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 \$15^\circ\$
from the measured decay width of the \$\eta\_c\$ meson. The pseudoscalar glueball
mass \$m\_G\$, and 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\_G1.4\$ GeV obtained from the
\$\eta\$-\$\eta'\$-\$G\$ mixing is confirmed, while \$m\_qq\$ grows to above the pion
mass, and thus increases perturbative QCD (PQCD) 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 PQCD predictions for \$Br(B\to\eta'K)\$ by 20\%, but
does not alter those for \$Br(B\toK)\$. The puzzle due to the large
\$Br(B\to\eta'K)\$ data is then resolved.
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