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Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes

Nov 22, 2019
36 pages
Published in:
  • JHEP 01 (2020) 068
  • Published: Jan 13, 2020
e-Print:
DOI:
Report number:
  • UUITP-47/19,
  • SLAC-PUB-17488
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Abstract: (Springer)
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 Nf_{f} massless supersymmetric quarks. This generalizes the previously observed cancellation of weight-2 terms in the superconformal theory, where Nf_{f} = 2Nc_{c} for gauge group SU(Nc_{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.
Note:
  • 36 pages + appendices + references; v2: fixed references and minor typos
  • Scattering Amplitudes
  • Supersymmetric Gauge Theory
  • quantum chromodynamics: supersymmetry
  • loop integral
  • infrared
  • anomalous dimension
  • factorization
  • supersymmetry: 2
  • scattering amplitude
  • gauge field theory: SU(2)