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

Abstract

We compute various form factors involved in $B\to D^{(\ast )}$ 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 $D^{(\ast )}$ mesons is fixed using data of the nonleptonic decays $B\to D^{(\ast )}\pi$, from which the ratio of the decay constants $f_{D^{\ast }}/f_D=0.92$ is obtained. We then derive the spectrum of the semileptonic decay $B\to D^{\ast }\ell \nu$ in the fast recoil region of the $D^{\ast }$ meson, and extract the CKM matrix element $|V_{cb}|=0.043\times (0.12\mathrm{GeV}/f_B)\times (0.14\mathrm{GeV}/f_D)$, $f_B$ 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 $B\to D{D}_s$, 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.

Comments: 19 pages in Latex, 7 figures in ps