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 ${\varphi }_{+}^B(\omega ,\mu )$, defined with a cutoff $\omega \le {\Lambda }_{\mathrm{UV}}$. The leading hadronic power corrections are given in terms of the parameter $\overline{\Lambda }=m_B-m_b$. 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 $\omega \gg \mu$. By solving the evolution equation for the distribution amplitude, an integral representation for ${\varphi }_{+}^B(\omega ,\mu )$ is obtained in terms an initial function ${\varphi }_{+}^B(\omega ,{\mu }_0)$ 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 ${\lambda }_B$.

• Received 29 September 2005

DOI:https://doi.org/10.1103/PhysRevD.72.094028