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Title: The four-loop six-gluon NMHV ratio function

We use the hexagon function bootstrap to compute the ratio function which characterizes the next-to-maximally-helicity-violating (NMHV) six-point amplitude in planar N = 4 super-Yang-Mills theory at four loops. A powerful constraint comes from dual superconformal invariance, in the form of a Q- differential equation, which heavily constrains the first derivatives of the transcendental functions entering the ratio function. At four loops, it leaves only a 34-parameter space of functions. Constraints from the collinear limits, and from the multi-Regge limit at the leading-logarithmic (LL) and next-to-leading-logarithmic (NLL) order, suffice to fix these parameters and obtain a unique result. We test the result against multi- Regge predictions at NNLL and N3LL, and against predictions from the operator product expansion involving one and two flux-tube excitations; all cross-checks are satisfied. We also study the analytical and numerical behavior of the parity-even and parity-odd parts on various lines and surfaces traversing the three-dimensional space of cross ratios. As part of this program, we characterize all irreducible hexagon functions through weight eight in terms of their coproduct. Furthermore, we provide representations of the ratio function in particular kinematic regions in terms of multiple polylogarithms.
Authors:
 [1] ;  [2] ;  [3]
  1. SLAC National Accelerator Lab., Stanford, CA (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)
  2. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  3. SLAC National Accelerator Lab., Stanford, CA (United States)
Publication Date:
OSTI Identifier:
1222459
Report Number(s):
SLAC-PUB--16352
Journal ID: ISSN 1029-8479; arXiv:1509.08127
DOE Contract Number:
AC02-76SF00515
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 1
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 Theory-HEP; HEPTH