Nucleon resonance parameters from Roy-Steiner equations

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 Padé 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 $\pi \pi \to \bar{N}N$. 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.

Comments: 9 pages, 1 figure; journal version