Exploring CP Violation with $B_c$ Decays

We point out that the pure ``tree’’ decays $B_c^{\pm }\to D_s^{\pm }D$ are particularly well suited to extract the CKM angle $\gamma$ through amplitude relations. In contrast to conceptually similar strategies using $B^\pm\to K^\pm D$or$B_d\to K^{\ast0} D$decays,theadvantageofthe$B_c$ approach is that the corresponding triangles have three sides of comparable length and do not involve small amplitudes. Decays of the type $B_c^{\pm }\to D^{\pm }D$ – the $U$-spin counterparts of $B_c^{\pm }\to D_s^{\pm }D$ – can be added to the analysis, as well as channels, where the $D_s^{\pm }$- and $D^{\pm }$-mesons are replaced by higher resonances.