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 resonance. Further, we study the Roper, , resonance, which lies beyond the strict domain of validity, in comparison to Padé approximants, comment on the role of subthreshold singularities in the -wave, and determine the residues of the , , and resonances in the -channel process . The latter allows us to test—for the first time fully model independently in terms of the respective residues—universality of the couplings and the Goldberger–Treiman relation expected if the scalars behaved as dilatons, in both cases revealing large deviations from the narrow-resonance limit.

中文翻译：

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Roy–Steiner 方程中的核子共振参数


考虑到复杂平面所需的分析延拓，可靠地确定核子共振的极参数和残数是众所周知的挑战。我们提供了对此类共振参数的全面分析，可通过π介子-核子散射的罗伊-施泰纳方程获得，这是一组部分波色散关系，结合了解析性、幺正性和交叉对称性的约束，尤其是共振。此外，我们研究了 Roper、 、 共振，与 Padé 近似相比，它超出了严格的有效性范围，评论了 - 波中阈下奇点的作用，并确定了 - 波中的 、 和 共振的留数。渠道流程。后者使我们能够测试——第一次完全独立地根据各自的留数进行建模——如果标量表现为膨胀子，则耦合的普遍性和戈德伯格-特雷曼关系预期，在两种情况下都揭示了与窄共振的巨大偏差限制。