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

Abstract

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 N 3LL, and against predictions from the operator product expansion involving one and two flux-tube excitations; all cross-checks are satisfied. We 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. As a result, we also provide representations of the ratio function in particular kinematic regions in terms of multiple polylogarithms.

Authors:
 [1];  [2];  [3]
  1. SLAC National Accelerator Lab., Menlo Park, CA (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)
  2. Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
  3. SLAC National Accelerator Lab., Menlo Park, CA (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1239131
Grant/Contract Number:  
AC03-76SF00515
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 1; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; scattering amplitudes; supersymmetric gauge theory; 1/N expansion

Citation Formats

Dixon, Lance J., von Hippel, Matt, and McLeod, Andrew J.. The four-loop six-gluon NMHV ratio function. United States: N. p., 2016. Web. doi:10.1007/JHEP01(2016)053.
Dixon, Lance J., von Hippel, Matt, & McLeod, Andrew J.. The four-loop six-gluon NMHV ratio function. United States. doi:10.1007/JHEP01(2016)053.
Dixon, Lance J., von Hippel, Matt, and McLeod, Andrew J.. Mon . "The four-loop six-gluon NMHV ratio function". United States. doi:10.1007/JHEP01(2016)053. https://www.osti.gov/servlets/purl/1239131.
@article{osti_1239131,
title = {The four-loop six-gluon NMHV ratio function},
author = {Dixon, Lance J. and von Hippel, Matt and McLeod, Andrew J.},
abstractNote = {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 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. As a result, we also provide representations of the ratio function in particular kinematic regions in terms of multiple polylogarithms.},
doi = {10.1007/JHEP01(2016)053},
journal = {Journal of High Energy Physics (Online)},
number = 1,
volume = 2016,
place = {United States},
year = {2016},
month = {1}
}

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