Relations for low-energy coupling constants in baryon chiral perturbation theory derived from the chiral quark model

TL;DR

This paper derives relations between low-energy constants in baryon chiral perturbation theory using the quark model symmetry, providing a way to connect $SU(2)$ and $SU(3)$ descriptions and reduce free parameters.

Contribution

It introduces a method to relate LECs in $SU(2)$ and $SU(3)$ baryon chiral perturbation theories based on quark model symmetry assumptions.

Findings

Derived relations between $SU(2)$ and $SU(3)$ LECs up to third order.

Numerical analysis supports the validity of these relations.

Constraints can reduce the number of free LECs when experimental data are limited.

Abstract

The quark model symmetry can be adopted to establish relations between the low-energy constants (LECs) in the baryon chiral perturbation theory ($\chi PT$) if one assumes that a baryon-baryon-meson coupling is described equivalently by a quark-quark-meson coupling at the quark level. Through the correspondence between the $SU(2)$ description and the $SU(3)$ description for the same coupling vertex at the quark level, we find some relations between the LECs in $SU(2)_{\chi PT}$ and $SU(3)_{\chi PT}$ up to the third chiral order. The $SU(3)_{\chi PT}$ LEC relations at the same order are also obtained. The numerical analysis roughly supports these relations. In the situation that the available experimental data are not enough, one may employ such constraints to reduce the number of LECs.