# Elastic and inelastic pion-nucleon scattering to fourth order in chiral perturbation theory

## TL;DR

This paper advances the theoretical understanding of pion-nucleon interactions by performing a fourth-order chiral perturbation theory analysis of elastic and inelastic scattering, improving data fits and low-energy constant determinations.

## Contribution

It extends previous work by combining elastic and inelastic scattering analyses at fourth order, incorporating the $ riangle$(1232) resonance, and utilizing Roy-Steiner data for better fit stability.

## Key findings

- Successful combined fit to experimental data in both channels
- Reduced correlations between low-energy constants
- Improved description with $ riangle$(1232) resonance contributions

## Abstract

We extend our previous study of elastic pion-nucleon scattering in the framework of chiral perturbation theory by performing a combined analysis of the reactions $\pi N \to \pi N$ and $\pi N \to \pi \pi N$. The calculation is carried out to fourth order in the chiral expansion using the heavy baryon approach and the covariant formulation supplemented with a modified version of the extended on-mass-shell renormalization scheme. We demonstrate that a combined fit to experimental data in both channels leads to a reduced amount of correlations between the low-energy constants. A satisfactory description of the experimental data in both channels is obtained, which is further improved upon including tree-level contributions of the $\Delta$(1232) resonance. We also explore a possibility of using the empirical information about $\pi N$ subthreshold parameters obtained recently by means of the Roy-Steiner equations to stabilize the fits.