Infrared Safe but Infinite: Soft-Gluon Divergences Inside the Physical Region∗

We show that QCD observables defined as infraredand collinear-safe, according to the usual Sterman-Weinberg criteria, can nevertheless be infinite at accessible points inside phase space, to any finite order of perturbation theory. Infrared finiteness is restored after resummation of divergent terms to all orders. The resulting characteristic structure, which we call a Sudakov shoulder, represents an interesting new class of QCD predictions. Research supported in part by the U.K. Science and Engineering Research Council and by the EC Programme “Human Capital and Mobility”, Network “Physics at High Energy Colliders”, contract CHRXCT93-0357 (DG 12 COMA).