Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes

Abstract

Abstract Using a careful choice of infrared (IR) subtraction scheme, we demonstrate cancellation of all terms with transcendental weights 0, 1, 2 from the finite part of the full-color two-loop four-gluon N $$ \mathcal{N} $$ = 2 supersymmetric QCD amplitude, with N f massless supersymmetric quarks. This generalizes the previously observed cancellation of weight-2 terms in the superconformal theory, where N f = 2N c for gauge group SU(N c ). The subtraction scheme follows naturally both from general IR factorization principles and from an integrand-level analysis of divergences in this amplitude. The divergences are written in terms of scalar triangle integrals whose expressions are known to all orders in the dimensional regulator ϵ = (4 − D)/2. We also present integrated expressions for the full-color two-loop four-point amplitudes with both matter and vectors on external legs in which lower-weight terms also cancel using an appropriate IR scheme. This provides us with values for the two-loop cusp, gluonic, and quark anomalous dimensions in N $$ \mathcal{N} $$ = 2 supersymmetric QCD, which are cross-checked between the three different amplitudes.

Keywords

• Scattering Amplitudes
• Supersymmetric Gauge Theory