$B$-Meson Distribution Amplitude from the $B\to \pi$ Form Factor

Abstract

Employing the light-cone sum rule approach in QCD, we relate the $B$-meson distribution amplitude to the $B\to \pi$ form factor at zero momentum transfer. In leading order, the sum rule is converted into a simple expression for the inverse moment $\lambda_B$ of the distribution amplitude $\phi_{+}^B$. Using as an input the $B\to\pi$ form factor calculated from the light-cone sum rule in terms of pion distribution amplitudes, we obtain an estimate: $\lambda_B =460 \pm 160 $ MeV. We investigate how this result is modified by the $B$-meson three-particle distribution amplitudes.