Pion-nucleon scattering to order $p^4$ in SU(3) heavy baryon chiral perturbation theory

TL;DR

This paper computes pion-nucleon scattering amplitudes up to fourth order in SU(3) heavy baryon chiral perturbation theory, fitting low-energy constants to experimental phase shifts and analyzing the convergence of the chiral expansion.

Contribution

It provides a detailed calculation of $ ext{T}$-matrices for $ ext{πN}$ scattering to order $p^4$, including fitting to data and analyzing convergence, extending chiral perturbation theory applications.

Findings

Scattering lengths and volumes agree with experimental data.

Chiral expansion shows good convergence below 200 MeV.

Method enables study of processes involving strangeness.

Abstract

We calculate the $T$-matrices of elastic pion-nucleon ($\pi N$) scattering up to fourth order in SU(3) heavy baryon chiral perturbation theory. The pertinent low-energy constants are determined by fitting to $\pi N$ phase shifts below 200 MeV pion laboratory momentum in the physical region. The scattering lengths and scattering volumes are extracted from the chiral amplitudes, and turn out to be in good agreement with those of other approaches and the available experimental values. We also discuss the subthreshold parameters and the related issues. On the basis of the various phase shifts, the threshold parameters and the subthreshold parameters, the convergence of the chiral expansion is analyzed in detail. The calculation provides the possibility to consider explicitly more complex processes involving strangeness.