to the standard Breit-Wigner form.
• The equivalent Breit-Wigner masses and widths exhibit strong energy dependence, reflecting the dynamical coupling to inelastic channels.
• The model captures resonance production and decay processes that cannot be described by standard eigenvalue equations alone.