Mass and width of the $\Delta(1232)$ resonance using complex-mass renormalization

TL;DR

This paper uses complex-mass renormalization within chiral effective field theory to analyze the pole mass and width of the $
2322$ resonance, demonstrating a consistent power-counting scheme and comparing convergence with the small-scale expansion.

Contribution

It introduces the complex-mass renormalization scheme for calculating resonance properties, showing its consistency and comparing it to existing methods.

Findings

CMS provides a consistent power-counting scheme.

Comparison shows different convergence behaviors between CMS and SSE.

Results improve understanding of $
2322$ resonance properties.

Abstract

We discuss the pole mass and the width of the $\Delta(1232)$ resonance to third order in chiral effective field theory. In our calculation we choose the complex-mass renormalization scheme (CMS) and show that the CMS provides a consistent power-counting scheme. In terms of the pion-mass dependence, we compare the convergence behavior of the CMS with the small-scale expansion (SSE).