On the size of isospin violation in low-energy pion-nucleon scattering

We present an analysis of isospin-breaking effects in threshold pion-nucleon scattering due to the light quark mass difference and the dominant virtual photon effects. We discuss the deviation from various relations, which are exact in the isospin limit. The size of the isospin-violating effects in the relations involving the isovector \(\pi N\) amplitudes is typically of the order of one percent. We also find a new remarkably large effect \((\sim 40%)\) in an isoscalar triangle relation connecting the charged and neutral pion scattering off protons.