General parametrization of theV→Pγmeson decays

We apply the general parametrization method [Phys. Rev. D 40, 2997 (1989)] to the radiative decays of the light vector mesons. The ratios $\frac{\Gamma (\omega \to \pi \gamma )}{\Gamma (\rho \to \pi \gamma )}$ and $\frac{\Gamma ({\eta }^{\prime }\to \rho \gamma )}{\Gamma ({\eta }^{\prime }\to \omega \gamma )}$, corrected for the difference in momenta, are predicted to be 9 (to all orders in flavor breaking) plus possible contributions from gluon annihilation diagrams. So far there is no evidence (inside ±15% errors) for gluon effects in the above ratios; $\phi \to {\pi }^0\gamma$ leads to the same conclusion. We show that if the gluon diagrams are indeed negligible, the parametrization of the $V\to P\gamma$ decays (which is exact and thus includes automatically configuration mixing and all the complexities of the Fock expansion of the hadron states) coincides with the results of the nonrelativistic quark model (NRQM); this clarifies again why the NRQM works, independently of the internal $\frac{v}{c}$ of the quarks. Another NRQM result shown here to be exact (to second order in flavor breaking) is $\frac{A(K^{*0\mathrm{}}\to K^0\gamma )}{A(K^{*+}\to K^{+}\gamma )}=-\frac{\mathrm{}(1+x)\mathrm{}}{\mathrm{}(2-x)\mathrm{}}(\mathrm{with} x=\frac{{\mu }_{\lambda }}{{\mu }_{\mathcal{N}}})$ for the $\gamma =\mathrm{decay}$ amplitudes of $K^{*0\mathrm{}}$ and $K^{*+}$ (in this case the gluon diagrams are absent).