Decay behaviors of possible ${\mathrm{\Lambda }}_{c\overline{c}}$ states in hadronic molecule pictures

In 2010, ${\mathrm{\Lambda }}_{c\overline{c}}^{*}$ states were predicted as the strange number $S=-1$ partners of $N_{c\overline{c}}^{*}$, which are well known now as the $P_c$ states and observed experimentally by the LHCb Collaboration. We analyze the decay behaviors of ${\mathrm{\Lambda }}_{c\overline{c}}$ as $S$-wave hadronic molecules within the effective Lagrangian framework by a similar method, which has been applied on $P_c$ states successfully. With partial widths of possible decay channels calculated, we find that ${\mathrm{\Lambda }}_{c\overline{c}}(4213)$ and ${\mathrm{\Lambda }}_{c\overline{c}}(4403)$, which are formed as pseudoscalar meson baryon molecules, mainly decay to the ${\eta }_c\mathrm{\Lambda }$ channel. For the two vector meson baryon molecule states, our results show that the total decay width with $J^P={\frac{1}{2}}^{-}$ is by one order of magnitude larger than that with $J^P={\frac{3}{2}}^{-}$. The decay patterns and relative decay ratios are very different for ${\mathrm{\Lambda }}_{c\overline{c}}(4370)$ being a $D_s^{*-}{\mathrm{\Lambda }}_c^{+}$ or ${\overline{D}}^{*}{\mathrm{\Xi }}_c$ molecule state. The main decay channels of ${\mathrm{\Lambda }}_{c\overline{c}}(4550)$ are ${\overline{D}}^{(*)}{\mathrm{\Xi }}_c^{(*,\prime )}$ because of the pseudoscalar meson exchange mechanism. In addition, ${\overline{D}}^{*}{\mathrm{\Xi }}_c$ is the dominant decay channel of ${\mathrm{\Lambda }}_{c\overline{c}}(4490)$, which is assumed as a $\overline{D}{\mathrm{\Xi }}_c^{*}$ bound state. These decay patterns of the ${\mathrm{\Lambda }}_{c\overline{c}}^{*}$ states would provide guidance for future experimental searches and help us to understand their internal structures.

Figure 1

Feynman diagram for the two-body decay of ${\mathrm{\Lambda }}_{c\overline{c}}$ in the molecule picture, where CM (CB) denotes the constituent meson (baryon) of the composite system, FM (FB) denotes the final meson (baryon), and EM denotes the exchanged meson.