$B$-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 ${\varphi }_{+}^B$. 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.

11 pages, 1 figure, version to appear in Phys.Lett.B