The chiral representation of the $\pi N$ scattering amplitude and the pion-nucleon sigma term

TL;DR

This paper presents a new covariant chiral perturbation theory analysis of the $\pi N$ scattering amplitude, accurately describing experimental data and providing a precise determination of the pion-nucleon sigma term, with implications for hadronic physics.

Contribution

It introduces a novel Lorentz covariant approach that includes the $\Delta(1232)$ resonance and overcomes previous limitations, enabling precise sigma term extraction from scattering data.

Findings

Accurate description of phase shifts up to near resonance energies.

Determination of the sigma term as $\sigma_{\pi N}=59(7)$ MeV.

Modern data favor larger sigma term values.

Abstract

We present a novel analysis of the $\pi N$ scattering amplitude in Lorentz covariant baryon chiral perturbation theory renormalized in the extended-on-mass-shell scheme. This amplitude, valid up to $\mathcal{O}(p^3)$ in the chiral expansion, systematically includes the effects of the $\Delta(1232)$ in the $\delta$-counting, has the right analytic properties and is renormalization-scale independent. This approach overcomes the limitations that previous chiral analyses of the $\pi N$ scattering amplitude had, providing an accurate description of the partial wave phase shifts of the Karlsruhe-Helsinki and George-Washington groups up to energies just below the resonance region. We also study the solution of the Matsinos group which focuses on the parameterization of the data at low energies. Once the values of the low-energy constants are determined by adjusting the center-of-mass energy dependence of the amplitude to the scattering data, we obtain predictions on different observables. In particular, we extract an accurate value for the pion-nucleon sigma term, $ \sigma_{\pi N}$. This allows us to avoid the usual method of extrapolation to the unphysical region of the amplitude. Our study indicates that the inclusion of modern meson-factory and pionic-atom data favors relatively large values of the sigma term. We report the value $\sigma_{\pi N}=59(7)$MeV and comment on implications that this result may have.