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

Abstract

With the experimental evidences of $\overline{B}{}^0\to p\overline{p}$ and $B^{-}\to \Lambda \overline{p}$ 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 ${\overline{B}}_q\to \mathcal{B}\overline{\mathcal{B}}$, $\mathcal{B}\overline{\mathcal{D}}$, $\mathcal{D}\overline{\mathcal{B}}$ and $\mathcal{D}\overline{\mathcal{D}}$ decay rates, where $\mathcal{B}$ and $\mathcal{D}$ 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 $\overline{B}{}^0\to p\overline{p}$ and $B^{-}\to \Lambda \bar{p}$ modes are the first two modes with experimental evidences. Relations on rates are verified using the numerical results. We note that the predicted $B^{-}\to p\overline{{\Delta }^{++}}$ rate is close to the experimental bound, which has not been updated in the last ten years. Direct $CP$ asymmetries of all ${\overline{B}}_q\to \mathcal{B}\overline{\mathcal{B}}$, $\mathcal{B}\overline{\mathcal{D}}$, $\mathcal{D}\overline{\mathcal{B}}$ and $\mathcal{D}\overline{\mathcal{D}}$ modes are explored. Relations on $CP$ asymmetries are examined using the numerical results. The direct $CP$ asymmetry of $\overline{B}{}^0\to p\overline{p}$ decay can be as large as $\pm 50\%$. The $CP$ asymmetries of $\Delta S=-1$ pure penguin modes are constrained to be of few $\%$. 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.

Comments: To appear in Phys. Rev. D, 58 pages, 3 figures, 17 tables, some useful formulas from arXiv:1312.2335 are collected (with minor correction) in appendices