Consequences of theu−dquark mass difference forπ0→γγandπ+→e+νγ

Abstract

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, $\frac{m_d}{m_u}$, and that the Vaks-Ioffe relation is severely broken in a model-dependent way. Therefore, the experimental values of $\gamma =\frac{F_A}{F_V}$ must be corrected if $m_u\ne m_d$. All the models considered appear to indicate that the smallest value of $\gamma$ is preferred if $m_d>m_u$. However, none is in good agreement with the experiment within 1 standard deviation. The best values for $\pi \to e\nu \gamma$ are in the SU(2)×SU(2) $\sigma$ model.