  We show that the newly measured branching ratios of vector charmonia
($J/\psi$, $\psi^\prime$ and $\psi(3770))$ into $\gamma P$, where $P$ stands
for light pseudoscalar mesons $\pi^0$, $\eta$, and $\eta^\prime$, can be well
understood in the framework of vector meson dominance (VMD) in association with
the $\eta_c$-$\eta(\eta^\prime)$ mixings due to the axial gluonic anomaly.
These two mechanisms behave differently in $J/\psi$ and $\psi^\prime\to \gamma
P$. A coherent understanding of the branching ratio patterns observed in
$J/\psi(\psi^\prime)\to \gamma P$ can be achieved by self-consistently
including those transition mechanisms at hadronic level. The branching ratios
for $\psi(3770)\to\gamma P$ are predicted to be rather small.
