Radiative decay of the $\Xi(1620)$ in a hadronic molecule picture

Last year, the $\Xi(1620)$ state that is cataloged in the Particle Data Group (PDG) with only one star is reported again in the $\Xi^{-}\pi^{+}$ final state by the Belle Collaboration. Its properties not only the spectroscopy but also the decay width cannot be simply explained in the context of conventional constituent quark models. This intrigues an active discussion on the structure of this resonance. In this work, we study the radiative decays of the newly observed $\Xi(1620)$ assuming that it is a meson-baryon molecular state of $\Lambda\bar{K}$ and $\Sigma\bar{K}$ with spin-parity $J^P=1/2^{-}$ in our previous work. The partial decay widths of the $\Lambda\bar{K}-\Sigma\bar{K}$ molecular state into $\Xi\gamma$ and $\Xi\pi\gamma$ final states through hadronic loops are evaluated with the help of the effective Lagrangians. The partial widths for the $\Xi(1620)^0\to\gamma\Xi$ and $\Xi(1620)^0\to\gamma\Xi\pi$ are evaluated to be about $118.76-174.21$ KeV and $58.19-68.75$ eV, respectively, which may be accessible for the LHCb. If the $\Xi(1620)$ is $\Lambda\bar{K}-\Sigma\bar{K}$ molecule, the radiative transition strength $\Xi(1620)^0\to\gamma\bar{K}\Lambda$ is quite small and the decay width is of the order of 0.01 eV. Future experimental measurements of these processes can be useful to test the molecule interpretations of the $\Xi(1620)$.