The two-loop infrared structure of amplitudes with mixed gauge groups

The infrared structure of (multi-loop) scattering amplitudes is determined entirely by the identities of the external particles participating in the scattering. The two-loop infrared structure of pure QCD amplitudes has been known for some time. By computing the two-loop amplitudes for ff⟶ X and ff⟶ V_1V_2 scattering in an SU ( N )× SU ( M )× U (1) gauge theory, I determine the anomalous dimensions which govern the infrared structure for any massless two-loop amplitude.