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Exploring charmonia $η_{c} (6 S, 7 S)$ in the $Λ_{c}^{+} \bar{Λ}_{c}^{-}$ invariant mass spectrum of $B^{0} \to K_{S}^{0} Λ_{c}^{+} \bar{Λ}_{c}^{-}$

Cheng-Xi Liu^1,2,3,4,*, Jun-Zhang Wang^5,†, and Xiang Liu ^1,2,3,4,‡

¹School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
²Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China
³MoE Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, China
⁴Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China
⁵Department of Physics and Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 401331, China

^*Contact author: liuchx2025@lzu.edu.cn
^†Contact author: wangjzh@cqu.edu.cn
^‡Contact author: xiangliu@lzu.edu.cn

Phys. Rev. D 114, 074050 – Published 23 October, 2026

DOI: https://doi.org/10.1103/5lcd-6ml6

Abstract

We analyze the $B^{0} \to K_{S}^{0} Λ_{c}^{+} \bar{Λ}_{c}^{-}$ decay recently observed by the LHCb Collaboration. The $Λ_{c}^{+} \bar{Λ}_{c}^{-}$ invariant-mass spectrum exhibits an accumulation near 4.63 GeV, which we investigate together with the accompanying $Λ_{c}^{+} K_{S}^{0}$ spectrum constrained by the known $Ξ_{c} (2923)$ and $Ξ_{c} (2939)$ states. Our amplitude model includes a nonresonant term, the two established $Ξ_{c}$ contributions, and high-lying charmonium states in the $Λ_{c}^{+} \bar{Λ}_{c}^{-}$ channel. Guided by screened Godfrey-Isgur and quark-pair-creation calculations, we test the 4.63 GeV enhancement with a fixed $η_{c} (6 S)$ amplitude at $(M_{1}, Γ_{1}) = (4629.00, 24.20) MeV$ , which improves the description of the 4.63 GeV region, and examine a fixed $η_{c} (7 S)$ contribution at $(M_{2}, Γ_{2}) = (4718.84, 22.84) MeV$ , which improves the higher-mass region of the spectrum. We also evaluate the $η_{c} (n S) \to Λ_{c}^{+} \bar{Λ}_{c}^{-}$ baryonic decays via a hadron-loop mechanism and estimate the $B^{0} \to K_{S}^{0} η_{c} (n S)$ production in naive factorization. Within the narrow width approximation, the fit yields a $B (B^{0} \to K_{S}^{0} η_{c} (6 S)) \times B (η_{c} (6 S) \to Λ_{c}^{+} \bar{Λ}_{c}^{-})$ 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.

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Phys. Rev. D 114, 074050– Published 23 October, 2026

Vol. 114, Iss. 7 — 1 October 2026

Received 18 August 2026
Accepted 18 September 2026

DOI: https://doi.org/10.1103/5lcd-6ml6

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Exploring charmonia $η_{c} (6 S, 7 S)$ in the $Λ_{c}^{+} \bar{Λ}_{c}^{-}$ invariant mass spectrum of $B^{0} \to K_{S}^{0} Λ_{c}^{+} \bar{Λ}_{c}^{-}$

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Exploring charmonia ηc(6S,7S) in the Λc+Λ¯ c− invariant mass spectrum of B0→KS0Λc+Λ¯ c−

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Exploring charmonia $η_{c} (6 S, 7 S)$ in the $Λ_{c}^{+} \bar{Λ}_{c}^{-}$ invariant mass spectrum of $B^{0} \to K_{S}^{0} Λ_{c}^{+} \bar{Λ}_{c}^{-}$