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

TL;DR

This paper investigates the mixing between $\eta$, $\eta'$ and pseudoscalar glueballs using $B_{d/s} o J/ ext{Psi} \eta^{(')}$ decays, revealing large glueball content in $\eta^{(')}$ and explaining large $B_d o K ext{eta'}$ decays.

Contribution

It introduces a formalism for $\eta$-$ ext{eta'}$-$G$ mixing in heavy meson decays, aligning theoretical predictions with experimental data and extending to tetramixing including $ ext{eta}_c$.

Findings

Predicted branching ratios match Belle data with a mixing angle $ heta_G \\approx 30^ extdegree$.

Large pseudoscalar glueball content in $\eta^{(')}$ is implied by decay measurements.

The formalism explains large $B_d o K ext{eta'}$ decay rates.

Abstract

We point out that the recent Belle measurements of the $B_{d/s} \to J/\Psi \eta^{(')}$ decays imply large pseudoscalar glueball contents in the $\eta^{(\prime)}$ meson. These decays are studied in the perturbative QCD (PQCD) approach, considering the $\eta$-$\eta'$-$G$ mixing, where $G$ represents the pseudoscalar glueball. It is shown that the PQCD predictions for the $B_{d/s} \to J/\Psi \eta^{(')}$ branching ratios agree well with the data for the mixing angle $\phi_G\approx 30^\circ$ between the flavor-singlet state and the pure pseudoscalar glueball. Extending the formalism to the $\eta$-$\eta'$-$G$-$\eta_c$ tetramixing, the abnormally large observed $B_d\to K\eta'$ 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.