$B_c(B){\to}D l\tilde{\nu}$ form factors in Light-Cone Sum Rules and the $D$-meson distribution amplitude

Abstract

In this paper we calculate the weak form factors of the decays $B_c(B)\to Dl\tilde\nu$ by using the chiral current correlator within the framework of the QCD light-cone sum rules (LCSR). The expressions of the form factors only depend on the leading twist distribution amplitude (DA) of the $D$ meson. Three models of the $D$-meson distribution amplitude are employed and the calculated form factor $F_{B_c\to D}(0)$ is given. Our prediction, by using the $D$-meson distribution amplitude with the exponential suppression at the end points, is compatible with other approaches, and favors the three-points sum rules (3PSR) approach with the Coulumb corrections included.