Symmetry schemes, mixing angles, and meson decays

The $V\to P\gamma$, $P\to \mathrm{PP}\gamma$, $P\to \gamma \gamma$, and $V\to \mathrm{PPP}$ decays are investigated in two schemes that have had a measured degree of success in the understanding of $V\to P\gamma$ and $P\to V\gamma$ decays. These are (i) a nonetbreaking but SU(3)-preserving scheme with noncanonical angles ${\theta }_P$ and ${\theta }_V$ and (ii) an SU(3)-breaking scheme with canonical ${\theta }_P$ and ${\theta }_V$. In a fit to all available data the problem of understanding the experimental $\rho \to \pi \gamma$ rate is much worse than the case where a fit is made to only the $V\to P\gamma$ data.