A unitarity compatible approach to one-loop amplitudes with massive fermions

  • Simon BadgerEmail author
  • Christian Brønnum-Hansen
  • Francesco Buciuni
  • Donal O’Connell
Open Access
Regular Article - Theoretical Physics


We explain how one-loop amplitudes with massive fermions can be computed using only on-shell information. We first use the spinor-helicity formalism in six dimensions to perform generalised unitarity cuts in d dimensions. We then show that divergent wave-function cuts can be avoided, and the remaining ambiguities in the renormalised amplitudes can be fixed, by matching to universal infrared poles in 4 − 2ϵ dimensions and ultraviolet poles in 6 − 2ϵ dimensions. In the latter case we construct an effective Lagrangian in six dimensions and reduce the additional constraint to an on-shell tree-level computation.


Perturbative QCD Scattering Amplitudes Field Theories in Higher Dimensions Effective Field Theories 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Supplementary material

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Simon Badger
    • 1
    Email author
  • Christian Brønnum-Hansen
    • 2
  • Francesco Buciuni
    • 1
  • Donal O’Connell
    • 2
  1. 1.Institute for Particle Physics Phenomenology, Ogden Centre for Fundamental Physics, Department of PhysicsUniversity of DurhamDurhamU.K.
  2. 2.Higgs Centre for Theoretical Physics, School of Physics and AstronomyThe University of EdinburghEdinburghU.K.

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