The 't Hooft coupling and baryon mass splitting in the large-N chiral model

TL;DR

This paper investigates how the 't Hooft coupling influences baryon mass differences within a large-N chiral quark model, finding a specific coupling value that matches observed baryon masses.

Contribution

It introduces a method to relate the 't Hooft coupling to baryon mass splittings using a large-N chiral model, providing a quantitative estimate of the coupling.

Findings

The 't Hooft coupling that fits baryon mass data is approximately 1.57.

The coupling is small, with $g_{t}^{2}/(4\pi N_{c}) extless extless 1.

The model successfully reproduces hyperfine splittings of octet and decuplet baryons.

Abstract

We study the 't Hooft coupling $g_{t}$ and the mass splitting of the ground-state baryons in a chiral quark model inspired by the large $N_{c}$ QCD. Depending on $g_{t}$ the Hartree wavefunction of light quark in baryons is used to map the mass hyperfine splittings for the octet and decuplet baryons. The 't Hooft coupling $g_{t}$ that reproduces the data of baryon masses is determined to be around $1.57$, which is small in the sense that $g_{t}^{2}/(4\pi N_{c})\ll $$1$.