Implications on $η$-$η'$-glueball mixing from $B_{d/s} \to J/Ψη^{(')}$ Decays

Abstract

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