Speaker
Prof.
Hsiang-nan Li
(Academia Sinica)
Description
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 $m_G\approx 1.4$ GeV obtained from the $\eta$-$\eta'$-$G$
mixing is confirmed, while $m_{qq}$ grows to above the pion mass,
and thus increases perturbative QCD (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 $Br(B\to\eta K)$. The puzzle due to the large
$Br(B\to\eta'K)$ data is then resolved.
