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 04:00:00 UTC 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)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Science Foundation (NSF); Betty Moore Foundation

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

OSTI ID:: 1239131

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

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu Journal of High Energy Physics, Vol. 2019, Issue 1 https://doi.org/10.1007/jhep01(2019)186	journal	January 2019
Heptagons from the Steinmann cluster bootstrap Dixon, Lance J.; Drummond, James; Harrington, Thomas Journal of High Energy Physics, Vol. 2017, Issue 2 https://doi.org/10.1007/jhep02(2017)137	journal	February 2017
Fermionic Glauber operators and quark reggeization Moult, Ian; Solon, Mikhail P.; Stewart, Iain W. Journal of High Energy Physics, Vol. 2018, Issue 2 https://doi.org/10.1007/jhep02(2018)134	journal	February 2018
Cluster adjacency beyond MHV Drummond, James; Foster, Jack; Gürdoğan, Ömer Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/jhep03(2019)086	journal	March 2019
Cluster adjacency and the four-loop NMHV heptagon Drummond, James; Foster, Jack; Gürdoğn, Ömer Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/jhep03(2019)087	journal	March 2019
The Sklyanin bracket and cluster adjacency at all multiplicity Golden, John; McLeod, Andrew J.; Spradlin, Marcus Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/jhep03(2019)195	journal	March 2019
Boundaries of amplituhedra and NMHV symbol alphabets at two loops Prlina, I.; Spradlin, M.; Stankowicz, J. Journal of High Energy Physics, Vol. 2018, Issue 4 https://doi.org/10.1007/jhep04(2018)049	journal	April 2018
The two-loop symbol of all multi-Regge regions Bargheer, Till; Papathanasiou, Georgios; Schomerus, Volker Journal of High Energy Physics, Vol. 2016, Issue 5 https://doi.org/10.1007/jhep05(2016)012	journal	May 2016
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
Bootstrapping pentagon functions Chicherin, Dmitry; Henn, Johannes; Mitev, Vladimir Journal of High Energy Physics, Vol. 2018, Issue 5 https://doi.org/10.1007/jhep05(2018)164	journal	May 2018
Elliptic polylogarithms and Feynman parameter integrals Broedel, Johannes; Duhr, Claude; Dulat, Falko Journal of High Energy Physics, Vol. 2019, Issue 5 https://doi.org/10.1007/jhep05(2019)120	journal	May 2019
Prescriptive unitarity Bourjaily, Jacob L.; Herrmann, Enrico; Trnka, Jaroslav Journal of High Energy Physics, Vol. 2017, Issue 6 https://doi.org/10.1007/jhep06(2017)059	journal	June 2017
Landau singularities from the amplituhedron Dennen, T.; Prlina, I.; Spradlin, M. Journal of High Energy Physics, Vol. 2017, Issue 6 https://doi.org/10.1007/jhep06(2017)152	journal	June 2017
The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy Del Duca, Vittorio; Druc, Stefan; Drummond, James Journal of High Energy Physics, Vol. 2018, Issue 6 https://doi.org/10.1007/jhep06(2018)116	journal	June 2018
The double pentaladder integral to all orders Caron-Huot, Simon; Dixon, Lance J.; von Hippel, Matt Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/jhep07(2018)170	journal	July 2018
Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series Broedel, Johannes; Duhr, Claude; Dulat, Falko Journal of High Energy Physics, Vol. 2018, Issue 8 https://doi.org/10.1007/jhep08(2018)014	journal	August 2018
Rationalizing loop integration Bourjaily, Jacob L.; McLeod, Andrew J.; von Hippel, Matt Journal of High Energy Physics, Vol. 2018, Issue 8 https://doi.org/10.1007/jhep08(2018)184	journal	August 2018
Bootstrapping the QCD soft anomalous dimension Almelid, Øyvind; Duhr, Claude; Gardi, Einan Journal of High Energy Physics, Vol. 2017, Issue 9 https://doi.org/10.1007/jhep09(2017)073	journal	September 2017
Bootstrapping two-loop Feynman integrals for planar N = 4 $$ \mathcal{N}=4 $$ sYM Henn, Johannes; Herrmann, Enrico; Parra-Martinez, Julio Journal of High Energy Physics, Vol. 2018, Issue 10 https://doi.org/10.1007/jhep10(2018)059	journal	October 2018
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
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
Gravity on-shell diagrams Herrmann, Enrico; Trnka, Jaroslav Journal of High Energy Physics, Vol. 2016, Issue 11 https://doi.org/10.1007/jhep11(2016)136	journal	November 2016
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
Five-loop four-point integrand of N = 8 supergravity as a generalized double copy Bern, Zvi; Carrasco, John Joseph; Chen, Wei-Ming Physical Review D, Vol. 96, Issue 12 https://doi.org/10.1103/physrevd.96.126012	journal	December 2017
Analytic Form of the Two-Loop Planar Five-Gluon All-Plus-Helicity Amplitude in QCD Gehrmann, T.; Henn, J. M.; Lo Presti, N. A. Physical Review Letters, Vol. 116, Issue 6 https://doi.org/10.1103/physrevlett.116.062001	journal	February 2016
Bootstrapping a Five-Loop Amplitude Using Steinmann Relations Caron-Huot, Simon; Dixon, Lance J.; McLeod, Andrew Physical Review Letters, Vol. 117, Issue 24 https://doi.org/10.1103/physrevlett.117.241601	journal	December 2016
Analytic Result for a Two-Loop Five-Particle Amplitude Chicherin, D.; Gehrmann, T.; Henn, J. M. Physical Review Letters, Vol. 122, Issue 12 https://doi.org/10.1103/physrevlett.122.121602	journal	March 2019
Full-Color Two-Loop Four-Gluon Amplitude in N = 2 Supersymmetric QCD Duhr, Claude; Johansson, Henrik; Kälin, Gregor Physical Review Letters, Vol. 123, Issue 24 https://doi.org/10.1103/physrevlett.123.241601	journal	December 2019
All-Order Amplitudes at any Multiplicity in the Multi-Regge Limit Del Duca, V.; Druc, S.; Drummond, J. M. Physical Review Letters, Vol. 124, Issue 16 https://doi.org/10.1103/physrevlett.124.161602	journal	April 2020
Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory Basso, Benjamin; Dixon, Lance J.; Papathanasiou, Georgios Physical Review Letters, Vol. 124, Issue 16 https://doi.org/10.1103/physrevlett.124.161603	journal	April 2020
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
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
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
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 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
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
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
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 Johannes, Broedel,; Martin, Sprenger, ETH Zurich https://doi.org/10.3929/ethz-b-000117036	text	January 2016
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
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
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 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
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

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