Understanding the radiative decays of vector charmonia to light pseudoscalar mesons

We show that the newly measured branching ratios of vector charmonia ($J\mathrm{/}\psi$, ${\psi }^{\mathrm{\prime }}$ and $\psi (3770))$ into $\gamma P$, where $P$ stands for light pseudoscalar mesons ${\pi }^0$, $\eta$, and ${\eta }^{\mathrm{\prime }}$, can be well understood in the framework of vector meson dominance (VMD) in association with the ${\eta }_c$-$\eta ({\eta }^{\mathrm{\prime }})$ mixings due to the axial gluonic anomaly. These two mechanisms behave differently in $J\mathrm{/}\psi$ and $\psi^\prime\to \gamma P$\mathrm{.}Acoherentunderstandingofthebranchingratiopatternsobservedin$J/\psi(\psi^\prime)\to \gamma P$ 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.