Charmonium decays into ${\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$ pair governed by the hadronic loop mechanism

In this work, we investigate the open-charm decay process $\psi \to {\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$ via the hadronic loop mechanism for vector charmonia above ${\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$ threshold. The branching ratios of these vector charmonium states to ${\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$ are estimated. The charmonium explanation of the $Y(4630)$ observed in $e^{+}{e}^{-}\to {\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$ is tested. Furthermore, for the predicted higher vector charmonia above 4.7 GeV, the branching ratios $\mathcal{B}[\psi (nS)\to {\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c]$ with $n=7$, 8, 9 are found to be of the order of magnitude of ${10}^{-4}-{10}^{-3}$ while $\mathcal{B}[\psi (mD)\to {\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c]$ with $m=6$, 7, 8 are of the order of magnitude of ${10}^{-3}-{10}^{-2}$. The experimental signals of these missing charmonium states are discussed. The search for them may be an interesting topic in the future BESIII and Belle II experiments.

Figure 1

The established charmonium states and comparison with $D\overline{D}$ and ${\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$ thresholds.

Figure 2

The schematic diagrams of a hadronic loop mechanism that contribute to $\psi \to {\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$.

Figure 3

The $\alpha$ dependence on the calculated branching ratios of ${\psi }_{6S-5D}^{\prime }\to {\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$ and ${\psi }_{6S-5D}^{\prime \prime }\to {\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$. Here, we take positive and negative values of mixing angle $\theta$ to present the decay behavior of ${\psi }_{6S-5D}^{\prime }$ and ${\psi }_{6S-5D}^{\prime \prime }$. The gray band represents the extracted branching ratio by the experimental data of $e^{+}{e}^{-}\to {\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$ [22].

Figure 4

The $\alpha$ dependence of the predicted branching ratios of the decay of higher $S$-wave charmonia to ${\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$.

Figure 5

The $\alpha$ dependence of the predicted branching ratios of the decay of higher $D$-wave charmonia to ${\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$.

Figure 6

Our fit result to experimental data of $e^{+}{e}^{-}\to {\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$ from Belle [6] and BESIII [49].