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

We present the four-loop remainder function for six-gluon scattering with maximal helicity violation in planar NN = 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.
Authors:
Publication Date:
OSTI Identifier:
1122506
Report Number(s):
SLAC-PUB--15902
Journal ID: ISSN 1029-8479; arXiv:1402.3300
DOE Contract Number:
AC02-76SF00515
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2014; Journal Issue: 6
Publisher:
Springer Berlin
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS Scattering AmplitudesWilson’t Hooft and Polyakov loopsExtended Supersymmetry