Factorization and Sudakov resummation in leptonic radiativeBdecay

Soft-collinear effective theory is used to prove factorization of the $\overrightarrow{B}\gamma l\nu$ decay amplitude at leading power in $\Lambda {/m}_b,$ including a demonstration of the absence of nonvalence 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 renormalization properties of the leading-order B-meson light-cone distribution amplitude. As a by-product, the evolution equation for heavy-collinear current operators in soft-collinear effective theory is derived.