The Constituent Chiral Quark Model Revisited

TL;DR

This paper revisits the Constituent Chiral Quark Model, analyzing its renormalizability, counterterm dependence on g_A, and its ability to reproduce low-energy constants with a phenomenologically fixed quark mass.

Contribution

It provides a detailed analysis of the model's renormalization properties and demonstrates its effectiveness in matching low-energy constants with a specific quark mass value.

Findings

Model reproduces low-energy constants well with M_Q = 190±40 MeV

Renormalizability depends on g_A, minimized at g_A=1

Model has limitations for complex low-energy observables

Abstract

We reconsider the Constituent Chiral Quark Model of Manohar and Georgi in the presence of $SU(3)_{L}\times SU(3)_{R}$ external sources. As recently emphasized by Weinberg, the corresponding effective Lagrangian is renormalizable in the Large--${\rm N_c}$ limit. We show, however, that the number of the required counterterms depends crucially on the value of $g_A$ and it is minimized for $g_A =1$. We then find that with a rather small value for the constituent quark mass, which we fix phenomenologically to $M_Q =(190\pm 40)\MeV$, the model reproduces rather well the values of several well known low energy constants. We also comment on the limitations of the model as well as on a few {\it exceptional} applications, to more complicated low--energy observables, where one can expect the model to make reasonably good predictions.