Measurement of the pseudoscalar mixing angle and $η^{\prime}$ gluonium content with KLOE detector

Abstract

We have measured the ratio $R_ϕ=BR(ϕ\to η^{\prime} γ)/BR(ϕ\to ηγ)$ by looking for the radiative decays $ϕ\to η^{\prime} γ$ and $ϕ\to ηγ$ in the final states $π^+π^-$ 7 $γ$'s and 7 $γ$'s respectively, in a sample of $\sim 1.3\cdot 10^{9}$ $ϕ$ mesons produced at the Frascati $ϕ$-factory. We obtain $R_ϕ=(4.77\pm0.09_{stat}\pm0.19_{sys})\cdot 10^{-3}$ from which we derive $BR(ϕ\to η^{\prime} γ)=(6.20\pm0.11_{stat}\pm0.25_{sys})\cdot 10^{-5}$. In the hypothesis of no gluonium content we extract the pseudoscalar mixing angle in the quark-flavor basis $ϕ_P=(41.4\pm0.3_{stat}\pm0.7_{sys}\pm0.6_{th})^{\circ}$. Combining the value of $R_ϕ$ with other constraints, we estimate the gluonium fractional content of $η^{\prime}$ meson as $Z^2 = 0.14\pm0.04$ and the mixing angle $ϕ_P = (39.7\pm0.7)^{\circ}$.