Radiative $ϕ$$-$meson decays and $η$-$η^\prime$ mixing: a QCD sum rule analysis

Abstract

The radiative transitions $ϕ\to ηγ$ and $ϕ\to η^\prime γ$ are analysed using QCD sum-rules. The results we obtain for ${\cal B}(ϕ\to ηγ)=(1.15 \pm 0.2) 10^{-2}$ and ${\cal B}(ϕ\to η^\prime γ)=(1.18 \pm 0.4) 10^{-4}$ are in very good agreement with existing experimental data. The related issue of $η-η^\prime$ mixing is discussed and we give predictions for the $η$ and $η^\prime$ decay constants in the framework of a mixing scheme in the quark-flavour basis.