  The $B$-meson light-cone distribution amplitude is a central quantity
governing non-perturbative hadronic dynamics in exclusive $B$ decays. We show
that the information needed to describe such processes at leading power in
$\Lambda_{\rm QCD}/m_b$ is most directly contained in its Laplace transform
$\tilde\phi_+(\eta)$. We derive the renormalization-group (RG) equation
satisfied by this function and present its exact solution. We express the
RG-improved QCD factorization theorem for the decay $B^-\to\gamma\ell^-\bar\nu$
in terms of $\tilde\phi_+(\eta)$ and show that it is explicitly independent of
the factorization scale. We propose an unbiased parameterization of
$\tilde\phi_+(\eta)$ in terms of a small set of uncorrelated hadronic
parameters.
