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

الأصل · EN

We extend the analysis of elastic pion-nucleon scattering up to O(p⁴) level using 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=1.13 GeV are performed to pin down the free low energy constants. A good description to 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 phase shift data up to √s=1.20 GeV. As phenomenological applications, we investigate chiral correction to the Goldberger-Treiman relation %ΔGT 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 pion-nucleon sigma term σπₙ 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 σπₙ=52±7 MeV from the fit without Δ(1232), and σπₙ=45±6 MeV from the fit with explicit Δ(1232).