Isospin violation in pion–nucleon scattering

We construct the complete effective chiral pion–nucleon Lagrangian in the presence of virtual photons to one loop. As an application, we consider strong and electromagnetic isospin violation for scattering of neutral pions off nucleons. We show that for the scattering lengths these isospin violating terms are of the same size as the purely hadronic ones. We also analyze isospin-violating effects for the σ-term. These can be as large as 10% for the absolute value but are negligible for the shift to the Cheng–Dashen point.