Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes

TL;DR

This paper demonstrates the cancellation of low transcendental weight terms in two-loop supersymmetric QCD amplitudes through a carefully chosen IR subtraction scheme, revealing new insights into the structure of divergences and finite parts.

Contribution

It introduces a novel IR subtraction scheme that cancels low-weight transcendental terms in two-loop amplitudes of supersymmetric QCD, extending previous superconformal results.

Findings

Cancellation of weight-0,1,2 terms in finite parts

Explicit expressions for two-loop amplitudes with matter and vectors

Determination of two-loop cusp and anomalous dimensions

Abstract

Using a careful choice of infrared (IR) subtraction scheme, we demonstrate the cancellation of all terms with transcendental weights 0,1,2 from the finite part of the full-color two-loop four-gluon $\mathcal{N}=2$ 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 $\epsilon=(4-D)/2$. 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 $\mathcal{N}=2$ supersymmetric QCD, which are cross-checked between the three different amplitudes.