$\pi N$ Scattering in the $\Delta(1232)$ Region in an Effective Field Theory

TL;DR

This paper extends heavy-baryon chiral perturbation theory to effectively describe pion-nucleon scattering across a broad energy range, including the delta resonance region, and compares it with existing models.

Contribution

It introduces a generalized framework for heavy-baryon chiral perturbation theory that covers the entire pion-nucleon scattering spectrum from threshold to the delta peak.

Findings

Accurately describes P-wave phase shifts in the delta region

Provides a unified approach bridging threshold and resonance energies

Shows consistency with existing models in the literature

Abstract

We develop a generalized version of heavy-baryon chiral perturbation theory to describe pion-nucleon scattering in a kinematic domain that extends continuously from threshold to the delta-isobar peak. The $P$-wave phase shifts are used to illustrate this framework. We also compare our approach with those in the literature that concern the delta resonance.