On Radiative $ϕ\to ηγ$, $ϕ\to η^\prime γ$ Decays

Abstract

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