Implications on $\eta$-${\eta }^{\prime }$-glueball mixing from $B_{d/s}\to J/\Psi {\eta }^{{(}^{\prime })}$ Decays

Abstract

We point out that the recent Belle measurements of the $B_{d/s}\to J/\Psi {\eta }^{{(}^{\prime })}$ decays imply large pseudoscalar glueball contents in the ${\eta }^{(\prime )}$ meson. These decays are studied in the perturbative QCD (PQCD) approach, considering the $\eta$-${\eta }^{\prime }$-$G$ mixing, where $G$ represents the pseudoscalar glueball. It is shown that the PQCD predictions for the $B_{d/s}\to J/\Psi {\eta }^{{(}^{\prime })}$ branching ratios agree well with the data for the mixing angle ${\varphi }_G\approx 30^{\circ }$ between the flavor-singlet state and the pure pseudoscalar glueball. Extending the formalism to the $\eta$-${\eta }^{\prime }$-$G$-${\eta }_c$ tetramixing, the abnormally large observed $B_d\to K{\eta }^{\prime }$ branching ratios are also explained. The proposed mixing formalism is applicable to other heavy meson decays into ${\eta }^{(\prime )}$ mesons, and could be tested by future LHCb and Super-$B$ factory data.

Comments: Improved version, references added, 7 pages, 1 figure