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Integrand oxidation and one-loop colour-dual numerators in \( \mathcal{N}=4 \) gauge theory

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Abstract

We present a systematic method to determine BCJ numerators for one-loop amplitudes that explores the global constraints on the loop momentum dependence. We apply this method to amplitudes in \( \mathcal{N}=4 \) gauge theory, working out detailed examples up to seven points in both the MHV and the NMHV sectors. We see no obstruction to the application of our method to higher point one-loop amplitudes. The structure of Jacobi identities between BCJ numerators is seen to be closely connected to that of algebraic integrand reductions. We discuss the consequences for one-loop \( \mathcal{N}=8 \) supergravity amplitudes obtained through the double copy prescription. Moreover, in the MHV sector, we show how to obtain simple BCJ box numerators using a relationship with amplitudes in self-dual gauge theory. We also introduce simpler trace-type formulas for integrand reductions.

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  1. Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark

    N. Emil J. Bjerrum-Bohr, Tristan Dennen, Ricardo Monteiro & Donal O’Connell

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  1. N. Emil J. Bjerrum-Bohr
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  2. Tristan Dennen
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  3. Ricardo Monteiro
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  4. Donal O’Connell
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Correspondence to Ricardo Monteiro.

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Bjerrum-Bohr, N.E.J., Dennen, T., Monteiro, R. et al. Integrand oxidation and one-loop colour-dual numerators in \( \mathcal{N}=4 \) gauge theory. J. High Energ. Phys. 2013, 92 (2013). https://doi.org/10.1007/JHEP07(2013)092

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