Hidden-charm decays of $Y(4390)$ in a hadronic molecular scenario

In the present work, the hidden-charm decays of $Y(4390)$ are investigated in a $D^{*}{\overline{D}}_1+\mathrm{H}.\mathrm{c}.$ molecular scenario. We find in this frame the observation of the $Y(4390)$ in the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$ process and the absence of this state in the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ process are very natural. The partial width of $Y(4390)\to {\pi }^{+}{\pi }^{-}{h}_c$ could reach up to 1.26 MeV, which is large enough to be observed. The result also indicates that the partial widths of $Y(4390)\to \eta J/\psi$ and $Y(4390)\to \eta h_c$ are of the same order of magnitude as the one of $Y(4390)\to {\pi }^{+}{\pi }^{-}{h}_c$, which could be tested by the precise measurements at BES III and Belle II.

Figure 1

Diagrams contribute to the considered hidden-charm decays. Diagrams $(a)-(b)$ indicate $Y(4390)\to {\pi }^{+}{\pi }^{-}{h}_c$ process via $Z_c^{\prime }$. Diagrams ($c$) and ($d$) are correspond to the $\eta /{\eta }^{\prime }$ transitions from $Y(4390)$ to $J/\psi$ and $h_c$, respectively.

Figure 2

The $\alpha$ dependences of the partial width of $Y(4390)\to {\pi }^{+}{\pi }^{-}{h}_c$.

Figure 3

The partial widths of the hidden-charm decay of $Y(4390)$ depending on the model parameter $\alpha$.