Roy-Steiner-equation analysis of pion-nucleon scattering

TL;DR

This paper employs Roy-Steiner equations to analyze pion-nucleon scattering, extracting precise scattering lengths, phase shifts, and the sigma-term, while ensuring consistency with fundamental symmetries and experimental data.

Contribution

It provides a comprehensive Roy-Steiner analysis of pion-nucleon scattering, including solutions for partial waves, error estimates, and extraction of the sigma-term with isospin-breaking corrections.

Findings

Accurate low-energy phase shifts and subthreshold parameters obtained.

Precise determination of the pion-nucleon sigma-term.

Validation of chiral perturbation theory matching with data.

Abstract

We review the structure of Roy-Steiner equations for pion-nucleon scattering, the solution for the partial waves of the t-channel process $\pi\pi\to \bar N N$, as well as the high-accuracy extraction of the pion-nucleon S-wave scattering lengths from data on pionic hydrogen and deuterium. We then proceed to construct solutions for the lowest partial waves of the s-channel process $\pi N\to \pi N$ and demonstrate that accurate solutions can be found if the scattering lengths are imposed as constraints. Detailed error estimates of all input quantities in the solution procedure are performed and explicit parameterizations for the resulting low-energy phase shifts as well as results for subthreshold parameters and higher threshold parameters are presented. Furthermore, we discuss the extraction of the pion-nucleon $\sigma$-term via the Cheng-Dashen low-energy theorem, including the role of isospin-breaking corrections, to obtain a precision determination consistent with all constraints from analyticity, unitarity, crossing symmetry, and pionic-atom data. We perform the matching to chiral perturbation theory in the subthreshold region and detail the consequences for the chiral convergence of the threshold parameters and the nucleon mass.