Perturbative QCD study of $B\to D^{(*)}$ decays

We compute various form factors involved in $B\to D^{(*)}$ transitions based on the perturbative QCD formalism, which includes Sudakov effects from the resummation of large radiative corrections in a heavy-light system. A two-parameter model wave function for $D^{(*)}$ mesons is fixed using data of the nonleptonic decays $B\to D^{(*)}\pi$, from which the ratio of the decay constants $f_{D^*}/f_D=0.92$ is obtained. We then derive the spectrum of the semileptonic decay $B\to D^{*}\ell\nu$ in the fast recoil region of the $D^*$ meson, and extract the CKM matrix element $|V_{cb}|=0.043\times(0.12 {\rm GeV}/f_B)\times(0.14 {\rm GeV}/f_D)$, $f_B$ and $f_D$ being the $B$ and $D$ meson decay constants, respectively. Here we adopt the convention with the pion decay constant $f_\pi=93$ MeV. With these outcomes, we evaluate the decay rate of $B\to DD_s$, and estimate the ratio $f_{D_s}/f_D=0.98$ from data. Contributions of internal $W$-emission and $W$-exchange diagrams are briefly discussed.