Study of Λ⁰_b to Λ D decays with the rescattering mechanism

We employ the final-state rescattering mechanism to systematically investigate the non-leptonic decays $\Lambda_b^0 \to \Lambda D$ (where $D = D^0$, $\overline{D}^0$, $D_+$, $D_-$), which can help improve the experimental precision of the $CP$-violating phase angle $\gamma$. The framework integrates short-distance factorizable amplitudes with long-distance non-factorizable contributions arising from hadronic triangle rescattering diagrams. We find that the final-state rescattering contributions are essential, not only because they provide the strong phases necessary for $CP$ violation, but also because they enhance the $\overline{D}^0 \Lambda$ branching fraction by two orders of magnitude. Numerically, we calculate the branching ratios of the channels with different partial waves, as well as the corresponding $CP$-violating observables. In particular, the direct $CP$ asymmetries $a_{CP}^{\mathrm{dir}}(D_+) = 0.28^{+0.07}_{-0.11}$ and $a_{CP}^{\mathrm{dir}}(D_-) = -0.14^{+0.06}_{-0.04}$ are found to be very significant. These results provide a reliable theoretical benchmark and can be tested against future measurements from the LHCb experiment.