Hadronic decays of possible pseudoscalar $P$-wave $D{\bar{D}}^{\ast }\mathrm{/}\bar{D}{D}^{\ast }$ molecular state

Recently, the new structure $G(3900)$ observed by the BESIII Collaboration in the $e^{+}{e}^{-}\to D\bar{D}$ was identified to be the $P$-wave $D{\bar{D}}^{\ast }\mathrm{/}\bar{D}{D}^{\ast }$ vector molecular resonance using a unified meson exchange model. Apart from the vector $P$-wave state, a possible pseudoscalar $P$-wave molecular state of the $D{\bar{D}}^{\ast }\mathrm{/}\bar{D}{D}^{\ast }$ [called $G_0(3900)$ for short] was also predicted, which is likely to be observed in future experiments. Within the molecular framework, we calculated the partial decay widths for a series of hadronic decays of the $G_0$, including $G_0\to \omega ({\rho }^0)J\mathrm{/}\psi$, ${\pi }^{+}{\pi }^{-}{\eta }_c(1S)$, ${\pi }^{+}{\pi }^{-}{\chi }_{c1}(1P)$, and $D^0{\bar{D}}^0{\pi }^0$. Under present model parameters, the hidden-charm decay modes are dominated by the $G_0\to \omega J\mathrm{/}\psi$ and $G_0\to {\pi }^{+}{\pi }^{-}{\eta }_c(1S)$, and the partial widths can reach 1 MeV and 0.1 MeV, respectively. The open-charm channel $G_0\to D^0{\bar{D}}^0{\pi }^0$ exhibits a rather small decay rate ($\sim 0.1\mathrm{k}\mathrm{e}\mathrm{V}$). In terms of our present predictions, we suggest BESIII and Belle II to search for the pseudoscalar $P$-wave $D{\bar{D}}^{\ast }\mathrm{/}\bar{D}{D}^{\ast }$ molecular state with $J^{PC}=0^{-+}$ in the hidden-charm processes $G_0\to \omega J\mathrm{/}\psi$ or $G_0\to {\pi }^{+}{\pi }^{-}{\eta }_c(1S)$.