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The infrared structure of (multi-loop) scattering amplitudes is determinedentirely by the identities of the external particles participating in thescattering. The two-loop infrared structure of pure \qcd\ amplitudes has beenknown for some time. By computing the two-loop amplitudes for$\bar{f}\,f\longrightarrow X$ and $\bar{f}\,f\longrightarrow V_1\,V_2$scattering in an $SU(N)\times SU(M)\times U(1)$ gauge theory, I determine theanomalous dimensions which govern the infrared structure for any masslesstwo-loop amplitude.

The Two-Loop Infrared Structure of Amplitudes with Mixed Gauge Groups