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 Δ(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 f0(500), ρ(770), and f0(980) resonances in the t-channel process ππ→N¯N. The latter allows us to test—for the first time fully model independently in terms of the respective residues—universality of the ρ(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.