  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
$\Xi(1620)$.
