Nucleon resonance parameters from Roy-Steiner equations

TL;DR

This paper uses Roy-Steiner equations to accurately determine nucleon resonance parameters, including the $ ho(770)$ and $f_0(500)$, providing model-independent insights into their properties and couplings.

Contribution

It offers a comprehensive, model-independent analysis of nucleon and meson resonance parameters using Roy-Steiner equations, including the first determination of certain residues and tests of universality and the Goldberger-Treiman relation.

Findings

Accurate resonance parameters for $ ho(770)$ and $f_0(500)$ obtained.

Tested universality of $ ho(770)$ couplings and the Goldberger-Treiman relation.

Identified deviations from narrow-resonance limit in scalar and vector mesons.

Abstract

A reliable determination of the pole parameters and residues of nucleon resonances is notoriously challenging, given the required analytic continuation into the complex plane. We provide a comprehensive analysis of such resonance parameters accessible with Roy-Steiner equations for pion-nucleon scattering - a set of partial-wave dispersion relations that combines the constraints from analyticity, unitarity, and crossing symmetry - most prominently of the $\Delta(1232)$ resonance. Further, we study the Roper, $N(1440)$, resonance, which lies beyond the strict domain of validity, in comparison to Pad\'e approximants, comment on the role of subthreshold singularities in the $S$-wave, and determine the residues of the $f_0(500)$, $\rho(770)$, and $f_0(980)$ resonances in the $t$-channel process $\pi\pi\to\bar NN$. The latter allows us to test - for the first time fully model independently in terms of the respective residues - universality of the $\rho(770)$ couplings and the Goldberger-Treiman relation expected if the scalars behaved as dilatons, in both cases revealing large deviations from the narrow-resonance limit.