Two-body baryonic Bu,d,s and Bc to charmless final state decays

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We study the rates and direct $CP$ violations of two-body baryonic ${\overline{B}}_{u,d,s}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ and ${B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ decays, where the final state baryons include low-lying octet and decuplet baryons. We incorporate topological amplitude formalism and the factorization approach. Asymptotic relations at large ${m}_{b}$ are used to simplify decay amplitudes. Using the most up-to-date data on ${\overline{B}}^{0}\ensuremath{\rightarrow}p\overline{p}$ and ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\overline{p}$ decay rates as inputs, rates and direct $CP$ violations of ${\overline{B}}_{u,d,s}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ decays are revised and predicted. It is interesting that the results on rates satisfy all existing experimental bounds and some are close to the bounds. Factorization diagrams contribute to penguin-exchange, exchange, annihilation, and penguin-annihilation amplitudes. Although the resulting penguin-exchange factorization amplitudes are sizable, the rest suffer from severe chiral suppression and are sensitive to nonfactorizable contributions. As the ${\overline{B}}_{s}\ensuremath{\rightarrow}p\overline{p}$ decay is governed by exchange and penguin annihilation amplitudes, the rate predicted in factorization calculation is very rare, but it can be enhanced by including nonfactorizable contributions. The case where the rate is enhanced to saturate the present experimental bound through the enhancement on exchange or penguin-annihilation amplitudes is discussed. As annihilation modes ${B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ decays from factorization calculation are found to be very rare, but they can be enhanced by including nonfactorizable contributions as well. Small direct $CP$ violations of pure penguin modes in $\mathrm{\ensuremath{\Delta}}S=\ensuremath{-}1$ ${\overline{B}}_{u,d,s}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ decays are robust predictions of the SM, while vanishing direct $CP$ violations of exchange modes in ${\overline{B}}_{u,d,s}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ decays and in all ${B}_{c}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathbf{\text{B}}\overline{\mathbf{\text{B}}}}^{\ensuremath{'}}$ decay modes are null tests of the SM.