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The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory

Dixon, Lance J.; Drummond, James M.; Duhr, Claude; Pennington, Jeffrey

The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory Thumbnail


Authors

Lance J. Dixon

James M. Drummond

Claude Duhr

Jeffrey Pennington



Abstract

We present the four-loop remainder function for six-gluon scattering with maximal helicity violation in planar N = 4 super-Yang-Mills theory, as an analytic function of three dual-conformal cross ratios. The function is constructed entirely from its analytic properties, without ever inspecting any multi-loop integrand. We employ the same approach used at three loops, writing an ansatz in terms of hexagon functions, and fixing coefficients in the ansatz using the multi-Regge limit and the operator product expansion in the near-collinear limit. We express the result in terms of multiple polylogarithms, and in terms of the coproduct for the associated Hopf algebra. From the remainder function, we extract the BFKL eigenvalue at next-to-next-to-leading logarithmic accuracy (NNLLA), and the impact factor at N3LLA. We plot the remainder function along various lines and on one surface, studying ratios of successive loop orders. As seen previously through three loops, these ratios are surprisingly constant over large regions in the space of cross ratios, and they are not far from the value expected at asymptotically large orders of perturbation theory.

Citation

Dixon, L. J., Drummond, J. M., Duhr, C., & Pennington, J. (2014). The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory. Journal of High Energy Physics, 2014(6), Article 116. https://doi.org/10.1007/jhep06%282014%29116

Journal Article Type Article
Acceptance Date May 9, 2014
Online Publication Date Jun 19, 2014
Publication Date Jun 19, 2014
Deposit Date Apr 3, 2018
Publicly Available Date May 25, 2018
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Electronic ISSN 1029-8479
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2014
Issue 6
Article Number 116
DOI https://doi.org/10.1007/jhep06%282014%29116
Public URL https://durham-repository.worktribe.com/output/1336037

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
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.





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