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

Abstract

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

Comments: 17 pages, 9 figures, revtex and epsfig.sty, 1 figure and references added, some comments are added