Consistency between SU(3) and SU(2) chiral perturbation theory for the nucleon mass

TL;DR

This paper investigates the consistency between SU(3) and SU(2) chiral perturbation theories for the nucleon mass by matching effective parameters and analyzing their dependence on the strange quark mass.

Contribution

It provides a detailed matching of nucleon mass parameters between SU(3) and SU(2) chiral theories, supporting the validity of low-energy constants across sectors.

Findings

Effective parameters are consistent between SU(3) and SU(2) theories.

Weak dependence of parameters on strange quark mass near physical value.

Supports previous assumptions about the strange quark mass influence.

Abstract

Treating the strange quark mass as a heavy scale compared to the light quark mass, we perform a matching of the nucleon mass in the SU(3) sector to the two-flavor case in covariant baryon chiral perturbation theory. The validity of the $19$ low-energy constants appearing in the octet baryon masses up to next-to-next-to-next-to-leading order~\cite{Ren:2014vea} is supported by comparing the effective parameters (the combinations of the $19$ couplings) with the corresponding low-energy constants in the SU(2) sector~\cite{Alvarez-Ruso:2013fza}. In addition, it is shown that the dependence of the effective parameters and the pion-nucleon sigma term on the strange quark mass is relatively weak around its physical value, thus providing support to the assumption made in Ref.~\cite{Alvarez-Ruso:2013fza}.