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All orders results for self-crossing Wilson loops mimicking double parton scattering

Dixon, Lance J. and Esterlis, Ilya (2016) All orders results for self-crossing Wilson loops mimicking double parton scattering. Journal of High Energy Physics, 2016 (7). Art. No. 116. ISSN 1126-6708. doi:10.1007/JHEP07(2016)116.

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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 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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Additional Information:© 2016 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. Article funded by SCOAP3. Received: February 21, 2016; Accepted: June 24, 2016; Published: July 21, 2016. We are grateful to Benjamin Basso, Andrei Belitsky, Johannes Broedel, Simon Caron-Huot, John Joseph Carrasco, Claude Duhr, Matt von Hippel, Gregory Korchemsky, Andrew McLeod, Tom Melia, Amit Sever, Georgios Papathanasiou, Mads Søgaard, Martin Sprenger, Pedro Vieira and Jara Trnka for useful discussions and comments. We would particularly like to thank Johannes Broedel and Martin Sprenger for providing us with the w → −1 limit of their high-loop order MRK expressions, as well as Benjamin Basso, Simon Caron-Huot, Amit Sever and Pedro Vieira for pointing out an error in the NMHV discussion in the first version of this paper. This research was supported by the US Department of Energy under contract DE-AC02-76SF00515 and grant DE-SC0011632, by the Walter Burke Institute, by the Gordon and Betty Moore Foundation through Grant No. 776 to the Caltech Moore Center for Theoretical Cosmology and Physics. LD thanks Caltech, the Aspen Center for Physics and the NSF Grant #1066293 for hospitality. Figures in this paper were made with Jaxodraw [82, 83], based on Axodraw [84].
Group:Walter Burke Institute for Theoretical Physics, Moore Center for Theoretical Cosmology and Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-AC02-76SF00515
Department of Energy (DOE)DE-SC0011632
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Gordon and Betty Moore Foundation776
Subject Keywords:1/N Expansion, Scattering Amplitudes, Supersymmetric gauge theory
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Issue or Number:7
Record Number:CaltechAUTHORS:20160210-144009886
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Official Citation:Dixon, L.J. & Esterlis, I. J. High Energ. Phys. (2016) 2016: 116. doi:10.1007/JHEP07(2016)116
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64383
Deposited By: Joy Painter
Deposited On:10 Feb 2016 23:33
Last Modified:10 Nov 2021 23:30

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