Violation of PCAC and two-body baryonic $B$ and $D_s$ decays

Abstract

We study the two-body baryonic $B$ and $D_s$ decays based on the annihilation mechanism without the partial conservation of axial-vector current (PCAC) at the GeV scale. We demonstrate that the contributions of $B^{-}\to \Lambda \bar{p}$, $B^{-}\to {\Sigma }^0\bar{p}$ and ${\bar{B}}_s^0\to \Lambda \bar{\Lambda }$ are mainly from the scalar and pseudoscalar currents with their branching ratios predicted to be around $(3.5,5.3,5.3)\times 10^{-8}$, respectively, exactly the sizes of $\mathcal{B}(B\to \mathbf{B}{\bar{\mathbf{B}}}^{\prime })$ established by the data. We also apply the annihilation mechanism to all of the charmless two-body baryonic $B$ and $D_s$ decays. In particular, we can explain $\mathcal{B}({\bar{B}}_{(s)}^0\to p\bar{p})$ of order $10^{-8}$ and $\mathcal{B}(D_s^{+}\to p\bar{n})$ of order $10^{-3}$, which are from the axial-vector currents. In addition, the branching ratios of ${\bar{B}}^0\to \Lambda \bar{\Lambda }$, $B^{-}\to n\bar{p}$, and $B^{-}\to {\Sigma }^{-}{\bar{\Sigma }}^0$ are predicted to be $(0.3,3.2,9.6)\times 10^{-8}$, which can be measured by LHCb and viewed as tests for the violation of PCAC at the GeV scale.

Comments: 12 pages, 1 figure, revised version accepted by PRD