Analyses of pion-nucleon elastic scattering amplitudes up to $O(p^4)$ in extended-on-mass-shell subtraction scheme

Abstract

We extend the analysis of elastic pion-nucleon scattering up to $O(p^4)$ 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 $\sqrt{s}=1.13$ 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 $O(p^4)$, considerably improved with respect to the $O(p^3)$-level analyses found in previous literature. Also, the leading order contribution from explicit $\Delta (1232)$ resonance and partially-included $\Delta (1232)$ loop contribution are included to describe phase shift data up to $\sqrt{s}=1.20$ GeV. As phenomenological applications, we investigate chiral correction to the Goldberger-Treiman relation %${\Delta }_{GT}$ and find that it converges rapidly, and the $O(p^3)$ correction is found to be very small: $\simeq 0.2$. We also get a reasonable prediction of pion-nucleon sigma term ${\sigma }_{\pi N}$ up to $O(p^4)$ by performing fits including both the pion-nucleon partial wave phase shift data and the lattice QCD data. We report that ${\sigma }_{\pi N}=52\pm 7$ MeV from the fit without $\Delta (1232)$, and ${\sigma }_{\pi N}=45\pm 6$ MeV from the fit with explicit $\Delta (1232)$.

The final version published in Phys.Rev. D 87, 054019 (2013)

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