Abstract
Loop-level scattering amplitudes for massless particles have singularities in regions where tree amplitudes are perfectly smooth. For example, a 2 → 4 gluon scattering process has a singularity in which each incoming gluon splits into a pair of gluons, followed by a pair of 2 → 2 collisions between the gluon pairs. This singularity mimics double parton scattering because it occurs when the transverse momentum of a pair of outgoing gluons vanishes. The singularity is logarithmic at fixed order in perturbation theory. We exploit the duality between scattering amplitudes and polygonal Wilson loops to study six-point amplitudes in this limit to high loop order in planar \( \mathcal{N} \) = 4 super-Yang-Mills theory. The singular configuration corresponds to the limit in which a hexagonal Wilson loop develops a self-crossing. The singular terms are governed by an evolution equation, in which the hexagon mixes into a pair of boxes; the mixing back is suppressed in the planar (large N c) limit. Because the kinematic dependence of the box Wilson loops is dictated by (dual) conformal invariance, the complete kinematic dependence of the singular terms for the self-crossing hexagon on the one nonsingular variable is determined to all loop orders. The complete logarithmic dependence on the singular variable can be obtained through nine loops, up to a couple of constants, using a correspondence with the multi-Regge limit. As a byproduct, we obtain a simple formula for the leading logs to all loop orders. We also show that, although the MHV six-gluon amplitude is singular, remarkably, the transcendental functions entering the non-MHV amplitude are finite in the same limit, at least through four loops.
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23 August 2016
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ArXiv ePrint: 1602.02107
An erratum to this article can be found online at http://dx.doi.org/10.1007/JHEP08(2016)131.
An erratum to this article is available at https://doi.org/10.1007/JHEP08(2016)131.
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Dixon, L.J., Esterlis, I. All orders results for self-crossing Wilson loops mimicking double parton scattering. J. High Energ. Phys. 2016, 116 (2016). https://doi.org/10.1007/JHEP07(2016)116
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DOI: https://doi.org/10.1007/JHEP07(2016)116