Relativistic chiral representation of the $\pi N$ scattering amplitude I: The Goldberger-Treiman relation

TL;DR

This paper employs covariant Baryon Chiral Perturbation Theory with the EOMS scheme to analyze $ N$ scattering, successfully addressing the Goldberger-Treiman deviation and extending the validity range of the theoretical description.

Contribution

It demonstrates that the EOMS scheme provides superior convergence in covariant ChPT and resolves the longstanding issue of extracting the Goldberger-Treiman deviation.

Findings

EOMS scheme achieves better convergence than Infrared Regularization.

Reliable extraction of Goldberger-Treiman deviation from partial wave analyses.

Unitarization techniques extend the model's validity up to approximately 200 MeV.

Abstract

In this work we study the $\pi N$ scattering process within the Baryon Chiral Perturbation Theory framework in the covariant scheme of Extended-On-Mass-Shell (EOMS). We compare the description obtained in this scheme with the previously obtained using the Infrared Regularization scheme and show that EOMS accomplishes the best convergence, being able to extract from partial wave analyses reliable values of important quantities as the Goldberger-Treiman deviation. In regard to the latter, we solve the long-standing problem concerning to the extraction of the Goldberger-Treiman deviation with covariant ChPT that jeopardized the applicability of ChPT to the $\pi N$ system. We also show the potential of the unitarization techniques applied to the perturbative calculation in the EOMS scheme, that allow us to increase the range of validity of our description up to $\approx 200$ MeV in $\sqrt{s}$.