$B \to D^{(*)}$ form factors in perturbative QCD

Abstract

We calculate the $B\to D^{(*)}$ form factors in the heavy-quark and large-recoil limits in the perturbative QCD framework based on $k_T$ factorization theorem, assuming the hierachy $M_B\gg M_{D^{(*)}}\gg \bar\Lambda$, with the $B$ meson mass $M_B$, the $D^{(*)}$ meson mass $M_{D^{(*)}}$, and the heavy meson and heavy quark mass difference $\bar\Lambda$. The qualitative behavior of the light-cone $D^{(*)}$ meson wave function and the associated Sudakov resummation are derived. The leading-power contributions to the $B\to D^{(*)}$ form factors, characterized by the scale $\bar\Lambda\sqrt{M_B/M_{D^{(*)}}}$, respect the heavy-quark symmetry. The next-to-leading-power corrections in $1/M_B$ and $1/M_{D^{(*)}}$, characterized by a scale larger than $\sqrt{\bar\Lambda M_B}$, are estimated to be less than 20%. The $D^{(*)}$ meson wave function is determined from the fit to the observed $B\to D^{(*)} l\nu$ decay spectrum, which can be employed to make predictions for nonleptonic decays, such as $B\to D^{(*)}\pi(\rho)$.