Rates and $CP$ asymmetries of Charmless Two-body Baryonic $B_{u,d,s}$ Decays

With the experimental evidences of $\bar{B}{}^0\to p\bar{p}$ and $B^{-}\to \mathrm{\Lambda }\bar{p}$ decays, it is now possible to extract both tree and penguin amplitudes of the charmless two-body baryonic $B$ decays for the first time. The extracted penguin-tree ratio agrees with the expectation. Using the topological amplitude approach with the experimental results on $\overline B {}^0\to p \overline{p}$and$B^-\to\Lambda\bar p$ decay rates as input, predictions on all other ${\bar{B}}_q\to \mathcal{B}\bar{\mathcal{B}}$, ${\cal B} \overline {\cal D}$,${\cal D} \overline {\cal B}$and${\cal D} \overline {\cal D}$decayrates,where${\mathcal B}$and${\cal D}$ are the low lying octet and decuplet baryons, respectively, are given. It is non-trivial that the results do not violate any existing experimental upper limit. From the analysis it is understandable that why $\bar{B}{}^0\to p\bar{p}$ and $B^{-}\to \mathrm{\Lambda }\bar{p}$ modes are the first two modes with experimental evidences. Relations on rates are verified using the numerical results. We note that the predicted $B^{-}\to p\overline{{\mathrm{\Delta }}^{++}}$ rate is close to the experimental bound, which has not been updated in the last ten years. Direct $CP$ asymmetries of all ${\bar{B}}_q\to \mathcal{B}\bar{\mathcal{B}}$, ${\cal B} \overline {\cal D}$,${\cal D} \overline {\cal B}$and${\cal D} \overline {\cal D}$modesareexplored\mathrm{.}Relationson$CP$ asymmetries are examined using the numerical results. The direct $CP$ asymmetry of $\overline B {}^0\to p \overline{p}$decaycanbeaslargeas$\pm 50%$\mathrm{.}The$CP$asymmetriesof$\Delta S=-1$purepenguinmodesareconstrainedtobeoffew$%$. These modes are expected to be sensitive to New Physics contributions and are good candidates to be added to the list of the tests of the Standard Model.