Analyses of pion-nucleon elastic scattering amplitudes up to O(p4) in the extended-on-mass-shell subtraction scheme

We extend the analysis of elastic pion-nucleon scattering up to O(p⁴) level using the extended-on-mass-shell subtraction scheme within the framework of covariant baryon chiral perturbation theory. Numerical fits to partial wave phase shift data up to s=1.13GeV are performed to pin down the free low energy constants. A good description of the existing phase shift data is achieved. We find a good convergence for the chiral series at O(p⁴), considerably improved with respect to the O(p³)-level analyses found in previous literature. Also, the leading order contribution from explicit Δ(1232) resonance and partially-included Δ(1232) loop contribution are included to describe the phase shift data up to s=1.20GeV. As phenomenological applications, we investigate chiral corrections to the Goldberger-Treiman relation and find that it converges rapidly, and the O(p³) correction is found to be very small: ≃0.2%. We also get a reasonable prediction of the pion-nucleon sigma term σ_πN up to O(p⁴) by performing fits including both the pion-nucleon partial wave phase shift data and the lattice QCD data. We report that σ_πN=52±7MeV from the fit without Δ(1232), and σ_πN=45±6MeV from the fit with explicit Δ(1232).