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

Abstract

The study of two-body charmed anti-charmed baryonic $\overline B\to {\bf B}_c \overline {\bf B}_c$ 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 $\overline B\to {\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf { 3_f})$, ${\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf {\bar 6_f})$ and ${\bf B}_c(\bf 6_f) \overline {\bf B}_c(\bf {\bar 6_f})$ 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 $\overline B\to {\bf B}_c(\bf {\bar 3_f}) \overline {\bf B}_c(\bf { 3_f})$ 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 $\overline B\to {\bf B}_c \overline {\bf B}_c$ decays.