Prediction of $B_c\to D\pi$ in the pQCD approach

Abstract

We investigate the branching ratios and direct CP asymmetries of $B_c^{+}\to D^0{\pi }^{+}$ and $B_c^{+}\to D^{+}{\pi }^0$ 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 $B_c^{+}\to D^0{\pi }^{+}$ and $B_c^{+}\to D^{+}{\pi }^0$ 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: $A_{cp}^{\mathrm{dir}}(B_c^{\pm }\to D^0{\pi }^{\pm })\approx -50$ and $A_{cp}^{\mathrm{dir}}(B_c^{\pm }\to D^{\pm }{\pi }^0)\approx 25$ when $\gamma =55^{\circ }$, which can be tested in the coming LHC.

Comments: The numerical results have been updated and some errors have been corrected. (10 pages, 16 figures, revtex4)