Hadronic decays of possible pseudoscalar $P$-wave $D\bar{D}^\ast/\bar{D}D^\ast$ 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 $D\bar{D}^\ast/\bar{D}D^\ast$ 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 $D\bar{D}^\ast/\bar{D}D^\ast$ [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 $G_0\to ω(ρ^0) J/ψ$, $π^+π^- η_c (1S)$, $π^+π^- χ_{c1} (1P)$, and $D^0\bar{D}^0π^0$. Under present model parameters, the hidden-charm decay modes are dominated by the $G_0\toωJ/ψ$ and $G_0\toπ^+π^-η_c (1S)$, and the partial widths can reach 1 MeV and 0.1 MeV, respectively. The open-charm channel $G_0\to D^0\bar{D}^0π^0$ exhibits a rather small decay rate ($\sim 0.1~\mathrm{keV}$). In terms of our present predictions, we suggest BESIII and Belle II to search for the pseudoscalar $P$-wave $D\bar{D}^\ast / \bar{D}D^\ast$ molecular state with $J^{PC} = 0^{-+}$ in the hidden-charm processes $G_0 \to ωJ/ψ$ or $G_0 \to π^+π^-η_c(1S)$.