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Kinematic Hopf Algebra for Bern-Carrasco-Johansson Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory

Andreas Brandhuber, Gang Chen, Henrik Johansson, Gabriele Travaglini, and Congkao Wen
Phys. Rev. Lett. 128, 121601 – Published 25 March 2022
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Abstract

We present a closed formula for all Bern-Carrasco-Johansson (BCJ) numerators describing D-dimensional tree-level scattering amplitudes in a heavy-mass effective field theory with two massive particles and an arbitrary number of gluons. The corresponding gravitational amplitudes obtained via the double copy directly enter the computation of black-hole scattering and gravitational-wave emission. Our construction is based on finding a kinematic algebra for the numerators, which we relate to a quasishuffle Hopf algebra. The BCJ numerators thus obtained have a compact form and intriguing features: gauge invariance is manifest, locality is respected for massless exchange, and they contain poles corresponding to massive exchange. Counting the number of terms in a BCJ numerator for n2 gluons gives the Fubini numbers Fn3, reflecting the underlying quasishuffle Hopf algebra structure. Finally, by considering an appropriate factorization limit, the massive particles decouple, and we thus obtain a kinematic algebra and all tree-level BCJ numerators for D-dimensional pure Yang-Mills theory.

  • Received 8 December 2021
  • Accepted 1 March 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.121601

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Particles & Fields

Authors & Affiliations

Andreas Brandhuber1,*, Gang Chen1,†, Henrik Johansson2,3,‡, Gabriele Travaglini1,§, and Congkao Wen1,∥

  • 1Centre for Theoretical Physics, Department of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
  • 2Department of Physics and Astronomy, Uppsala University, Box 516, 75120 Uppsala, Sweden
  • 3Nordita, Stockholm University and KTH Royal Institute of Technology, Hannes Alfvéns väg 12, 10691 Stockholm, Sweden

  • *a.brandhuber@qmul.ac.uk
  • g.chen@qmul.ac.uk
  • henrik.johansson@physics.uu.se
  • §g.travaglini@qmul.ac.uk
  • c.wen@qmul.ac.uk

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Issue

Vol. 128, Iss. 12 — 25 March 2022

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