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

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 e…