ScalarB→πandD→πform factors in QCD

QCD sum rules on the light cone are derived for the sum $f^{+}{+f}^{-}$ of the $\overrightarrow{B}\pi$ and $\overrightarrow{D}\pi$ form factors taking into account contributions up to twist four. Combining the results with the corresponding $f^{+}$ form factors calculated previously by the same method, we obtain the scalar form factors $f^0.$ Our sum rule predictions are compared with lattice results, current-algebra constraints, and quark-model calculations. Furthermore, we calculate decay distributions and the integrated width for the semileptonic decay $\overrightarrow{B}\pi \overline{\tau }{\nu }_{\tau }$ which is sensitive to $f^0.$ Finally, the dependence of the sum rules on the heavy quark mass and the asymptotic scaling laws are discussed.