Model-independent properties of the B -meson distribution amplitude

The operator product expansion is used to obtain model-independent predictions for the first two moments of the renormalized $B$-meson light-cone distribution amplitude ${\ensuremath{\phi}}_{+}^{B}(\ensuremath{\omega},\ensuremath{\mu})$, defined with a cutoff $\ensuremath{\omega}\ensuremath{\le}{\ensuremath{\Lambda}}_{\mathrm{UV}}$. The leading hadronic power corrections are given in terms of the parameter $\overline{\ensuremath{\Lambda}}={m}_{B}\ensuremath{-}{m}_{b}$. From the cutoff dependence of the zeroth moment an analytical expression for the asymptotic behavior of the distribution amplitude is derived, which exhibits a negative radiation tail for $\ensuremath{\omega}\ensuremath{\gg}\ensuremath{\mu}$. By solving the evolution equation for the distribution amplitude, an integral representation for ${\ensuremath{\phi}}_{+}^{B}(\ensuremath{\omega},\ensuremath{\mu})$ is obtained in terms an initial function ${\ensuremath{\phi}}_{+}^{B}(\ensuremath{\omega},{\ensuremath{\mu}}_{0})$ defined at a lower renormalization scale. A realistic model of the $B$-meson light-cone distribution amplitude is proposed, which satisfies the moment relations and has the correct asymptotic behavior. This model provides an estimate for the first inverse moment and the associated parameter ${\ensuremath{\lambda}}_{B}$.