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

The four-loop remainder function and multi-Regge behavior at NNLLA in planar N = 4 super-Yang-Mills theory
The four-loop remainder function and multi-Regge behavior at NNLLA in planar N = 4 super-Yang-Mills theory
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.
1-58
Dixon, Lance J.
771aff61-aeac-479c-b3eb-e701b88e664b
Drummond, James
3ea15544-457f-4e72-8ad0-60f3136841db
Duhr, Claude
7bb86906-9c06-4901-8a48-9016ed3a8c6e
Pennington, Jeffrey
af48966d-3336-472f-9d20-633a1d4671e2
Dixon, Lance J.
771aff61-aeac-479c-b3eb-e701b88e664b
Drummond, James
3ea15544-457f-4e72-8ad0-60f3136841db
Duhr, Claude
7bb86906-9c06-4901-8a48-9016ed3a8c6e
Pennington, Jeffrey
af48966d-3336-472f-9d20-633a1d4671e2

Dixon, Lance J., Drummond, James, Duhr, Claude and Pennington, Jeffrey (2014) The four-loop remainder function and multi-Regge behavior at NNLLA in planar N = 4 super-Yang-Mills theory. Journal of High Energy Physics, 2014 (6), 1-58, [116]. (doi:10.1007/JHEP06(2014)116).

Record type: Article

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.

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More information

Accepted/In Press date: 9 May 2014
e-pub ahead of print date: 19 June 2014
Published date: 19 June 2014
Organisations: Theoretical Partical Physics Group

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Local EPrints ID: 402039
URI: http://eprints.soton.ac.uk/id/eprint/402039
PURE UUID: 3f93d09e-3f47-4715-936c-9ed62b08c8a7

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Date deposited: 27 Oct 2016 08:44
Last modified: 12 Nov 2021 17:55

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Contributors

Author: Lance J. Dixon
Author: James Drummond
Author: Claude Duhr
Author: Jeffrey Pennington

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