Radiative decays of the $\hat{I}\text{c◯}(2012)$ as a hadronic molecule

Abstract

We present a theoretical investigation of the radiative decay process $\hat{I}\text{c◯}(2012)\to {\hat{I}}^3\hat{I}\text{c◯}$, where the $\hat{I}\text{c◯}(2012)$ resonance with spin-parity $J^P={\frac{3}{2}}^{-}$, is treated as a dynamically generated state from $\bar{K}\hat{I}ž(1530)$ and $\hat{I}\cdot \hat{I}\text{c◯}$ in $s$-wave and $\bar{K}\hat{I}ž$ in $d$-wave. The radiative decay width of the $\hat{I}\text{c◯}(2012)$ is calculated using a triangular loop mechanism, where the $\hat{I}\text{c◯}(2012)$ couples to the $\bar{K}\hat{I}ž(1530)$ channel. Subsequently, the final state interactions between $\hat{I}ž(1530)$ and $\bar{K}$ transition to a photon and $\hat{I}\text{c◯}$ through the exchange of a $\hat{I}ž$ baryon. Our calculations yield a radiative decay width of $13.2_{-3.9}^{+4.5}$ KeV, with uncertainties arising from the model parameters. This result provides valuable insights into the nature of the $\hat{I}\text{c◯}(2012)$ 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 $\hat{I}\text{c◯}(2012)$.