The Study of Rare $B_c\to D_{s,d}^{(\ast )}l\bar{l}$ Decays

In this paper, we study rare decays $B_c\to D_{s,d}^{(\ast )}l\bar{l}$ within the Standard Model. The penguin, box, annihilation, color-favored cascade and color-suppressed cascade contributions are included. Based on our calculation, the annihilation and color-favored cascade diagrams play important roles in the differential branching fractions, forward-backward asymmetries, longitudinal polarizations of the final vector mesons and leptonic longitudinal polarization asymmetries. More importantly, color-favored cascade decays largely enhance the resonance cascade contributions. To avoid the resonance cascade contribution pollution, new cutting regions are put forward.