$D^{\ast }D\pi$ and $B^{\ast }B\pi$ couplings in QCD

We calculate the $D^{\ast }D\pi$ and $B^{\ast }B\pi$ couplings using QCD sum rules on the light-cone. In this approach, the large-distance dynamics is incorporated in a set of pion wave functions. We take into account two-particle and three-particle wave functions of twist 2, 3 and 4. The resulting values of the coupling constants are $g_{D^{\ast }D\pi }=12.5\pm 1$ and $g_{B^{\ast }B\pi }=29\pm 3$. From this we predict the partial width $ \Gamma (D^{*+} \ra D^0 \pi^+ )=32 \pm 5~ keV $. We also discuss the soft-pion limit of the sum rules which is equivalent to the external axial field approach employed in earlier calculations. Furthermore, using $g_{B^{\ast }B\pi }$ and $g_{D^{\ast }D\pi }$ the pole dominance model for the $B\text{ra}\pi$ and $D\text{ra}\pi$ semileptonic form factors is compared with the direct calculation of these form factors in the same framework of light-cone sum rules.