Meson mass splittings in unquenched quark models (EEF70)

TL;DR

This paper develops general theorems for meson mass splittings in unquenched quark models, providing new formulas and predictions that account for coupled-channel effects and confirming some quenched model results.

Contribution

It generalizes perturbation theory theorems to full coupled-channel systems and introduces a new formula for physical state mass splittings in unquenched quark models.

Findings

Unquenching decreases S-wave hyperfine splitting but preserves its relation to $e^+e^-$ width.

The P-wave hyperfine splitting remains zero after unquenching.

Mass splitting ratios used to discriminate models are largely unaffected by unquenching.

Abstract

General results are obtained for meson mass splittings and mixings in unquenched (coupled-channel) quark models. Theorems derived previously in perturbation theory are generalised to the full coupled-channel system. A new formula is obtained for the mass splittings of physical states in terms of the splittings of the valence states. The S-wave hyperfine splitting decreases due to unquenching, but its relation to the vector $e^+e^-$ width is unchanged; this yields a prediction for the missing $\eta_b(3S)$. The ordinary (quenched) quark model result that the P-wave hyperfine splitting vanishes also survives unquenching. A ratio of mass splittings used to discriminate quarkonium potential models is scarcely affected by unquenching.