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Isospin Violation in Pion-Nucleon Scattering at Threshold

T. E. O. Ericson
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Abstract

We discuss the electromagnetic corrections to the pion-nucleon scattering lengths generated by minimal e. m. coupling from a knowledge of the low energy expansion of the pion-nucleon elastic scattering amplitude as well as from the nucleon and delta pole terms, all a consequence of purely strong interactions. We assume the heavy baryon limit; the e.m. and axial form factors and the masses are used with their empirical values, such that there is no free parameter. The different terms have a clear physical and intuitive origin. In particular, a large isospin breaking contribution to the isoscalar term appears for 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 pionic hydrogen.

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T. E. O. Ericson. 2005-04-27. Isospin Violation in Pion-Nucleon Scattering at Threshold. https://arxiv.org/abs/hep-ph/0504258

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