Factorization and Sudakov Resummation in

Soft-collinear effective theory is used to prove factorization of the B → γlν decay amplitude at leading power in Λ/mb, including a demonstration of the absence of non-valence Fock states and of the finiteness of the convolution integral in the factorization formula. Large logarithms entering the hard-scattering kernel are resummed by performing a two-step perturbative matching onto the low-energy effective theory, and by solving evolution equations derived from the renormal-ization properties of the leading-order B-meson light-cone distribution amplitude. As a byproduct, the evolution equation for heavy-collinear current operators in soft-collinear effective theory is derived. *Work supported by Department of Energy contract DE-AC03-76SF00515.