Prediction of $B_c\to Dπ$ in the pQCD approach

Abstract

We investigate the branching ratios and direct CP asymmetries of $B_c^+\to D^0π^+$ and $B_c^+\to D^+π^0$ decays in the PQCD approach. All the diagrams with emission topology or annihilation topology are calculated strictly. A branching ratio of $10^{-6}$ and $10^{-7}$ for $B_c^+\to D^0π^+$ and $B_c^+\to D^+π^0$ decay is predicted, respectively. Because of the different weak phase and strong phase from penguin operator and two kinds of tree operator contributions, we predict a possible large direct CP violation: $A^{\rm dir}_{cp} (B_c^\pm \to D^0 π^\pm)\approx -50%$ and $A^{\rm dir}_{cp} (B_c^\pm \to D^\pm π^0)\approx 25%$ when $γ=55^\circ$, which can be tested in the coming LHC.