Renormalization approach to constituent quark models of Quarkonium

TL;DR

This paper applies renormalization techniques to constituent quark models of Quarkonium, reducing short-distance sensitivity and clarifying the roles of string tension and gluon exchange in binding and decays.

Contribution

It introduces a renormalization approach to constituent quark models, linking binding physics to string tension and decay processes to gluon exchange, improving model robustness.

Findings

Binding physics is linked to string tension.

Leptonic decays depend on gluon exchange potential.

Spectrum of S- and D- states is interconnected via tensor interaction.

Abstract

Constituent quark models, while successful, require a great deal of fine tuning of the short distance interactions by introducing phenomenological gluonic form factors which are ultimately designed to accurately reproduce the spectrum. We apply and develop renormalization ideas to reduce the short distance sensitivity and show that, as naively expected, but not explicitly implemented in the models, the physics of binding is entirely linked to the string tension whereas leptonic decays depend more on the gluon exchange potential. We also show how the spectrum of S- and D- $1^{--}$ states is successfully intertwined through the singular tensor interaction.