Infrared behavior of zero-mass Green's functions and the absence of quark confinement in perturbation theory

We present a simple proof that all Green's functions for nonexceptional Euclidean momenta in any renormalizable (but not superrenormalizable) field theory containing zero-mass particles are infrared finite. We discuss the relationship of a corollary result, that any physical discontinuity of Green's functions is also infrared finite, to the question of quark confinement in non-Abelian gauge theories.