Fixed-angle scattering in quantum field theory

We have examined the high-energy, fixed-angle behavior of exclusive scattering amplitudes in the context of renormalizable field theories. We find that renormalization-group techniques, asymptotic conformal invariance, and reasonable conjectures about the existence of the zero-mass limit of such theories allow one to understand simple power laws for fixed-angle scattering of the type proposed by Brodsky and Farrar and Matveev et al. Since our techniques rely on the existence of a smooth infrared limit of the underlying quantum field theory, they are unfortunately not powerful enough to discuss theories with vector mesons. Consequently, it remains moot whether the classical examples of asymptotically free theories really manifest simple fixed-angle scaling.