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

Abstract

Recently, the BESIII Collaboration reported two new decay processes $h_c(1P)\to {\hat{I}}^3\hat{I}\cdot$ and ${\hat{I}}^3\hat{I}{\cdot }^{\prime }$. 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 $h_c(1P)\to {\hat{I}}^3\hat{I}\cdot$ and ${\hat{I}}^3\hat{I}{\cdot }^{\prime }$ are orders of $10^{-4}\sim 10^{-3}$ and $10^{-3}\sim 10^{-2}$, respectively. The ratio $R_{h_c}=\mathcal{B}(h_c\to {\hat{I}}^3\hat{I}\cdot )/\mathcal{B}(h_c\to {\hat{I}}^3\hat{I}{\cdot }^{\prime })$ can reproduce the experimental measurements with the commonly acceptable $\hat{I}\pm$ range. This ratio provide us some information on the $\hat{I}\cdot -\hat{I}{\cdot }^{\prime }$ mixing, which may be helpful for us to test SU(3)-flavor symmetries in QCD.

11 pages, 5 figures, accepted for publication in EPJC