Pion photoproduction in chiral perturbation theory with explicit treatment of the $\Delta(1232)$ resonance

TL;DR

This paper investigates pion photoproduction on nucleons using chiral perturbation theory with explicit $4$Delta(1232)$4$ resonance inclusion, improving reaction description and fitting experimental data.

Contribution

It introduces a covariant chiral perturbation theory approach with explicit $4$Delta(1232)$4$ degrees of freedom and compares it to $4$Delta$-less$ methods, enhancing reaction modeling.

Findings

Explicit $4$Delta(1232)$4$ treatment improves data description.

Bayesian approach estimates theoretical truncation errors.

Results show better fit to pion photoproduction data.

Abstract

We study the reaction of pion photoproduction on the nucleon in the framework of chiral perturbation theory with explicit $\Delta(1232)$ degrees of freedom. In the covariant approach, we give results up to order $\epsilon^3$ in the small scale expansion scheme. Furthermore, we provide $\Delta$-less and $\Delta$-full results obtained in the heavy-baryon scheme to analyze the differences to the covariant approach. Low energy constants are fitted to multipole amplitudes using theoretical truncation errors estimated by a Bayesian approach. We also compare our findings to data of neutral pion production cross sections and polarization asymmetries. The description of the reaction is clearly improved by the explicit treatment of the $\Delta(1232)$ resonance.