Two analytical constraints on the $\eta$-${\eta }^{\prime }$ mixing

Abstract

We obtained two analytical constraints on the $\eta$-${\eta }^{\prime }$ mixing parameters by considering two-photon decays of $\eta$ and ${\eta }^{\prime }$ [$\eta ({\eta }^{\prime })\text{ra}\gamma \gamma$], and productions of $\eta$ and ${\eta }^{\prime }$ in the $e^{+}{e}^{-}$ scattering at large momentum transfer ($Q^2\text{ra}\infty$). Using the data given in the PDG98 for the decay processes and recent CLEO measurements on the meson-photon transition form factors, we estimate for the ${\eta }_8$-${\eta }_1$ mixing scheme the mixing angle to be $\theta =-14.5^{\circ }\pm 2.0^{\circ }$ and the ratio of the decay constants of singlet to octet to be $f_1/f_8=1.17\pm 0.08$. Applying our approach to the recently proposed $q\text{qbar}$-$s\text{sbar}$ mixing scheme, we obtain the mixing angle to be $\varphi =39.8^{\circ }\pm 1.8^{\circ }$ and the ratio of the decay constants of $s\text{sbar}$ state to $q\text{qbar}$ state to be $f_s/f_q=1.20\pm 0.10$.

Comments: 8 pages, RevTex, no figures