Abstract
With the purpose of taking scalar-meson mixing into account in the framework of the SU(3) \ifmmode\times\else\texttimes\fi{} SU(3) $\ensuremath{\sigma}$ model of L\'evy, we compute the ratio between the axial-vector form factor ${F}_{A}$ and the vector form factor ${F}_{V}$ for the $\ensuremath{\pi}\ensuremath{\rightarrow}e\ensuremath{\nu}\ensuremath{\gamma}$ decay. Our results do not agree with previous calculations in this model even in the limit of no scalar-meson mixing. However, we find agreement with the experimental values of $\frac{{F}_{A}}{{F}_{V}}$ for uncolored integrally charged quarks, and disagreement with colored fractionally charged quarks. This in turn implies that one must discard the SU(3) \ifmmode\times\else\texttimes\fi{} SU(3) $\ensuremath{\sigma}$ model or the quark-loop-dominance framework because this fits the meson radiative decays only for colored fractionally charged quarks.
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