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.