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:1222459

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

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

View Journal Article

Cite

Export

Save

Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

DOE Contract Number:: AC02-76SF00515

OSTI ID:: 1222459

Report Number(s):: SLAC-PUB-16352; arXiv:1509.08127

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

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

References (98)

Supersymmetric Yang-Mills theories Brink, Lars; Schwarz, John H.; Scherk, J. Nuclear Physics B, Vol. 121, Issue 1 https://doi.org/10.1016/0550-3213(77)90328-5	journal	March 1977
Light-cone superspace and the ultraviolet finiteness of the N=4 model Mandelstam, Stanley Nuclear Physics B, Vol. 213, Issue 1 https://doi.org/10.1016/0550-3213(83)90179-7	journal	March 1983
The ultra-violet finiteness of the N=4 Yang-Mills theory Brink, Lars; Lindgren, Olof; E. W. Nilsson, Bengt Physics Letters B, Vol. 123, Issue 5 https://doi.org/10.1016/0370-2693(83)91210-8	journal	April 1983
Miraculous ultraviolet cancellations in supersymmetry made manifest Howe, P. S.; Stelle, K. S.; Townsend, P. K. Nuclear Physics B, Vol. 236, Issue 1 https://doi.org/10.1016/0550-3213(84)90528-5	journal	April 1984
Review of AdS/CFT Integrability: An Overview Beisert, Niklas; Ahn, Changrim; Alday, Luis F. Letters in Mathematical Physics, Vol. 99, Issue 1-3 https://doi.org/10.1007/s11005-011-0529-2	journal	October 2011
Magic identities for conformal four-point integrals Drummond, James M.; Henn, Johannes; Smirnov, Vladimir A. Journal of High Energy Physics, Vol. 2007, Issue 01 https://doi.org/10.1088/1126-6708/2007/01/064	journal	January 2007
Gluon scattering amplitudes at strong coupling Alday, Luis F.; Maldacena, Juan Journal of High Energy Physics, Vol. 2007, Issue 06 https://doi.org/10.1088/1126-6708/2007/06/064	journal	June 2007
Dual superconformal symmetry of scattering amplitudes in super-Yang–Mills theory Drummond, J. M.; Henn, J.; Korchemsky, G. P. Nuclear Physics B, Vol. 828, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2009.11.022	journal	March 2010
Conformal properties of four-gluon planar amplitudes and Wilson loops Drummond, J. M.; Korchemsky, G. P.; Sokatchev, E. Nuclear Physics B, Vol. 795, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2007.11.041	journal	May 2008
MHV amplitudes in super-Yang–Mills and Wilson Loops Brandhuber, Andreas; Heslop, Paul; Travaglini, Gabriele Nuclear Physics B, Vol. 794, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2007.11.002	journal	May 2008
On planar gluon amplitudes/Wilson loops duality Drummond, J. M.; Henn, J.; Korchemsky, G. P. Nuclear Physics B, Vol. 795, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2007.11.007	journal	May 2008
Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes Drummond, J. M.; Henn, J.; Korchemsky, G. P. Nuclear Physics B, Vol. 826, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2009.10.013	journal	February 2010
Scattering amplitudes, Wilson loops and the string/gauge theory correspondence Alday, Luis F.; Roiban, Radu Physics Reports, Vol. 468, Issue 5 https://doi.org/10.1016/j.physrep.2008.08.002	journal	November 2008
Hexagon Wilson loop = six-gluon MHV amplitude Drummond, J. M.; Henn, J.; Korchemsky, G. P. Nuclear Physics B, Vol. 815, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2009.02.015	journal	July 2009
A current algebra for some gauge theory amplitudes Nair, V. P. Physics Letters B, Vol. 214, Issue 2 https://doi.org/10.1016/0370-2693(88)91471-2	journal	November 1988
Non-MHV Tree Amplitudes in Gauge Theory Georgiou, George; Glover, E. W. N.; Khoze, Valentin V. Journal of High Energy Physics, Vol. 2004, Issue 07 https://doi.org/10.1088/1126-6708/2004/07/048	journal	July 2004
Generating tree amplitudes in 𝒩 = 4 SYM and 𝒩 = 8 SG Bianchi, Massimo; Elvang, Henriette; Freedman, Daniel Z. Journal of High Energy Physics, Vol. 2008, Issue 09 https://doi.org/10.1088/1126-6708/2008/09/063	journal	September 2008
What is the simplest quantum field theory? Arkani-Hamed, Nima; Cachazo, Freddy; Kaplan, Jared Journal of High Energy Physics, Vol. 2010, Issue 9 https://doi.org/10.1007/JHEP09(2010)016	journal	September 2010
Eliminating spurious poles from gauge-theoretic amplitudes Hodges, Andrew Journal of High Energy Physics, Vol. 2013, Issue 5 https://doi.org/10.1007/JHEP05(2013)135	journal	May 2013
Dual superconformal invariance, momentum twistors and Grassmannians Mason, Lionel; Skinner, David Journal of High Energy Physics, Vol. 2009, Issue 11 https://doi.org/10.1088/1126-6708/2009/11/045	journal	November 2009
The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM Arkani-Hamed, N.; Bourjaily, J.; Cachazo, F. Journal of High Energy Physics, Vol. 2011, Issue 1 https://doi.org/10.1007/JHEP01(2011)041	journal	January 2011
The soft-collinear bootstrap: $ \mathcal{N} = {4} $ Yang-Mills amplitudes at six- and seven-loops Bourjaily, J. L.; DiRe, A.; Shaikh, A. Journal of High Energy Physics, Vol. 2012, Issue 3 https://doi.org/10.1007/JHEP03(2012)032	journal	March 2012
From d logs to dilogs; the super Yang-Mills MHV amplitude revisited Lipstein, Arthur E.; Mason, Lionel Journal of High Energy Physics, Vol. 2014, Issue 1 https://doi.org/10.1007/JHEP01(2014)169	journal	January 2014
The Amplituhedron Arkani-Hamed, Nima; Trnka, Jaroslav Journal of High Energy Physics, Vol. 2014, Issue 10 https://doi.org/10.1007/JHEP10(2014)030	journal	October 2014
Into the amplituhedron Arkani-Hamed, Nima; Trnka, Jaroslav Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)182	journal	December 2014
Bootstrapping the three-loop hexagon Dixon, Lance J.; Drummond, James M.; Henn, Johannes M. Journal of High Energy Physics, Vol. 2011, Issue 11 https://doi.org/10.1007/JHEP11(2011)023	journal	November 2011
Analytic result for the two-loop six-point NMHV amplitude in $ \mathcal{N} = {4} $ super Yang-Mills theory Dixon, Lance J.; Drummond, James M.; Henn, Johannes M. Journal of High Energy Physics, Vol. 2012, Issue 1 https://doi.org/10.1007/JHEP01(2012)024	journal	January 2012
Hexagon functions and the three-loop remainder function Dixon, Lance J.; Drummond, James M.; von Hippel, Matt Journal of High Energy Physics, Vol. 2013, Issue 12 https://doi.org/10.1007/JHEP12(2013)049	journal	December 2013
The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory Dixon, Lance J.; Drummond, James M.; Duhr, Claude Journal of High Energy Physics, Vol. 2014, Issue 6 https://doi.org/10.1007/JHEP06(2014)116	journal	June 2014
Bootstrapping six-gluon scattering in planar N=4 super-Yang-Mills theory Dixon, Lance; Drummond, James; Duhr, Claude Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2014) https://doi.org/10.22323/1.211.0077	conference	August 2014
Bootstrapping an NMHV amplitude through three loops Dixon, Lance J.; von Hippel, Matt Journal of High Energy Physics, Vol. 2014, Issue 10 https://doi.org/10.1007/JHEP10(2014)065	journal	October 2014
Classical Polylogarithms for Amplitudes and Wilson Loops Goncharov, A. B.; Spradlin, M.; Vergu, C. Physical Review Letters, Vol. 105, Issue 15 https://doi.org/10.1103/PhysRevLett.105.151605	journal	October 2010
An analytic result for the two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM Del Duca, Vittorio; Duhr, Claude; Smirnov, Vladimir A. Journal of High Energy Physics, Vol. 2010, Issue 3 https://doi.org/10.1007/JHEP03(2010)099	journal	March 2010
The two-loop hexagon Wilson loop in $ \mathcal{N} = 4 $ SYM Del Duca, Vittorio; Duhr, Claude; Smirnov, Vladimir A. Journal of High Energy Physics, Vol. 2010, Issue 5 https://doi.org/10.1007/JHEP05(2010)084	journal	May 2010
Multiple zeta values and periods of moduli spaces $\overline{\mathfrak{M}}_{0,n}$ Brown, Francis C. S. Annales scientifiques de l'École normale supérieure, Vol. 42, Issue 3 https://doi.org/10.24033/asens.2099	journal	January 2009
Motivic amplitudes and cluster coordinates Golden, J. K.; Goncharov, A. B.; Spradlin, M. Journal of High Energy Physics, Vol. 2014, Issue 1 https://doi.org/10.1007/JHEP01(2014)091	journal	January 2014
From polygons and symbols to polylogarithmic functions Duhr, Claude; Gangl, Herbert; Rhodes, John R. Journal of High Energy Physics, Vol. 2012, Issue 10 https://doi.org/10.1007/JHEP10(2012)075	journal	October 2012
Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes Duhr, Claude Journal of High Energy Physics, Vol. 2012, Issue 8 https://doi.org/10.1007/JHEP08(2012)043	journal	August 2012
Galois symmetries of fundamental groupoids and noncommutative geometry Goncharov, A. B. Duke Mathematical Journal, Vol. 128, Issue 2 https://doi.org/10.1215/S0012-7094-04-12822-2	journal	June 2005
Pulling the straps of polygons Gaiotto, Davide; Maldacena, Juan; Sever, Amit Journal of High Energy Physics, Vol. 2011, Issue 12 https://doi.org/10.1007/JHEP12(2011)011	journal	December 2011
Jumpstarting the all-loop S-matrix of planar $ \mathcal{N} = {4} $ super Yang-Mills Caron-Huot, S.; He, Song Journal of High Energy Physics, Vol. 2012, Issue 7 https://doi.org/10.1007/JHEP07(2012)174	journal	July 2012
N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution Bartels, J.; Lipatov, L. N.; Sabio Vera, A. The European Physical Journal C, Vol. 65, Issue 3-4 https://doi.org/10.1140/epjc/s10052-009-1218-5	journal	December 2009
MHV amplitude for <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mn>3</mml:mn><mml:mo>→</mml:mo><mml:mn>3</mml:mn></mml:math> gluon scattering in Regge limit Bartels, J.; Lipatov, L. N.; Prygarin, A. Physics Letters B, Vol. 705, Issue 5 https://doi.org/10.1016/j.physletb.2011.09.061	journal	November 2011
BFKL equation for the adjoint representation of the gauge group in the next-to-leading approximation at <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math> SUSY Fadin, V. S.; Lipatov, L. N. Physics Letters B, Vol. 706, Issue 4-5 https://doi.org/10.1016/j.physletb.2011.11.048	journal	January 2012
Single-valued harmonic polylogarithms and the multi-Regge limit Dixon, Lance J.; Duhr, Claude; Pennington, Jeffrey Journal of High Energy Physics, Vol. 2012, Issue 10 https://doi.org/10.1007/JHEP10(2012)074	journal	October 2012
When does the gluon reggeize? Caron-Huot, Simon Journal of High Energy Physics, Vol. 2015, Issue 5 https://doi.org/10.1007/JHEP05(2015)093	journal	May 2015
Adjoint BFKL at finite coupling: a short-cut from the collinear limit Basso, Benjamin; Caron-Huot, Simon; Sever, Amit Journal of High Energy Physics, Vol. 2015, Issue 1 https://doi.org/10.1007/JHEP01(2015)027	journal	January 2015
The Multi-Regge limit of NMHV amplitudes in N=4 SYM theory Lipatov, Lev; Prygarin, Alexander; Schnitzer, Howard J. Journal of High Energy Physics, Vol. 2013, Issue 1 https://doi.org/10.1007/JHEP01(2013)068	journal	January 2013
Spacetime and Flux Tube $S$ -Matrices at Finite Coupling for $N = 4$ Supersymmetric Yang-Mills Theory Basso, Benjamin; Sever, Amit; Vieira, Pedro Physical Review Letters, Vol. 111, Issue 9 https://doi.org/10.1103/PhysRevLett.111.091602	journal	August 2013
Space-time S-matrix and flux tube S-matrix II. Extracting and matching data Basso, Benjamin; Sever, Amit; Vieira, Pedro Journal of High Energy Physics, Vol. 2014, Issue 1 https://doi.org/10.1007/JHEP01(2014)008	journal	January 2014
Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions Basso, Benjamin; Sever, Amit; Vieira, Pedro Journal of High Energy Physics, Vol. 2014, Issue 8 https://doi.org/10.1007/JHEP08(2014)085	journal	August 2014
Space-time S-matrix and flux-tube S-matrix IV. Gluons and fusion Basso, Benjamin; Sever, Amit; Vieira, Pedro Journal of High Energy Physics, Vol. 2014, Issue 9 https://doi.org/10.1007/JHEP09(2014)149	journal	September 2014
Quantum mechanics of null polygonal Wilson loops Belitsky, A. V.; Derkachov, S. E.; Manashov, A. N. Nuclear Physics B, Vol. 882 https://doi.org/10.1016/j.nuclphysb.2014.03.007	journal	May 2014
Nonsinglet pentagons and NMHV amplitudes Belitsky, A. V. Nuclear Physics B, Vol. 896 https://doi.org/10.1016/j.nuclphysb.2015.05.002	journal	July 2015
Fermionic pentagons and NMHV hexagon Belitsky, A. V. Nuclear Physics B, Vol. 894 https://doi.org/10.1016/j.nuclphysb.2015.02.025	journal	May 2015
Generalized unitarity for super-amplitudes Drummond, J. M.; Henn, J.; Korchemsky, G. P. Nuclear Physics B, Vol. 869, Issue 3 https://doi.org/10.1016/j.nuclphysb.2012.12.009	journal	April 2013
One-loop n-point gauge theory amplitudes, unitarity and collinear limits Bern, Zvi; Dixon, Lance; Dunbar, David C. Nuclear Physics B, Vol. 425, Issue 1-2 https://doi.org/10.1016/0550-3213(94)90179-1	journal	August 1994
Harmonic Polylogarithms Remiddi, E.; Vermaseren, J. A. M. International Journal of Modern Physics A, Vol. 15, Issue 05 https://doi.org/10.1142/S0217751X00000367	journal	February 2000
Polylogarithmes multiples uniformes en une variable Brown, Francis C. S. Comptes Rendus Mathematique, Vol. 338, Issue 7 https://doi.org/10.1016/j.crma.2004.02.001	journal	April 2004
The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space Mason, Lionel; Skinner, David Journal of High Energy Physics, Vol. 2010, Issue 12 https://doi.org/10.1007/JHEP12(2010)018	journal	December 2010
Notes on the scattering amplitude — Wilson loop duality Caron-Huot, S. Journal of High Energy Physics, Vol. 2011, Issue 7 https://doi.org/10.1007/JHEP07(2011)058	journal	July 2011
Exciting the GKP string at any coupling Basso, B. Nuclear Physics B, Vol. 857, Issue 3 https://doi.org/10.1016/j.nuclphysb.2011.12.010	journal	April 2012
Factorization in one-loop gauge theory Bern, Zvi; Chalmers, Gordon Nuclear Physics B, Vol. 447, Issue 2-3 https://doi.org/10.1016/0550-3213(95)00226-I	journal	August 1995
Introduction to the GiNaC Framework for Symbolic Computation within the C++ Programming Language Bauer, Christian; Frink, Alexander; Kreckel, Richard Journal of Symbolic Computation, Vol. 33, Issue 1 https://doi.org/10.1006/jsco.2001.0494	journal	January 2002
Numerical evaluation of multiple polylogarithms Vollinga, Jens; Weinzierl, Stefan Computer Physics Communications, Vol. 167, Issue 3 https://doi.org/10.1016/j.cpc.2004.12.009	journal	May 2005
Harmonic sums and polylogarithms generated by cyclotomic polynomials Ablinger, Jakob; Blümlein, Johannes; Schneider, Carsten Journal of Mathematical Physics, Vol. 52, Issue 10 https://doi.org/10.1063/1.3629472	journal	October 2011
Two-loop master integrals for jets: the planar topologies Gehrmann, T.; Remiddi, E. Nuclear Physics B, Vol. 601, Issue 1-2 https://doi.org/10.1016/S0550-3213(01)00057-8	journal	May 2001
Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes Duhr, Claude ETH Zurich https://doi.org/10.3929/ethz-b-000058776	text	January 2012
Motivic amplitudes and cluster coordinates Golden, J. K.; Goncharov, Alexander B.; Spradlin, Marcus ETH Zurich https://doi.org/10.3929/ethz-b-000080905	text	January 2014
Single-valued harmonic polylogarithms and the multi-Regge limit J., Dixon, Lance; Claude, Duhr,; Jeffrey, Pennington, ETH Zurich https://doi.org/10.3929/ethz-b-000059748	text	January 2012
Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes Drummond, J. M.; Henn, J.; Korchemsky, G. P. arXiv https://doi.org/10.48550/arxiv.0712.1223	text	January 2007
Hexagon Wilson loop = six-gluon MHV amplitude Drummond, J. M.; Henn, J.; Korchemsky, G. P. arXiv https://doi.org/10.48550/arxiv.0803.1466	text	January 2008
Generating Tree Amplitudes in N=4 SYM and N=8 SG Bianchi, Massimo; Elvang, Henriette; Freedman, Daniel Z. arXiv https://doi.org/10.48550/arxiv.0805.0757	text	January 2008
N=4 supersymmetric Yang Mills scattering amplitudes at high energies: the Regge cut contribution Bartels, J.; Lipatov, L. N.; Vera, A. Sabio arXiv https://doi.org/10.48550/arxiv.0807.0894	text	January 2008
What is the Simplest Quantum Field Theory? Arkani-Hamed, Nima; Cachazo, Freddy; Kaplan, Jared arXiv https://doi.org/10.48550/arxiv.0808.1446	text	January 2008
Eliminating spurious poles from gauge-theoretic amplitudes Hodges, Andrew arXiv https://doi.org/10.48550/arxiv.0905.1473	preprint	January 2009
An Operator Product Expansion for Polygonal null Wilson Loops Alday, Luis F.; Gaiotto, Davide; Maldacena, Juan arXiv https://doi.org/10.48550/arxiv.1006.2788	text	January 2010
Classical Polylogarithms for Amplitudes and Wilson Loops Goncharov, Alexander B.; Spradlin, Marcus; Vergu, C. arXiv https://doi.org/10.48550/arxiv.1006.5703	text	January 2010
Exciting the GKP string at any coupling Basso, B. arXiv https://doi.org/10.48550/arxiv.1010.5237	text	January 2010
Review of AdS/CFT Integrability: An Overview Beisert, Niklas; Ahn, Changrim; Alday, Luis F. arXiv https://doi.org/10.48550/arxiv.1012.3982	text	January 2010
Pulling the straps of polygons Gaiotto, Davide; Maldacena, Juan; Sever, Amit arXiv https://doi.org/10.48550/arxiv.1102.0062	text	January 2011
Bootstrapping the three-loop hexagon Dixon, Lance J.; Drummond, James M.; Henn, Johannes M. arXiv https://doi.org/10.48550/arxiv.1108.4461	text	January 2011
From polygons and symbols to polylogarithmic functions Duhr, Claude; Gangl, Herbert; Rhodes, John R. arXiv https://doi.org/10.48550/arxiv.1110.0458	text	January 2011
Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory Dixon, Lance J.; Drummond, James M.; Henn, Johannes M. arXiv https://doi.org/10.48550/arxiv.1111.1704	text	January 2011
Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes Duhr, Claude arXiv https://doi.org/10.48550/arxiv.1203.0454	text	January 2012
The Multi-Regge limit of NMHV Amplitudes in N=4 SYM Theory Lipatov, Lev; Prygarin, Alexander; Schnitzer, Howard J. arXiv https://doi.org/10.48550/arxiv.1205.0186	text	January 2012
Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data Basso, Benjamin; Sever, Amit; Vieira, Pedro arXiv https://doi.org/10.48550/arxiv.1306.2058	text	January 2013
Quantum mechanics of null polygonal Wilson loops Belitsky, A. V.; Derkachov, S. E.; Manashov, A. N. arXiv https://doi.org/10.48550/arxiv.1401.7307	text	January 2014
The four-loop remainder function and multi-Regge behavior at NNLLA in planar N=4 super-Yang-Mills theory Dixon, Lance J.; Drummond, James M.; Duhr, Claude arXiv https://doi.org/10.48550/arxiv.1402.3300	text	January 2014
Wilson loop OPE, analytic continuation and multi-Regge limit Hatsuda, Yasuyuki arXiv https://doi.org/10.48550/arxiv.1404.6506	text	January 2014
Nonsinglet pentagons and NMHV amplitudes Belitsky, A. V. arXiv https://doi.org/10.48550/arxiv.1407.2853	text	January 2014
Adjoint BFKL at finite coupling: a short-cut from the collinear limit Basso, Benjamin; Caron-Huot, Simon; Sever, Amit arXiv https://doi.org/10.48550/arxiv.1407.3766	text	January 2014
Bootstrapping six-gluon scattering in planar ${\cal N}=4$ super-Yang-Mills theory Dixon, Lance J.; Drummond, James M.; Duhr, Claude arXiv https://doi.org/10.48550/arxiv.1407.4724	preprint	January 2014
Bootstrapping an NMHV amplitude through three loops Dixon, Lance J.; von Hippel, Matt arXiv https://doi.org/10.48550/arxiv.1408.1505	text	January 2014
Fermionic pentagons and NMHV hexagon Belitsky, A. V. arXiv https://doi.org/10.48550/arxiv.1410.2534	text	January 2014
Numerical evaluation of multiple polylogarithms Vollinga, Jens; Weinzierl, Stefan arXiv https://doi.org/10.48550/arxiv.hep-ph/0410259	text	January 2004
One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits Bern, Z.; Dixon, L.; Dunbar, D. C. arXiv https://doi.org/10.48550/arxiv.hep-ph/9403226	text	January 1994
Harmonic Polylogarithms Remiddi, E.; Vermaseren, J. A. M. arXiv https://doi.org/10.48550/arxiv.hep-ph/9905237	text	January 1999

Cited By (41)

Cluster algebras and the subalgebra constructibility of the seven-particle remainder function Golden, John; McLeod, Andrew J. Journal of High Energy Physics, Vol. 2019, Issue 1 https://doi.org/10.1007/jhep01(2019)017	journal	January 2019
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
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
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
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
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
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

Similar Records

The four-loop six-gluon NMHV ratio function

Journal Article · Mon Jan 11 00:00:00 EST 2016 · Journal of High Energy Physics (Online) · OSTI ID:1222459

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

Hexagon functions and the three-loop remainder function

Journal Article · Sun Dec 01 00:00:00 EST 2013 · Journal of High Energy Physics (Online) · OSTI ID:1222459

Dixon, Lance J.; Drummond, James M.; von Hippel, Matt; +1 more

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

Journal Article · Thu Jun 19 00:00:00 EDT 2014 · Journal of High Energy Physics (Online) · OSTI ID:1222459

None, None

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Theory-HEP
HEPTH

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

Citation Formats

References (98)

Cited By (41)

Similar Records

Related Subjects