Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes

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.

36 pages + appendices + references; v2: fixed references and minor typos

References in corpus (21)

• New Relations for Gauge-Theory Amplitudes
• Classical Polylogarithms for Amplitudes and Wilson Loops
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Full one-loop amplitudes from tree amplitudes
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• Amplitudes and Spinor-Helicity in Six Dimensions
• Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD
• Bootstrapping the QCD soft anomalous dimension
• Four-gluon scattering at three loops, infrared structure and Regge limit
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• Wilson Loops in N=2 Superconformal Yang-Mills Theory
• Multi-Quark Colour Decompositions from Unitarity
• Analytic all-plus-helicity gluon amplitudes in QCD
• Subleading-color contributions to gluon-gluon scattering in N=4 SYM theory and relations to N=8 supergravity
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• The Infrared Structure of QCD Amplitudes and $H\to gg$ in FDH and DRED
• Four-particle scattering amplitudes in QCD at NNLO to higher orders in the dimensional regulator
• Four-point amplitudes in $\mathcal{N}=2$ SCQCD