Hadronic decays of B_c mesons with flavor SU(3)_F symmetry

We study implications of a recent observation of non-leptonic $B^+_c\to D^0 K^+$decayandaboundon$B^+_c\to D^0 \pi^+$ transition on CP-violating asymmetries in $B_c$ decays. In the U-spin symmetry limit, we derive a relation between the CP-asymmetries in the $B_c^{+}\to D^0{K}^{+}$ and $B_c^{+}\to D^0{\pi }^{+}$ channels and the corresponding branching ratios. We also derive several relations between non-leptonic $B_c$ decays into the final states with $D$ mesons in the flavor $SU(3{)}_F$ limit. We point out that a combined study of $SU(3{)}_F$ amplitudes in these decays can be used to constrain the angle $\gamma$ of the Cabibbo-Kobayashi-Maskawa (CKM) matrix.