$\eta_c$ mixing effects on charmonium and $B$ meson decays

TL;DR

This paper extends the $ ext{eta}$-$ ext{eta'}$-$G$ mixing formalism to include $ ext{eta}_c$, constrains mixing angles with experimental data, and shows how $ ext{eta}_c$ mixing improves predictions for certain B meson decay processes.

Contribution

The paper introduces the $ ext{eta}_c$ into the mixing formalism, constrains mixing angles with data, and demonstrates improved theoretical predictions for B meson decay branching ratios.

Findings

The $ ext{eta}_c$-$G$ mixing angle is about 11 degrees.

The pseudoscalar glueball mass $m_G$ is approximately 1.4 GeV.

Including $ ext{eta}_c$ mixing increases $Br(B\to\eta'K)$ predictions by 18%.

Abstract

We include the $\eta_c$ meson into the $\eta$-$\eta'$-$G$ mixing formalism constructed in our previous work, where $G$ represents the pseudoscalar gluball. The mixing angles in this tetramixing matrix are constrained by theoretical and experimental implications from relevant hadronic processes. Especially, the angle between $\eta_c$ and $G$ is found to be about $11^\circ$ from the measured decay widths of the $\eta_c$ meson. The pseudoscalar glueball mass $m_G$, the pseudoscalar densities $m_{qq,ss,cc}$ and the U(1) anomaly matrix elements associated with the mixed states are solved from the anomalous Ward identities. The solution $m_G\approx 1.4$ GeV obtained from the $\eta$-$\eta'$-$G$ mixing is confirmed, while $m_{qq}$ grows to above the pion mass, and thus increases perturbative QCD predictions for the branching ratios $Br(B\to\eta'K)$. We then analyze the $\eta_c$-mixing effects on charmonium magnetic dipole transitions, and on the $B\to\eta^{(\prime)}K_S$ branching ratios and CP asymmetries, which further improve the consistency between theoretical predictions and data. A predominant observation is that the $\eta_c$ mixing enhances the perturbative QCD predictions for $Br(B\to\eta'K)$ by 18%, but does not alter those for $Br(B\to\eta K)$. The puzzle due to the large $Br(B\to\eta'K)$ data is then resolved.