Threshold πNIsospin Violation

Abstract

We discuss the electromagnetic corrections to the πN scattering lengths generated by minimal e. m. coupling from a knowledge of the low energy expansion of the πN elastic scattering amplitude as well as from the nucleon and Δ pole terms, all taken for purely strong interactions. In the heavy baryon limit there is no free parameter, since masses and the e. m. and axial form factors are known. The different terms have a clear physical and intuitive origin. In particular, a large isospin breaking contribution to the isoscalar term appears in the elastic charged-pion scattering lengths. We attempt a comparison to the results from chiral effective field theory (EFT) with a physical interpretation of the empirical constants in that approach. The results are applied to the energy shift and width of the π-p atom.