Improved description of the $\pi N$-scattering phenomenology in covariant baryon chiral perturbation theory

TL;DR

This paper develops a covariant baryon chiral perturbation theory framework up to order p^3, including the Delta resonance, to analyze and describe pi-N scattering phenomenology accurately across a wide energy range.

Contribution

It introduces a systematic, model-independent approach using covariant baryon chiral perturbation theory with explicit Delta inclusion for pi-N scattering analysis.

Findings

Good convergence of the chiral expansion from low energies to above threshold

Phenomenological description consistent with partial wave analyses

Accurate analysis of low-energy theorems and scattering observables

Abstract

We present a novel analysis of the $\pi N$ scattering amplitude in covariant baryon chiral perturbation theory up to ${\cal O}(p^3)$ within the extended-on-mass-shell renormalization scheme and including the $\Delta(1232)$ explicitly in the $\delta$-counting. We take the hadronic phase shifts provided by partial wave analyses as basic experimental information to fix the low-energy constants. Subsequently, we study in detail the various observables and low-energy theorems related to the $\pi N$ scattering amplitude. In particular, we discuss the results and chiral expansion of the phase shifts, the threshold coefficients, the Goldberger-Treiman relation, the pion-nucleon sigma term and the extrapolation onto the subthreshold region. The chiral representation of the amplitude in the theory with the $\Delta$ presents a good convergence from very low energies in the subthreshold region up to energies well above threshold, leading also to a phenomenological description perfectly consistent with the one reported by the respective partial wave analyses and independent determinations. We conclude that a model-independent and systematic framework to analyze $\pi N$-scattering observables using directly experimental data shall be possible in covariant baryon chiral perturbation theory.