Relativistic chiral representation of the \pi N scattering amplitude

TL;DR

This paper compares relativistic chiral frameworks IR and EOMS for  scattering, finding EOMS provides more accurate low-energy phase shifts and extends better to higher energies, with consistent phenomenological parameters.

Contribution

It introduces a detailed analysis of  scattering using IR and EOMS schemes up to \, providing a comparative assessment of their effectiveness and physical consistency.

Findings

EOMS yields better low-energy phase shift descriptions.

EOMS provides a more realistic Goldberger-Treiman discrepancy.

EOMS extends the valid energy range up to   GeV.

Abstract

We have analyzed pion-nucleon scattering using the manifestly relativistic covariant frameworks of Infrared Regularization (IR) and Extended-On-Mass-Shell (EOMS) up to O(q^3) in the chiral expansion, where q is a generic small momentum. We describe the low-energy phase shifts with a similar quality as previously achieved with Heavy Baryon Chiral Perturbation Theory, being the EOMS description better than the IR one. The Goldberger-Treiman discrepancy is extracted from data of partial wave analyses using both schemes, obtaining an unacceptable large value for the case of IR due to the loop contribution. On the other hand, EOMS gives small values compatible with other phenomenological approaches. Finally, we have unitarized the amplitudes provided by both schemes to extend the range of our description obtaining a good agreement with the data up to energies of \sqrt{s}\approx 1.3 GeV for the EOMS scheme while IR can not go beyond energies of \sqrt{s}\approx 1.25 GeV due to the unphysical cut that this scheme introduces.