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

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 $B^-\to Λ\bar p$, $B^-\to Σ^0 \bar p$ and $\bar B^0_s\to Λ\bar Λ$ 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 ${\cal B}(B\to {\bf B\bar B'})$ 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 ${\cal B}(\bar B^0_{(s)}\to p\bar p)$ of order $10^{-8}$ and ${\cal B}(D_s^+\to p\bar n)$ of order $10^{-3}$, which are from the axial-vector currents. In addition, the branching ratios of $\bar B^0\to Λ\bar Λ$, $B^-\to n\bar p$, and $B^-\to Σ^- \barΣ^0$ 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.