$\Delta(1232)$ Contribution in the $\pi$-photoproduction on Nucleons in Covariant Chiral Perturbation Theory

TL;DR

This paper investigates the role of the $(1232)$ resonance in pion photoproduction on nucleons using covariant chiral perturbation theory up to third order, comparing with experimental data to refine theoretical parameters.

Contribution

It introduces a covariant chiral perturbation theory approach including the $(1232)$ resonance as an explicit degree of freedom for pion photoproduction.

Findings

Model agrees well with experimental data

Constrains low energy constants

Highlights importance of $(1232)$ in pion production

Abstract

We study the effects of the $\Delta$(1232) resonance as an effective degree of freedom for charged and neutral pion photo-production on nucleons. Different observables have been calculated for these processes by using relativistic chiral perturbation theory up to $\mathcal{O}(p^3)$ in the $ \delta$ counting, thus, including pion loops. We compare our model with a large database containing the available experimental data and constrain some unknown low energy constants.