Infrared structure of non-Abelian gauge theories

Abstract

The infrared structure of non-Abelian gauge theories is studied explicitly in the lowest nontrivial order in the coupling constant for fermion-fermion and fermion-gauge-boson scattering cross sections. The cancellation of the infrared-divergent terms is realized in physically sensible cross sections when they are expanded in a power series in the bare coupling constant, a situation similar to quantum electrodynamics. However, the renormalization of the coupling constant introduces another infrared singularity, so that the physically sensible cross sections of order ${\left(g_{\mathrm{ren}}\right)}^6$ are infrared divergent. This situation is completely foreign to the case of quantum electrodynamics.