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

Abstract

We study the doubly charmful two-body and three-body baryonic B decays $\bar{B}\to {\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}$ and $\bar{B}\to {\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}\bar{K}$. As pointed out before, a naive estimate of the branching ratio $\mathcal{O}(10^{-8})$ 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 ${\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}\bar{K}$ production can occur due to a charmonium-like resonance (e.g. X(4630) discovered by Belle) with a mass near the ${\Lambda }_c{\bar{\Lambda }}_c$ threshold. Motivated by the BaBar's observation of a resonance in the ${\Lambda }_c\bar{K}$ system with a mass of order 2930 MeV, we study in this work the contribution to $\bar{B}\to {\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}\bar{K}$ from the intermediate state ${\Xi }_c(2980)$ 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 $\sigma$ and $\pi$ meson exchanges in the configuration for $\bar{B}\to {\Xi }_c(2980){\bar{\Lambda }}_c$ and ${\Lambda }_c{\bar{\Lambda }}_c$, it is found that branching ratios of $\bar{B}\to {\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}\bar{K}$ and $\bar{B}\to {\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}$ are of order $3.5\times 10^{-4}$ and $5\times 10^{-5}$, respectively, in agreement with experiment except that the prediction for the ${\Lambda }_c{\bar{\Lambda }}_c{K}^{-}$ is slightly smaller. In conjunction with our previous analysis, we conclude that the enormously large rate of $\bar{B}\to {\Lambda }_c^{+}{\bar{\Lambda }}_c^{-}\bar{K}$ arises from the resonances ${\Xi }_c(2980)$ and X(4630).

Comments: 16 pages, 3 figures, 3 tables, version to appear in PRD