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.

9 pages, 1 figure; journal version

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• Pionic deuterium
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• Global Data-Driven Determination of Baryon Transition Form Factors
• Gravitational form factors of pions, kaons and nucleons from dispersion relations
• Advanced parametrisations for hadronic form factors
• On the pole trajectory of the subthreshold negative parity nucleon with varying pion masses
• Review on recent progress in the study of the $N^{\ast }(920)$ subthreshold singularity and the $\sigma /f_0(500)$ meson
• Dispersive determination of resonances from $\pi \pi$ scattering data
• Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints
• Nucleon mass: trace anomaly and $\sigma$-terms
• Understanding the 1P- and 2S-wave nucleon resonances within the extended Lee-Friedrichs Model