Leading order QCD corrections to the heavy to light meson transition form factor

Abstract

We calculate $O\left({\alpha }_s\right)$ corrections to the soft, wave-function-dependent, normalization $f_{+}\mathrm{}\left(0\right)\mathrm{}$ of the matrix element $〈\pi \left|\overline{q}{\gamma }^{\mu }Q\right|B〉$. We find these corrections to be large and strongly dependent on the meson wave functions in the momentum region where propagators in the hard amplitude become soft. The findings are compared with recent results for the $B\to \pi l\overline{\nu }$ branching ratio reported by CLEO.