Threshold resummation for exclusive<i>B</i>meson decays

We argue that double logarithmic corrections ${\ensuremath{\alpha}}_{s}{\mathrm{ln}}^{2}x$ need to be resummed in the perturbative QCD factorization theorem for exclusive B meson decays, when the end-point region with a momentum fraction $\stackrel{\ensuremath{\rightarrow}}{x}0$ is important. These double logarithms, being of collinear origin, are absorbed into a quark jet function, which is defined by a matrix element of a quark field attached by a Wilson line. The factorization of the jet function from the decay $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\gamma}l\overline{\ensuremath{\nu}}$ is proved to all orders. Threshold resummation for the jet function leads to a universal, i.e., process-independent, Sudakov factor, whose qualitative behavior is analyzed and found to smear the end-point singularities in heavy-to-light transition form factors.