Matching pion-nucleon Roy-Steiner equations to chiral perturbation theory

TL;DR

This paper integrates Roy-Steiner equations with chiral perturbation theory to determine low-energy constants in pion-nucleon scattering, analyzing uncertainties and the impact of the 232 resonance.

Contribution

It provides a novel matching of Roy-Steiner results with chiral perturbation theory up to NN3LO, including a detailed uncertainty and convergence analysis.

Findings

Determined low-energy constants with systematic uncertainties.

Analyzed the convergence of the chiral expansion.

Discussed the role of the 232 resonance in chiral EFT.

Abstract

We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the \Delta(1232) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.