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We analyze isospin breaking through quark mass differences and virtualphotons in the pion-nucleon scattering lengths in all physical channels in theframework of covariant baryon chiral perturbation theory. The so-calledtriangle relation is found to be violated by about 1.5 %. We encounter asubstantial isospin-breaking correction to neutral-pion-nucleon scatteringbeyond Weinberg's prediction due to a cusp effect. Finally, the application tohadronic atoms is briefly discussed.

Isospin-breaking corrections to the pion-nucleon scattering lengths