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Conformal invariance of the one-loop all-plus helicity scattering amplitudes

Journal of High Energy Physics volume 2020, Article number: 19 (2020) Cite this article

A preprint version of the article is available at arXiv.

Abstract

The massless QCD Lagrangian is conformally invariant and, as a consequence, so are the tree-level scattering amplitudes. However, the implications of this powerful symmetry at loop level are only beginning to be explored systematically. Even for finite loop amplitudes, the way conformal symmetry manifests itself may be subtle, e.g. in the form of anomalous conformal Ward identities. As they are finite and rational, the one-loop all-plus and single-minus amplitudes are a natural first step towards understanding the conformal properties of Yang-Mills theory at loop level. Remarkably, we find that the one-loop all-plus amplitudes are conformally invariant, whereas the single-minus are not. Moreover, we present a formula for the one-loop all-plus amplitudes where the symmetry is manifest term by term. Surprisingly, each term transforms covariantly under directional dual conformal variations. We prove the formula directly using recursive techniques, and check that it has the correct physical factorisations.

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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

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Affiliations

  1. Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, D-80805, München, Germany

    Johannes Henn, Bláithín Power & Simone Zoia

  2. Ludwig-Maximilians-Universität, Theresienstraße 37, 80333, München, Germany

    Bláithín Power

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  1. Johannes Henn
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  2. Bláithín Power
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Correspondence to Simone Zoia.

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ArXiv ePrint: 1911.12142

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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.

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Henn, J., Power, B. & Zoia, S. Conformal invariance of the one-loop all-plus helicity scattering amplitudes. J. High Energ. Phys. 2020, 19 (2020). https://doi.org/10.1007/JHEP02(2020)019

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  • DOI: https://doi.org/10.1007/JHEP02(2020)019

Keywords

  • Conformal and W Symmetry
  • Conformal Field Theory
  • Scattering Amplitudes
  • Perturbative QCD