Isospin breaking in low-energy pion-nucleon scattering.

Since isospin symmetry is only approximate, the discrepancy in this relation, D ; fCEX 2 sf1 2 f2dy p 2, is expected to be nonzero. Interesting physics lies in the violation of this relation beyond effects due to the hadronic mass differences and the Coulomb interaction. It is the purpose of this Letter to demonstrate that recent experimental data at low energies require a residual contribution to D, of the order of 20.012 fm in the s wave. This number is to be compared with the low-energy s-wave CEX amplitude of approximately 20.19 fm. There is a similar, but less well-determined, breaking in the p wave spin-flip amplitude. The triangle identity implies a bound on the elastic and charge-exchange cross sections given by