Calculation of the $B \to \pi $ Transition Matrix Element in QCD

Abstract

We describe the calculation of the $B\rightarrow \pi$ hadronic matrix element from operator product expansion near the light-cone in QCD. In the resulting sum rules, the form factors $f^+$ and $F_0$ determining this matrix element are expressed in terms of pion light-cone wave functions. We present predictions for $f^+$ and $F_0$ in the region of momentum transfer $0 \leq p^2 < m_b^2 - {\cal O}(\mbox{1 GeV}^2)$ taking into account the wave functions up to twist 4. We also discuss the extrapolation of the form factors to higher $p^2$ and their asymptotic dependence on the heavy quark mass.