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arXiv · 2312.15015

Nucleon resonance parameters from Roy-Steiner equations

Martin Hoferichter·Jacobo Ruiz de Elvira·Bastian Kubis·Ulf-G. Meißner
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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.

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Martin Hoferichter, Jacobo Ruiz de Elvira, Bastian Kubis, Ulf-G. Meißner. 2023-12-22. Nucleon resonance parameters from Roy-Steiner equations. https://doi.org/10.1016/j.physletb.2024.138698

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