Radiative decays, nonet symmetry, and SU(3) breaking

Abstract

We reexamine the problem of simultaneously describing in a consistent way all radiative and leptonic decays of light mesons $(\stackrel{\ensuremath{\rightarrow}}{V}P\ensuremath{\gamma},$ $\stackrel{\ensuremath{\rightarrow}}{P}V\ensuremath{\gamma},$ $\stackrel{\ensuremath{\rightarrow}}{P}\ensuremath{\gamma}\ensuremath{\gamma},$ $\stackrel{\ensuremath{\rightarrow}}{V}{e}^{+}{e}^{\ensuremath{-}})$. For this purpose, we rely on the hidden local symmetry model in both its anomalous and non-anomalous sectors. We show that the SU(3) symmetry breaking scheme proposed by Bando, Kugo and Yamawaki, supplemented with nonet symmetry breaking in the pseudoscalar sector, allows one to reach a nice agreement with all data, except for the ${K}^{*\ifmmode\pm\else\textpm\fi{}}$ radiative decay. An extension of this breaking pattern allows one to account for this particular decay mode too. Considered together, the whole set of radiative decays provides a pseudoscalar mixing angle ${\ensuremath{\theta}}_{P}\ensuremath{\simeq}\ensuremath{-}11\ifmmode^\circ\else\textdegree\fi{}$ and a value for ${\ensuremath{\theta}}_{V}$ which is $\ensuremath{\simeq}3\ifmmode^\circ\else\textdegree\fi{}$ from that of ideal mixing. We also show that it is impossible, in a practical sense, to disentangle the effects of nonet symmetry breaking and those of glue inside the ${\ensuremath{\eta}}^{\ensuremath{'}}$, using only light meson decays.