Exploring charmonia ${\eta }_c(6S,7S)$ in the ${\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}$ invariant mass spectrum of $B^0\to K_S^0{\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}$

Abstract

We analyze the $B^0\to K_S^0{\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}$ decay recently observed by the LHCb Collaboration. The ${\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}$ invariant-mass spectrum exhibits an accumulation near 4.63~GeV, which we investigate together with the accompanying ${\Lambda }_c^{+}{K}_S^0$ spectrum constrained by the known ${\Xi }_c(2923)$ and ${\Xi }_c(2939)$ states. Our amplitude model includes a nonresonant term, the two established ${\Xi }_c$ contributions, and high-lying charmonium states in the ${\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}$ channel. Guided by screened Godfrey--Isgur and quark-pair-creation calculations, we test the 4.63~GeV enhancement with a fixed ${\eta }_c(6S)$ amplitude at $(4629.00,24.20)$~MeV, {which improves the description of the 4.63~GeV region}, and examine a fixed ${\eta }_c(7S)$ contribution at $(4718.84,22.84)$~MeV, which improves the higher-mass region of the spectrum. We also evaluate the ${\eta }_c(nS)\to {\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}$ baryonic decays via a hadron-loop mechanism and estimate the $B^0\to K_S^0{\eta }_c(nS)$ production in naive factorization. Within the narrow width approximation, the fit yields a $\mathcal{B}(B^0\to K_S^0{\eta }_c(6S))\mathcal{B}({\eta }_c(6S)\to {\Lambda }_c^{+}{\bar{\Lambda }}_c^{-})$ of about $6.2\times 10^{-6}$, while the factorization and hadron-loop calculations give rates roughly one to three orders of magnitude lower than the above fitted ratio. These results highlight the need for more precise data and a full amplitude analysis to determine the line shapes and clarify the nature of the higher-mass contribution.

Comments: 12 pages, 4 figures and 3 tables