Large N_c Expansion in Chiral Quark Model of Mesons

TL;DR

This paper develops a systematic approach to the chiral quark model of mesons using a large N_c expansion, deriving effective Lagrangians and low energy constants that align with chiral perturbation theory.

Contribution

It introduces a next-to-leading order analysis of the SU(3) chiral quark model incorporating vector and axial-vector resonances, and connects the model with QCD sum rules and chiral perturbation theory.

Findings

Derived chiral effective Lagrangian up to next-to-leading order in 1/N_c.

Obtained low energy constants L_i consistent with ChPT.

Analyzed the effects of one-loop graphs of mesons systematically.

Abstract

We study SU(3)$_L\timesSU(3)_R$ chiral quark model of mesons up to the next to leading order of $1/N_c$ expansion. Composite vector and axial-vector mesons resonances are introduced via non-linear realization of chiral SU(3) and vector meson dominant. Effects of one-loop graphs of pseudoscalar, vector and axial-vector mesons is calculated systematically and the significant results are obtained. We also investigate correction of quark-gluon coupling and relationship between chiral quark model and QCD sum rules. Up to powers four of derivatives, chiral effective lagrangian of mesons is derived and evaluated to the next to leading order of $1/N_c$. Low energy limit of the model is examined. Ten low energy coupling constants $L_i(i=1,2,...,10)$ in ChPT are obtained and agree with ChPT well.