The four-loop six-gluon NMHV ratio function

Dixon, Lance J.; von Hippel, Matt; McLeod, Andrew J.

doi:10.1007/JHEP01(2016)053

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

Journal Article · Mon Jan 11 00:00:00 EST 2016 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP01(2016)053· OSTI ID:1239131

Dixon, Lance J. ^[1]; von Hippel, Matt ^[2]; McLeod, Andrew J. ^[3]

SLAC National Accelerator Lab., Menlo Park, CA (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)
Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
SLAC National Accelerator Lab., Menlo Park, CA (United States)

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.

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Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Betty Moore Foundation

Grant/Contract Number:: AC03-76SF00515; SC0011632; 1066293; 776

OSTI ID:: 1239131

Alternate ID(s):: OSTI ID: 1598894

Journal Information:: Journal of High Energy Physics (Online), Vol. 2016, Issue 1; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 96 works

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Yangian invariants and cluster adjacency in $$ \mathcal{N} $$ = 4 Yang-Mills Mago, Jorge; Schreiber, Anders; Spradlin, Marcus Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/jhep10(2019)099	journal	October 2019
Subleading power factorization with radiative functions Moult, Ian; Stewart, Iain W.; Vita, Gherardo Journal of High Energy Physics, Vol. 2019, Issue 11 https://doi.org/10.1007/jhep11(2019)153	journal	November 2019
Systematics of the multi-Regge three-loop symbol Bargheer, Till Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-12764	text	January 2017
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy Del Duca, Vittorio; Druc, Stefan; Drummond, James Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-02259	text	January 2018
The analytic structure of non-global logarithms: convergence of the dressed gluon expansion Larkoski, Andrew J.; Moult, Ian; Neill, Duff Journal of High Energy Physics, Vol. 2016, Issue 11 https://doi.org/10.1007/jhep11(2016)089	journal	November 2016
The two-loop symbol of all multi-Regge regions Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2016-02009	text	January 2016
Heptagons from the Steinmann Cluster Bootstrap Dixon, Lance J.; Drummond, James; Harrington, Thomas Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-00889	text	January 2017
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy Del Duca, Vittorio; Druc, Stefan; Drummond, James Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-03272	text	January 2018
Six-point remainder function in multi-Regge-kinematics: an efficient approach in momentum space Johannes, Broedel,; Martin, Sprenger, ETH Zurich https://doi.org/10.3929/ethz-b-000117036	text	January 2016
Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD Gehrmann, T.; Henn, J. M.; Lo Presti, N. A. American Physical Society https://doi.org/10.5167/uzh-129837	text	January 2016
Analytic Result for a Two-Loop Five-Particle Amplitude Chicherin, D.; Gehrmann, Thomas; Henn, J. M. American Physical Society https://doi.org/10.5167/uzh-183496	text	January 2019
All-order amplitudes at any multiplicity in the multi-Regge limit Del Duca, V.; Druc, S.; Drummond, J. M. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2020-01808	text	January 2020
Six-point remainder function in multi-Regge-kinematics: an efficient approach in momentum space Broedel, Johannes; Sprenger, Martin Journal of High Energy Physics, Vol. 2016, Issue 5 https://doi.org/10.1007/jhep05(2016)055	journal	May 2016
Systematics of the Multi-Regge Three-Loop Symbol Bargheer, Till Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2016-02553	text	January 2016
Cluster adjacency and the four-loop NMHV heptagon Drummond, James; Foster, Jack; Gürdoğan, Ömer Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-05809	text	January 2018
All-order amplitudes at any multiplicity in the multi-Regge limit Del Duca, V.; Druc, S.; Drummond, J. M. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2020-00194	text	January 2019
The double pentaladder integral to all ordersC Caron-Huot, Simon; Dixon, Lance J.; Von Hippel, Matt Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2018-05437	text	January 2018
All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit Del Duca, Vittorio; Druc, S.; Drummond, James M. ETH Zurich https://doi.org/10.3929/ethz-b-000412664	text	January 2020
Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu Springer https://doi.org/10.5167/uzh-172597	text	January 2019
Six-point remainder function in multi-Regge-kinematics: an efficient approach in momentum space Broedel, Johannes; Sprenger, Martin arXiv https://doi.org/10.48550/arxiv.1512.04963	preprint	January 2015
The Two-Loop Symbol of all Multi-Regge Regions Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker arXiv https://doi.org/10.48550/arxiv.1512.07620	text	January 2015
Gravity On-shell Diagrams Herrmann, Enrico; Trnka, Jaroslav arXiv https://doi.org/10.48550/arxiv.1604.03479	text	January 2016
Systematics of the Multi-Regge Three-Loop Symbol Bargheer, Till arXiv https://doi.org/10.48550/arxiv.1606.07640	text	January 2016
Bootstrapping a Five-Loop Amplitude Using Steinmann Relations Caron-Huot, Simon; Dixon, Lance J.; McLeod, Andrew arXiv https://doi.org/10.48550/arxiv.1609.00669	text	January 2016
The Analytic Structure of Non-Global Logarithms: Convergence of the Dressed Gluon Expansion Larkoski, Andrew J.; Moult, Ian; Neill, Duff arXiv https://doi.org/10.48550/arxiv.1609.04011	text	January 2016
Heptagons from the Steinmann Cluster Bootstrap Dixon, Lance J.; Drummond, James; Harrington, Thomas arXiv https://doi.org/10.48550/arxiv.1612.08976	text	January 2016
Boundaries of Amplituhedra and NMHV Symbol Alphabets at Two Loops Prlina, Igor; Spradlin, Marcus; Stankowicz, James arXiv https://doi.org/10.48550/arxiv.1712.08049	text	January 2017
Rationalizing Loop Integration Bourjaily, Jacob L.; McLeod, Andrew J.; von Hippel, Matt arXiv https://doi.org/10.48550/arxiv.1805.10281	text	January 2018
The Double Pentaladder Integral to All Orders Caron-Huot, Simon; Dixon, Lance J.; von Hippel, Matt arXiv https://doi.org/10.48550/arxiv.1806.01361	text	January 2018
Cluster adjacency beyond MHV Drummond, James; Foster, Jack; Gurdogan, Omer arXiv https://doi.org/10.48550/arxiv.1810.08149	text	January 2018
Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function Golden, John; McLeod, Andrew J. arXiv https://doi.org/10.48550/arxiv.1810.12181	text	January 2018
Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu arXiv https://doi.org/10.48550/arxiv.1811.11699	text	January 2018
Analytic result for a two-loop five-particle amplitude Chicherin, D.; Gehrmann, T.; Henn, J. M. arXiv https://doi.org/10.48550/arxiv.1812.11057	text	January 2018
Elliptic polylogarithms and Feynman parameter integrals Broedel, Johannes; Duhr, Claude; Dulat, Falko arXiv https://doi.org/10.48550/arxiv.1902.09971	text	January 2019
The Sklyanin Bracket and Cluster Adjacency at All Multiplicity Golden, John; McLeod, Andrew J.; Spradlin, Marcus arXiv https://doi.org/10.48550/arxiv.1902.11286	text	January 2019

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