The Scalar $B \to \pi$ and $D \to \pi$ Form Factors in QCD

QCD sum rules on the light-cone are derived for the sum $f^+ + f^-$ of the $B\to \pi$ and $D\to \pi$ 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 $B \to \pi \bar{\tau}\nu_\tau$ 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.