Isospin-breaking corrections to the pion-nucleon scattering lengths

Understand

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.