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

TL;DR

This paper advances the analysis of pion-nucleon elastic scattering by extending calculations to order $O(p^4)$ in covariant baryon chiral perturbation theory, achieving improved convergence and accurate phenomenological predictions.

Contribution

It provides a comprehensive $O(p^4)$ analysis of pion-nucleon scattering using extended-on-mass-shell scheme, including $ riangle(1232)$ effects and lattice data for the sigma term.

Findings

Good fit to phase shift data up to 1.13 GeV

Chiral series shows improved convergence at $O(p^4)$

Predicted pion-nucleon sigma term around 45-52 MeV

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 $\sigma_{\pi N}=52\pm7$ MeV from the fit without $\Delta(1232)$, and $\sigma_{\pi N}=45\pm6$ MeV from the fit with explicit $\Delta(1232)$.