Light hadronic decays of spin-0 partner of $X(3872)$

The $X(3872)$ is theoretically predicted to have a spin-0 partner state denoted as $X_0$. Assuming the $X_0$ as a $D\bar{D}$ molecular bound state, we calculate the decay widths of $X_0\to VV$ and $X_0 \to PP$ ($V$ and $P$ stand for light vector and pseudoscalar mesons, respectively) via intermediate charmed meson loops. Three different configurations of the $X_0$, i.e., pure neutral components ($\theta = 0$), isospin singlet ($\theta = \pi/4$) and pure charged components ($\theta = \pi/2$), are investigated. Within a commonly accepted range of the model parameter $\alpha$, the predicted decay widths of $X_0 \to VV$ are on the order of a few hundred $\mathrm{keV}$, while the decay widths of $X_0 \to PP$ can reach several $\mathrm{MeV}$. The $X_0 \to \rho\rho$ and $\pi\pi$ have larger decay rates. The relative width ratios between the channels are nearly model-independent. Moreover, among those channels only with isovector or isoscalar mesons, the relevant ratios are also independent of the phase angle. The predicted ratios are helpful for searching the $X_0$ in the future experiments at BESIII and Belle II.