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Double virtual corrections for gluon scattering at NNLO

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Abstract

We use the antenna subtraction method to isolate the double virtual infrared singularities present in gluonic scattering amplitudes at next-to-next-to-leading order. In previous papers, we derived the subtraction terms that rendered (a) the double real radiation tree-level process finite in the single and double unresolved regions of phase space and (b) the mixed single real radiation one-loop process both finite and well behaved in the unresolved regions of phase space. Here, we show how to construct the double virtual subtraction term using antenna functions with both initial- and final-state partons which remove the explicit infrared poles present in the two-loop amplitude. As an explicit example, we write down the subtraction term for the four-gluon two-loop process. The infrared poles are explicitly and locally cancelled in all regions of phase space leaving a finite remainder that can be safely evaluated numerically in four-dimensions.

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Authors and Affiliations

  1. Institute for Theoretical Physics, ETH, CH-8093, Zürich, Switzerland

    Aude Gehrmann-De Ridder & Joao Pires

  2. Institut für Theoretische Physik, Universität Zürich, Wintherturerstrasse 190, CH-8057, Zürich, Switzerland

    Thomas Gehrmann

  3. Institute for Particle Physics Phenomenology, University of Durham, South Road, Durham, DH1 3LE, England

    E.W.N. Glover

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  1. Aude Gehrmann-De Ridder
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  2. Thomas Gehrmann
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  3. E.W.N. Glover
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Correspondence to Joao Pires.

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Gehrmann-De Ridder, A., Gehrmann, T., Glover, E. et al. Double virtual corrections for gluon scattering at NNLO. J. High Energ. Phys. 2013, 26 (2013). https://doi.org/10.1007/JHEP02(2013)026

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