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

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