On Radiative $\phi \to \eta \gamma$, $\phi \to \eta^\prime \gamma$ Decays

Abstract

We use QCD sum-rules to study the decays $\phi \to \eta \gamma$ and $\phi \to \eta^\prime \gamma$, obtaining ${\cal B}(\phi \to \eta \gamma)=(1.15 \pm 0.2) 10^{-2}$ and ${\cal B}(\phi \to \eta^\prime \gamma)=(1.18 \pm 0.4) 10^{-4}$, in very good agreement with existing experimental data. We also discuss the issue of $\eta-\eta^\prime$ mixing, predicting the $\eta$ and $\eta^\prime$ decay constants in a mixing scheme in the quark-flavour basis.