Hidden strangeness in meson weak decays to baryon pair

We study the weak decays of heavy mesons into baryon pairs, focusing on channels dominated by annihilation-type diagrams, where short-distance (SD) contributions are highly suppressed. We focus on decays with small energy release to further ensure the dominance of long-distance (LD) physics. The final state interactions of the triangular diagrams do not require a cutoff, making our numerical results reliable. Moreover, the hidden strangeness in the intermediate state naturally avoids chiral suppression. The branching fractions are predicted to be ${\cal B}(D_s^+ \to p\overline{n}) = (1.43 \pm 0.10 ) \times 10^{-3}$ and ${\cal B} (B_s^0 \to \Lambda_c^+ \overline{\Lambda}_c^-) > 4.7 \times 10^{-5}$, respectively. The former is in agreement with the experimental data of $(1.22 \pm 0.11)\times 10^{-3}$, while the latter suggests that a measurement is now feasible. Using the experimental upper bound of ${\cal B} (B_s^0 \to \Lambda_c^+ \overline{\Lambda}_c^-) < 8 \times 10^{-5}$, we set a constraint on the coupling constant $g_{D^+ \Lambda_c^+ n} < 7.5$. The CP symmetry suggests that $B_{sH/L}^0 \to \Lambda_c^+ \overline{\Lambda}_c^-$ is dominated by $P/S$ wave. This selection rule distinguishes the SD and LD contributions, allowing experiments to further test our understanding in the nonperturbative region. We propose future measurements on $B^0 \to \Xi_c^+ \overline{\Xi}_c^-$ to test final state interaction mechanisms, predicting significant $SU(3)_F$ breaking effects with ${\cal B}(B^0 \to \Xi_c^+ \overline{\Xi}_c^-) / {\cal B} (B_s^0 \to \Lambda_c^+ \overline{\Lambda}_c^-) = 1.4\%$, contrary to the naive estimate of $5.3\%$.