Study on the radiative decays of $h_c$ via intermediate meson loops model

Abstract

Recently, the BESIII Collaboration reported two new decay processes $h_c(1P)\to γη$ and $γη^\prime$. Inspired by this measurement, we propose to study the radiative decays of $h_c$ via intermediate charmed meson loops in an effective Lagrangian approach. With the acceptable cutoff parameter range, the calculated branching ratios of $h_c(1P)\to γη$ and $γη^\prime$ are orders of $10^{-4}\sim 10^{-3}$ and $10^{-3} \sim 10^{-2}$, respectively. The ratio $R_{h_c}= \mathcal{B}( h_c\to γη)/\mathcal{B}( h_c\to γη^\prime )$ can reproduce the experimental measurements with the commonly acceptable $α$ range. This ratio provide us some information on the $η-η^\prime$ mixing, which may be helpful for us to test SU(3)-flavor symmetries in QCD.