Relativistic chiral representation of the π N scattering amplitude I: The Goldberger-Treiman relation

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 $\sqrt{s}$.