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The branching ratios and CP violations of the $B\to D\pi$ decays, includingboth the color-allowed and the color-suppressed modes, are investigated indetail within QCD framework by considering all diagrams which lead to threeeffective currents of two quarks. An intrinsic mass scale as a dynamical gluonmass is introduced to treat the infrared divergence caused by the softcollinear approximation in the endpoint regions, and the Cutkosky rule isadopted to deal with a physical-region singularity of the on mass-shell quarkpropagators. When the dynamical gluon mass $\mu_g$ is regarded as a universalscale, it is extracted to be around $\mu_g = 440$ MeV from one of thewell-measured $B\to D\pi$ decay modes. The resulting predictions for allbranching 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 theCabibbo-favored amplitudes, mixing-induced CP violations are predicted in the$B\to D^{\pm}\pi^{\mp}$ decays to be consistent with the experimental data at1-$\sigma$ level. More precise measurements will be helpful to extract weakangle $2\beta+\gamma$.

QCD Approach to B->D \pi Decays and CP Violation