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In this paper we calculate the weak form factors of the decays $B_c(B)\toDl\tilde\nu$ by using the chiral current correlator within the framework of theQCD light-cone sum rules (LCSR). The expressions of the form factors onlydepend on the leading twist distribution amplitude (DA) of the $D$ meson. Threemodels of the $D$-meson distribution amplitude are employed and the calculatedform factor $F_{B_c\to D}(0)$ is given. Our prediction, by using the $D$-mesondistribution amplitude with the exponential suppression at the end points, iscompatible with other approaches, and favors the three-points sum rules (3PSR)approach with the Coulumb corrections included.Comment: 12 pages, 3 figure

B c ( B )→ Dl tilde nu Form Factors in Light-Cone Sum Rules and the D -Meson Distribution Amplitude

B _c ( B )→ Dl tilde nu Form Factors in Light-Cone Sum Rules and the D -Meson Distribution Amplitude