Study of \bar B\to Λ_c\bar Λ_c and \bar B\to Λ_c\bar Λ_c \bar K

Abstract

We study the doubly charmful two-body and three-body baryonic B decays $\bar B\to Λ_c^+\bar Λ_c^-$ and $\bar B\to Λ_c^+\bar Λ_c^- \bar K$. As pointed out before, a naive estimate of the branching ratio ${\cal O}(10^{-8})$ for the latter decay is too small by three to four orders of magnitude compared to experiment. Previously, it has been shown that a large enhancement for the $Λ_c^+\barΛ_c^-\bar K$ production can occur due to a charmonium-like resonance (e.g. X(4630) discovered by Belle) with a mass near the $Λ_c\barΛ_c$ threshold. Motivated by the BaBar's observation of a resonance in the $Λ_c \bar K$ system with a mass of order 2930 MeV, we study in this work the contribution to $\bar B\toΛ_c^+\barΛ_c^-\bar K$ from the intermediate state $Ξ_c(2980)$ which is postulated to be a first positive-parity excited $D$-wave charmed baryon state. Assuming that a soft $q\bar q$ quark pair is produced through the $σ$ and $π$ meson exchanges in the configuration for $\bar B\to Ξ_c(2980)\barΛ_c$ and $Λ_c\barΛ_c$, it is found that branching ratios of $\bar B\to Λ_c^+\bar Λ_c^- \bar K$ and $\bar B\to Λ_c^+\bar Λ_c^-$ are of order $3.5\times 10^{-4}$ and $5\times 10^{-5}$, respectively, in agreement with experiment except that the prediction for the $Λ_c\barΛ_c K^-$ is slightly smaller. In conjunction with our previous analysis, we conclude that the enormously large rate of $\bar B\to Λ_c^+\bar Λ_c^-\bar K$ arises from the resonances $Ξ_c(2980)$ and X(4630).