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Colour-Kinematics duality for one-loop rational amplitudes

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Abstract

Colour-kinematics duality is the conjecture of a group theory-like structure for the kinematic dependence of scattering amplitudes in gauge theory and gravity. This structure has been verified at tree level in various ways, but similar progress to all multiplicity has been lacking at loop level, where the power of the duality would be most significant. Here we explore colour-kinematics duality at one loop using the self-dual sector as a starting point. The duality is shown to exist in pure Yang-Mills theory for two infinite classes of amplitudes: amplitudes with any number of particles either all of the same helicity or with one particle helicity opposite the rest. We provide a simple Lagrangian-based argument in favour of the double copy relation between gauge theory and gravity amplitudes in these classes, and provide some explicit examples. We further discuss aspects of the duality which persist after integration, leading to relations among partial amplitudes. Finally, we describe form factors in the self-dual theory at tree level which also satisfy the duality.

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Authors and Affiliations

  1. II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, D- 22761, Hamburg, Germany

    Rutger H. Boels & Reinke Sven Isermann

  2. The Niels Bohr International Academy and Discovery Center, The Niels Bohr Institute, Blegdamsvej 17, Copenhagen, 2100, Denmark

    Ricardo Monteiro & Donal O’Connell

Authors
  1. Rutger H. Boels
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  2. Reinke Sven Isermann
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  3. Ricardo Monteiro
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  4. Donal O’Connell
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Correspondence to Reinke Sven Isermann.

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ArXiv ePrint: 1301.4165

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Boels, R.H., Isermann, R.S., Monteiro, R. et al. Colour-Kinematics duality for one-loop rational amplitudes. J. High Energ. Phys. 2013, 107 (2013). https://doi.org/10.1007/JHEP04(2013)107

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