Relations for low-energy constants in baryon chiral perturbation theory with explicit $\Delta(1232)$ derived from the chiral quark model

TL;DR

This paper derives relations between low-energy constants in baryon chiral perturbation theory with explicit $(1232)$ and quark models, aiding future studies involving these baryons.

Contribution

It establishes the first detailed relations between LECs in chiral Lagrangians with $(1232)$ and quark-level models up to third order.

Findings

Derived ten structure correspondences between LECs and quark model parameters.

Revealed the increased complexity compared to spin-1/2 baryon cases.

Provided a framework for future $(1232)$ baryon investigations.

Abstract

We study the relations between low-energy constants (LECs) in the chiral Lagrangians with $\Delta(1232)$ and those in the quark-level description model up to the third chiral order. Ten structure correspondences are involved in getting the relations. This situation is more complicated than the spin-1/2 baryon case. The obtained results may help to further investigations involving the $\Delta(1232)$ baryons.