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

TL;DR

This paper extends the understanding of the infrared structure of two-loop scattering amplitudes to theories with mixed gauge groups, providing explicit anomalous dimensions for such complex gauge interactions.

Contribution

It computes the two-loop amplitudes for specific processes in an $SU(N) imes SU(M) imes U(1)$ gauge theory, revealing the infrared structure and anomalous dimensions for mixed gauge groups.

Findings

Determined the two-loop infrared structure for mixed gauge group amplitudes.

Computed anomalous dimensions for processes in $SU(N) imes SU(M) imes U(1)$.

Extended known infrared structure results beyond pure QCD.

Abstract

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 $\bar{f}\,f\longrightarrow X$ and $\bar{f}\,f\longrightarrow V_1\,V_2$ scattering in an $SU(N)\times SU(M)\times U(1)$ gauge theory, I determine the anomalous dimensions which govern the infrared structure for any massless two-loop amplitude.