Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

TL;DR

This paper performs a third-order covariant baryon chiral perturbation theory calculation of pion-nucleon scattering including explicit Delta resonances, fitting phase shifts and predicting threshold parameters and sigma terms.

Contribution

It introduces a comprehensive third-order calculation with explicit Delta resonances in a covariant framework, fitting phase shifts and predicting various scattering and sigma term parameters.

Findings

Achieves satisfactory fit to phase shifts from Roy-Steiner analysis.

Predicts D and F wave phase shifts consistent with GWU analysis.

Calculates octet baryon sigma terms and discusses the pion-nucleon sigma term.

Abstract

We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the $S$- and $P$-partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the $D$ and $F$ waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.