Large CP Asymmetries from Final-State Interactions in Charmful Baryonic Decays of $B^0 \to \Xi_c^+ \overline{\Xi}_c^-$ and $B_s^0 \to \Lambda_c^+ \overline{\Lambda}_c^-$

We study the direct CP asymmetries in the decays of $B^0 \to \Xi_c^+ \overline{\Xi}_c^-$ and $B_s^0 \to \Lambda_c^+ \overline{\Lambda}_c^-$, emphasizing the critical role of final-state interactions (FSIs). In these channels, the small energy release and annihilation topology suppress short-distance contributions while enhancing long-distance effects. By separating the decay amplitudes into S and P waves, we show that the P-wave component, carrying only a single weak phase, contributes negligibly to CP asymmetries. In contrast, the S-wave amplitude, strongly modified by FSIs, acquires a substantial strong phase that enables interference among multiple weak phases, producing large CP-violating effects. Numerically, we find sizable asymmetries of $a_{CP}^{\text{dir}} = 0.88 \pm 0.05 \pm 0.10$ for $B^0 \to \Xi_c^+ \overline{\Xi}_c^-$ and $a_{CP}^{\text{dir}} = -0.106 \pm 0.019 \pm 0.010$ for $B_s^0 \to \Lambda_c^+ \overline{\Lambda}_c^-$, where the first and second uncertainties stem from the poorly known hadron couplings and the omission of the $B^0 \to K^+ K^- \to \Xi_c^+ \overline{\Xi}_c^-$ rescattering process. For practical feasibility, we restrict our analysis to intermediate states involving pseudoscalar mesons, which yield tractable loop integrals. Excited intermediate states, such as $D^{(*)} \overline{D}^{(*)}$, are omitted because their inclusion would require handling non-renormalizable interactions, introducing substantial ambiguity. These results, combined with the relatively large branching fractions, make these modes prime targets for experimental searches at LHCb and Belle II, potentially offering new insights into strong dynamics and nonperturbative QCD in heavy-hadron decays.