Investigations on the charmless decays of $X(3872)$ in intermediate meson loops model

The charmless decay processes of $X(3872)$ provide us a good platform to study the nature and the decay mechanism of $X(3872)$. Based on a molecular nature of $X(3872)$ as a $\bar{D}D^*$ bound state, we have investigated the charmless decays $X(3872) \to VV$ and $VP$ via intermediate $D^*{\bar D} +c.c.$ meson loops, where $V$ and $P$ stand for light vector and pseudoscalar mesons, respectively. We discuss three cases, i.e., pure neutral components ($\theta=0$), isospin singlet ($\theta=\pi/4$) and neutral components dominant ($\theta = \pi/6$), where $\theta$ is a phase angle describing the proportion of neutral and charged constituents. The proportion of neutral and charged constituent have an influence on the decay widths of $X(3872) \to VV$ and $VP$. With the coupling constant of $X(3872)$ to the $\bar{D}D^*$ channel obtained under the molecule ansatz of $X(3872)$ resonance, the predicted decay widths of $X(3872)\rightarrow VV$ are about tens of keVs, while the decay width can reach a few hundreds of keVs for $X(3872)\to VP$. The dependence of these ratios between different decay modes of $X(3872)\to VV$ and $X(3872)\to VP$ to the mixing angle $\theta$ is also investigated. It is expected that the theoretical calculations here can be tested by future experiments.