Radiative decays of the $\Omega(2012)$ as a hadronic molecule

We present a theoretical investigation of the radiative decay process $\Omega(2012) \to \gamma \Omega$, where the $\Omega(2012)$ resonance with spin-parity $J^P=\frac{3}{2}^-$, is treated as a dynamically generated state from $\bar{K}\Xi(1530)$ and $\eta \Omega$ in $s$-wave and $\bar{K}\Xi$ in $d$-wave. The radiative decay width of the $\Omega(2012)$ is calculated using a triangular loop mechanism, where the $\Omega(2012)$ couples to the $\bar{K} \Xi(1530)$ channel. Subsequently, the final state interactions between $\Xi(1530)$ and $\bar{K}$ transition to a photon and $\Omega$ through the exchange of a $\Xi$ baryon. Our calculations yield a radiative decay width of $13.2 ^{+4.5}_{-3.9}$ KeV, with uncertainties arising from the model parameters. This result provides valuable insights into the nature of the $\Omega(2012)$ resonance and its decay dynamics. It is expected that the calculations presented here could be verified by future experiments, which would open a new door for studying the still elusive nature of the $\Omega(2012)$.