Isospin Violations in the Pion-Nucleon System

We examine the effect of isospin-violating meson-nucleon coupling constants on low-energy pion-nucleon scattering. We compute the couplings in the context of a nonrelativistic quark model. The difference between the up and down constituent masses induces a coupling of the neutral pion to the proton that is slightly larger than the corresponding one for the neutron. This difference generates a large isospin-violating correction---proportional to the isospin-even contribution arising from the nucleon Born terms---to the charge-exchange ($π^{-}p \rightarrow π^{0}n$) amplitude. In contrast to the isospin-conserving case, this correction is not cancelled by $σ$-meson exchange; in our model there is no isospin-violating $NNσ$ coupling at $q^2=0$. As a result, we find a violation of the triangle identity consistent with the one reported by Gibbs, Ai, and Kaufmann from a recent analysis of pion-nucleon data.

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