Consequences of the u-d quark mass difference for π0 → γγ and π+ → e+νγ

Radiative pion decay is studied in the framework of several relativistic quark models with or without a sigma scalar meson, within the one-loop approximation. The new feature that we consider is that the quark masses are nondegenerate. It is found that the form factors are very sensitive to the quark mass ratio, m/sub d//m/sub u/, and that the Vaks-Ioffe relation is severely broken in a model-dependent way. Therefore, the experimental values of γ = F/sub A//F/sub V/ must be corrected if m/sub u/ not = m/sub d/. All the models considered appear to indicate that the smallest value of γ is preferred if m/sub d/ > m/sub u/. However, none is in good agreement with the experiment within 1 standard deviation. The best values for π → eνγ are in the SU(2) x SU(2) sigma model