Light baryon masses in different large-$N_c$ limits

TL;DR

This paper analyzes how light baryon masses scale in different large-$N_c$ limits using a relativistic constituent quark model, confirming previous results with a new analytical approach applicable to massless quarks.

Contribution

It provides an analytical proof of baryon mass scaling in three large-$N_c$ limits within a relativistic constituent quark framework, extending previous heavy-quark results.

Findings

Baryon masses scale as $N_c$ in 't Hooft limit.

Baryon masses scale as $N_c^2$ in QCD$_{{ m AS}}$ limit.

Baryon masses are independent of $N_c$ in Corrigan-Ramond limit.

Abstract

We investigate the behavior of light baryon masses in three inequivalent large-$N_c$ limits: 't~Hooft, QCD$_{{\rm AS}}$ and Corrigan-Ramond. Our framework is a constituent quark model with relativistic-type kinetic energy, stringlike confinement and one-gluon-exchange term, thus leading to well-defined results even for massless quarks. We analytically prove that the light baryon masses scale as $N_c$, $N_c^2$ and $1$ in the 't~Hooft, QCD$_{{\rm AS}}$ and Corrigan-Ramond limits respectively. Those results confirm previous ones obtained by using either diagrammatic methods or constituent approaches, mostly valid for heavy quarks.