QCD Approach to B → Dπ Decays and CP Violation

The branching ratios and CP violations of the B → Dπ decays, including both the color-allowed and the color-suppressed modes, are investigated in detail within QCD framework by considering all diagrams that lead to three effective currents of two quarks. An intrinsic mass scale as a dynamical gluon mass is introduced to treat the infrared divergence caused by the soft collinear approximation in the endpoint regions, and the Cutkosky rule is adopted to deal with a physical-region singularity of the on mass-shell quark propagators. When the dynamical gluon mass μg is regarded as a universal scale, it is extracted to be around μg = 440 MeV from one of the well-measured B → Dπ decay modes. The resulting predictions for all branching ratios are in agreement with the current experimental measurements. As these decays have no penguin contributions, there are no direct CP asymmetries. Due to interference between the Cabibbo-suppressed and the Cabibbo-favored amplitudes, mixing-induced CP violations are predicted in the B → D±πmp decays to be consistent with the experimental data at 1-σ level. More precise measurements will be helpful to extracting weak angle 2β + γ.