Applicability of Perturbative QCD to $B\to D$ Decays

We examine the applicability of perturbative QCD to $B$ meson decays into $D$ mesons. We find that the perturbative QCD formalism, which includes Sudakov effects at intermediate energy scales, is applicable to the semi-leptonic decay $B\to D l\nu$, when the $D$ meson recoils fast. Following this conclusion, we analyze the two-body non-leptonic decays $B\to D\pi$ and $B\to DD_s$. By comparing our predictions with experimental data, we extract the matrix element $|V_{cb}|=0.044$.