Revisiting two-body charmed anti-charmed baryonic $B$ decays

Abstract

The study of two-body charmed anti-charmed baryonic $\overline{B}\to {\mathbf{B}}_c{\overline{\mathbf{B}}}_c$ decays using the topological amplitude approach is revisited. We include the $b\to u\bar{u}q$ contributions, in addition to the $b\to c\bar{c}q$ contributions, to these decays. The topological decomposition of $\overline{B}\to {\mathbf{B}}_c({\bar{3}}_{\mathbf{f}}){\overline{\mathbf{B}}}_{\mathbf{c}}(3_{\mathbf{f}})$, ${\mathbf{B}}_c(6_{\mathbf{f}}){\overline{\mathbf{B}}}_{\mathbf{c}}(3_{\mathbf{f}})$, ${\mathbf{B}}_c({\bar{3}}_{\mathbf{f}}){\overline{\mathbf{B}}}_{\mathbf{c}}({\bar{6}}_{\mathbf{f}})$ and ${\mathbf{B}}_c(6_{\mathbf{f}}){\overline{\mathbf{B}}}_{\mathbf{c}}({\bar{6}}_{\mathbf{f}})$ decay amplitudes are updated accordingly. Although the $b\to u\bar{u}q$ contributions are CKM suppressed in $\Delta S=-1$ transitions, their effects are significantly amplified in $\Delta S=0$ transitions, as the relative size of the CKM factors in $b\to u\bar{u}q$ and $b\to c\bar{c}q$ contributions in $\Delta S=0$ transitions is enlarged by ${\lambda }^{-2}$, roughly a factor of 20, from the one in $\Delta S=-1$ transitions. Present data in $\overline{B}\to {\mathbf{B}}_c({\bar{3}}_{\mathbf{f}}){\overline{\mathbf{B}}}_{\mathbf{c}}(3_{\mathbf{f}})$ decay rates allow or even slightly prefer non-negligible $b\to u\bar{u}q$ contributions. These $b\to u\bar{u}q$ contributions can allow much larger rates for $B^{-}\to {\Xi }_c^0{\bar{\Xi }}_c^{-}$, $\overline{B}{}_s^0\to {\Lambda }_c^{+}{\bar{\Xi }}_c^{-}$ and $\overline{B}{}^0\to {\Xi }_c^{+}{\bar{\Xi }}_c^{-}$ decays than those only have $b\to c\bar{c}d$ contributions. Measuring these decays will be interesting and useful in clarifying the role of $b\to u\bar{u}q$ contributions in two-body charmed anti-charmed baryonic $\overline{B}\to {\mathbf{B}}_c{\overline{\mathbf{B}}}_c$ decays.

Comments: 22 pages, 4 figures, 10 tables