Isospin-breaking corrections to the pion-nucleon scattering lengths
Martin Hoferichter, Bastian Kubis, Ulf-G. Mei{\ss}ner
TL;DR
This paper investigates isospin-breaking effects in pion-nucleon scattering lengths using covariant baryon chiral perturbation theory, revealing a 1.5% violation of the triangle relation and significant corrections in neutral-pion channels.
Contribution
It provides a comprehensive analysis of isospin-breaking corrections in all physical channels within a covariant chiral framework, highlighting effects beyond previous predictions.
Findings
Triangle relation violated by about 1.5%
Significant isospin-breaking correction in neutral-pion-nucleon scattering
Discussion on implications for hadronic atoms
Abstract
We analyze isospin breaking through quark mass differences and virtual photons in the pion-nucleon scattering lengths in all physical channels in the framework of covariant baryon chiral perturbation theory. The so-called triangle relation is found to be violated by about 1.5 %. We encounter a substantial isospin-breaking correction to neutral-pion-nucleon scattering beyond Weinberg's prediction due to a cusp effect. Finally, the application to hadronic atoms is briefly discussed.
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