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Analytic continuation of the Sudakov form factor in QCD.

We exhibit a solution to the evolution equation for the Sudakov form factor in QCD with massless quarks, which exponentiates infrared poles in dimensional continuation as well as logarithms of momentum transfer. We use this solution to construct an expression for the absolute value of the ratio of timelike to spacelike form factors, in which the infrared finiteness of the ratio is manifest. Finally, we compare this result to explicit calculations of the form factor available in the literature. Most of the large two-loop corrections to the absolute value of the ratio come from the exponentiation of one-loop corrections, including the effect of the running coupling.