Differential equations from unitarity cuts: nonplanar hexa-box integrals

Abreu, Samuel; Page, Ben; Zeng, Mao

doi:10.1007/jhep01(2019)006

Title: Differential equations from unitarity cuts: nonplanar hexa-box integrals

Journal Article · Wed Jan 02 00:00:00 EST 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep01(2019)006· OSTI ID:1611255

Abreu, Samuel ^[1]; Page, Ben ^[1];

^[2]

Albert-Ludwigs-Univ., Freiburg (Germany)
Univ. of California, Los Angeles, CA (United States)

We compute ϵ-factorized differential equations for all dimensionally-regularized integrals of the nonplanar hexa-box topology, which contribute for instance to 2-loop 5-point QCD amplitudes. A full set of pure integrals is presented. For 5-point planar topologies, Gram determinants which vanish in 4 dimensions are used to build compact expressions for pure integrals. Using unitarity cuts and computational algebraic geometry, we obtain a compact IBP system which can be solved in 8 hours on a single CPU core, overcoming a major bottleneck for deriving the differential equations. Alternatively, assuming prior knowledge of the alphabet of the nonplanar hexa-box, we reconstruct analytic differential equations from 30 numerical phase-space points, making the computation almost trivial with current techniques. We solve the differential equations to obtain the values of the master integrals at the symbol level. Full results for the differential equations and solutions are included as supplementary material.

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Research Organization:: Univ. of California, Los Angeles, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0009937

OSTI ID:: 1611255

Journal Information:: Journal of High Energy Physics (Online), Vol. 2019, Issue 1; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 31 works

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References (72)

Multiloop integrals in dimensional regularization made simple Henn, Johannes M. arXiv https://doi.org/10.48550/arxiv.1304.1806	text	January 2013
Explicit solutions of the multi-loop integral recurrence relations and its application Baikov, P. A. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 389, Issue 1-2 https://doi.org/10.1016/S0168-9002(97)00126-5	journal	April 1997
Cuts of Feynman Integrals in Baikov representation Frellesvig, Hjalte; Papadopoulos, Costas G. arXiv https://doi.org/10.48550/arxiv.1701.07356	text	January 2017
A New Algorithm For The Generation Of Unitarity-Compatible Integration By Parts Relations Schabinger, Robert M. arXiv https://doi.org/10.48550/arxiv.1111.4220	text	January 2011
Multiloop Integrals in Dimensional Regularization Made Simple Henn, Johannes M. Physical Review Letters, Vol. 110, Issue 25 https://doi.org/10.1103/PhysRevLett.110.251601	journal	June 2013
Eliminating spurious poles from gauge-theoretic amplitudes Hodges, Andrew arXiv https://doi.org/10.48550/arxiv.0905.1473	preprint	January 2009
The diagrammatic coaction and the algebraic structure of cut Feynman integrals Abreu, Samuel; Britto, Ruth; Duhr, Claude Proceedings of 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology) — PoS(RADCOR2017) https://doi.org/10.22323/1.290.0002	conference	July 2018
Reducing differential equations for multiloop master integrals Lee, Roman N. arXiv https://doi.org/10.48550/arxiv.1411.0911	text	January 2014
Cuts of Feynman integrals in Baikov representation Papadopoulos, Costas; Frellesvig, Hjalte Axel Proceedings of 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology) — PoS(RADCOR2017) https://doi.org/10.22323/1.290.0006	conference	July 2018
Evidence for a nonplanar amplituhedron Bern, Zvi; Herrmann, Enrico; Litsey, Sean Journal of High Energy Physics, Vol. 2016, Issue 6 https://doi.org/10.1007/JHEP06(2016)098	journal	June 2016
FIRE5: a C++ implementation of Feynman Integral REduction Smirnov, Alexander V. arXiv https://doi.org/10.48550/arxiv.1408.2372	text	January 2014
Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA Meyer, Christoph Computer Physics Communications, Vol. 222 https://doi.org/10.1016/j.cpc.2017.09.014	journal	January 2018
epsilon : A tool to find a canonical basis of master integrals Prausa, Mario Computer Physics Communications, Vol. 219 https://doi.org/10.1016/j.cpc.2017.05.026	journal	October 2017
Differential equations on unitarity cut surfaces Zeng, Mao Journal of High Energy Physics, Vol. 2017, Issue 6 https://doi.org/10.1007/JHEP06(2017)121	journal	June 2017
Generalized unitarity and one-loop amplitudes in super-Yang–Mills Britto, Ruth; Cachazo, Freddy; Feng, Bo Nuclear Physics B, Vol. 725, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2005.07.014	journal	October 2005
Pentagon functions for massless planar scattering amplitudes Gehrmann, T.; Henn, J. M.; Lo Presti, N. A. Springer https://doi.org/10.5167/uzh-157572	text	January 2018
A Two-Loop Five-Gluon Helicity Amplitude in QCD Badger, Simon; Frellesvig, Hjalte; Zhang, Yang arXiv https://doi.org/10.48550/arxiv.1310.1051	text	January 2013
Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity Abreu, Samuel; Cordero, Fernando Febres; Ita, Harald arXiv https://doi.org/10.48550/arxiv.1712.03946	text	January 2017
Pentagon functions for massless planar scattering amplitudes Gehrmann, T.; Henn, J. M.; Lo Presti, N. A. Journal of High Energy Physics, Vol. 2018, Issue 10 https://doi.org/10.1007/JHEP10(2018)103	journal	October 2018
Implications of nonplanar dual conformal symmetry Chicherin, D.; Henn, J. M.; Sokatchev, E. Journal of High Energy Physics, Vol. 2018, Issue 9 https://doi.org/10.1007/JHEP09(2018)012	journal	September 2018
Differential equations method. New technique for massive Feynman diagram calculation Kotikov, A. V. Physics Letters B, Vol. 254, Issue 1-2 https://doi.org/10.1016/0370-2693(91)90413-K	journal	January 1991
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
Multiple polylogarithms, cyclotomy and modular complexes Goncharov, A. B. Mathematical Research Letters, Vol. 5, Issue 4 https://doi.org/10.4310/MRL.1998.v5.n4.a7	journal	January 1998
Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections Böhm, Janko; Georgoudis, Alessandro; Larsen, Kasper J. ETH Zurich https://doi.org/10.3929/ethz-b-000289820	text	January 2018
Mathematical Aspects of Scattering Amplitudes Duhr, Claude 2014 Theoretical Advanced Study Institute in Elementary Particle Physics, Journeys Through the Precision Frontier: Amplitudes for Colliders https://doi.org/10.1142/9789814678766_0010	conference	November 2015
First Look at Two-Loop Five-Gluon Scattering in QCD Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu Physical Review Letters, Vol. 120, Issue 9 https://doi.org/10.1103/PhysRevLett.120.092001	journal	March 2018
Evidence for a Nonplanar Amplituhedron Bern, Zvi; Herrmann, Enrico; Litsey, Sean arXiv https://doi.org/10.48550/arxiv.1512.08591	text	January 2015
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
Fuchsia : A tool for reducing differential equations for Feynman master integrals to epsilon form Gituliar, Oleksandr; Magerya, Vitaly Computer Physics Communications, Vol. 219 https://doi.org/10.1016/j.cpc.2017.05.004	journal	October 2017
FIRE5: A C++ implementation of Feynman Integral REduction Smirnov, A. V. Computer Physics Communications, Vol. 189 https://doi.org/10.1016/j.cpc.2014.11.024	journal	April 2015
Fuchsia : A tool for reducing differential equations for Feynman master integrals to epsilon form Gituliar, Oleksandr; Magerya, Vitaly Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-11208	text	January 2017
Two-Loop Four-Gluon Amplitudes from Numerical Unitarity Abreu, S.; Cordero, F. Febres; Ita, H. Physical Review Letters, Vol. 119, Issue 14 https://doi.org/10.1103/physrevlett.119.142001	journal	October 2017
Scattering Amplitudes from Superconformal Ward Identities Chicherin, D.; Henn, J. M.; Sokatchev, E. Physical Review Letters, Vol. 121, Issue 2 https://doi.org/10.1103/physrevlett.121.021602	journal	July 2018
Pulling the straps of polygons Gaiotto, Davide; Maldacena, Juan; Sever, Amit arXiv https://doi.org/10.48550/arxiv.1102.0062	text	January 2011
epsilon: A tool to find a canonical basis of master integrals Prausa, Mario arXiv https://doi.org/10.48550/arxiv.1701.00725	text	January 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
Integration by parts: The algorithm to calculate β-functions in 4 loops Chetyrkin, K. G.; Tkachov, F. V. Nuclear Physics B, Vol. 192, Issue 1 https://doi.org/10.1016/0550-3213(81)90199-1	journal	November 1981
Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D Lee, R. N. arXiv https://doi.org/10.48550/arxiv.0911.0252	text	January 2009
One-loop amplitudes for e+e− to four partons Bern, Zvi; Dixon, Lance; Kosower, David A. Nuclear Physics B, Vol. 513, Issue 1-2 https://doi.org/10.1016/S0550-3213(97)00703-7	journal	March 1998
Dual Conformal Structure Beyond the Planar Limit Bern, Zvi; Enciso, Michael; Shen, Chia-Hsien Physical Review Letters, Vol. 121, Issue 12 https://doi.org/10.1103/PhysRevLett.121.121603	journal	September 2018
Kira - A Feynman Integral Reduction Program Maierhoefer, Philipp; Usovitsch, Johann; Uwer, Peter Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-12460	text	January 2017
Cuts of Feynman Integrals in Baikov representation Frellesvig, Hjalte; Papadopoulos, Costas G. Journal of High Energy Physics, Vol. 2017, Issue 4 https://doi.org/10.1007/JHEP04(2017)083	journal	April 2017
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
Integration by Parts: an Introduction Grozin, A. G. International Journal of Modern Physics A, Vol. 26, Issue 17 https://doi.org/10.1142/S0217751X11053687	journal	July 2011
Feynman Diagrams and Differential Equations Argeri, Mario; Mastrolia, Pierpaolo arXiv https://doi.org/10.48550/arxiv.0707.4037	text	January 2007
Reducing differential equations for multiloop master integrals Lee, Roman N. Journal of High Energy Physics, Vol. 2015, Issue 4 https://doi.org/10.1007/JHEP04(2015)108	journal	April 2015
Automatic Integral Reduction for Higher Order Perturbative Calculations Anastasiou, C.; Lazopoulos, A. Journal of High Energy Physics, Vol. 2004, Issue 07 https://doi.org/10.1088/1126-6708/2004/07/046	journal	July 2004
Integration by parts: An introduction Grozin, A. G. arXiv https://doi.org/10.48550/arxiv.1104.3993	text	January 2011
One-loop pentagon integral in d dimensions from differential equations in ϵ-form Kozlov, Mikhail G.; Lee, Roman N. Journal of High Energy Physics, Vol. 2016, Issue 2 https://doi.org/10.1007/JHEP02(2016)021	journal	February 2016
Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections Böhm, Janko; Georgoudis, Alessandro; Larsen, Kasper J. Journal of High Energy Physics, Vol. 2018, Issue 9 https://doi.org/10.1007/JHEP09(2018)024	journal	September 2018
A new algorithm for the generation of unitarity-compatible integration by parts relations Schabinger, Robert M. Journal of High Energy Physics, Vol. 2012, Issue 1 https://doi.org/10.1007/JHEP01(2012)077	journal	January 2012
Towards a Basis for Planar Two-Loop Integrals Gluza, Janusz; Kajda, Krzysztof; Kosower, David A. arXiv https://doi.org/10.48550/arxiv.1009.0472	text	January 2010
High-Precision Calculation of Multiloop Feynman Integrals by Difference Equations Laporta, S. International Journal of Modern Physics A, Vol. 15, Issue 32 https://doi.org/10.1142/S0217751X00002159	journal	December 2000
Singularities and Discontinuities of Feynman Amplitudes Cutkosky, R. E. Journal of Mathematical Physics, Vol. 1, Issue 5 https://doi.org/10.1063/1.1703676	journal	September 1960
A first look at two-loop five-gluon scattering in QCD Badger, Simon; Brønnum-Hansen, Christian; Hartanto, Heribertus Bayu arXiv https://doi.org/10.48550/arxiv.1712.02229	text	January 2017
Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form Gituliar, O.; Magerya, V. arXiv https://doi.org/10.48550/arxiv.1701.04269	text	January 2017
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
Azurite : An algebraic geometry based package for finding bases of loop integrals Georgoudis, Alessandro; Larsen, Kasper J.; Zhang, Yang Computer Physics Communications, Vol. 221 https://doi.org/10.1016/j.cpc.2017.08.013	journal	December 2017
Kira—A Feynman integral reduction program Maierhöfer, P.; Usovitsch, J.; Uwer, P. Computer Physics Communications, Vol. 230 https://doi.org/10.1016/j.cpc.2018.04.012	journal	September 2018
Explicit solutions of the 3-loop vacuum integral recurrence relations Baikov, P. A. Physics Letters B, Vol. 385, Issue 1-4 https://doi.org/10.1016/0370-2693(96)00835-0	journal	September 1996
Fusing gauge theory tree amplitudes into loop amplitudes Bern, Zvi; Dixon, Lance; Dunbar, David C. Nuclear Physics B, Vol. 435, Issue 1-2 https://doi.org/10.1016/0550-3213(94)00488-Z	journal	February 1995
Explicit solutions of the n--loop vacuum integral recurrence relations Baikov, P. A. arXiv https://doi.org/10.48550/arxiv.hep-ph/9604254	preprint	January 1996
Bootstrapping pentagon functions Chicherin, Dmitry; Henn, Johannes; Mitev, Vladimir arXiv https://doi.org/10.48550/arxiv.1712.09610	text	January 2017
Space–time dimensionality as complex variable: Calculating loop integrals using dimensional recurrence relation and analytical properties with respect to Lee, R. N. Nuclear Physics B, Vol. 830, Issue 3 https://doi.org/10.1016/j.nuclphysb.2009.12.025	journal	May 2010
Two-loop master integrals for jets: the non-planar topologies Gehrmann, T.; Remiddi, E. Nuclear Physics B, Vol. 601, Issue 1-2 https://doi.org/10.1016/S0550-3213(01)00074-8	journal	May 2001
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
The analytical value of the electron (g − 2) at order α3 in QED Laporta, S.; Remiddi, E. Physics Letters B, Vol. 379, Issue 1-4 https://doi.org/10.1016/0370-2693(96)00439-X	journal	June 1996
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
Differential equations for two-loop four-point functions Gehrmann, T.; Remiddi, E. Nuclear Physics B, Vol. 580, Issue 1-2 https://doi.org/10.1016/S0550-3213(00)00223-6	journal	July 2000
The analytical value of the electron (g-2) at order alpha^3 in QED Laporta, S.; Remiddi, E. arXiv https://doi.org/10.48550/arxiv.hep-ph/9602417	text	January 1996
Dimensionally-regulated pentagon integrals Bern, Zvi; Dixon, Lance; Kosower, David A. Nuclear Physics B, Vol. 412, Issue 3 https://doi.org/10.1016/0550-3213(94)90398-0	journal	January 1994
Differential equations for Feynman graph amplitudes Remiddi, E. Il Nuovo Cimento A, Vol. 110, Issue 12 https://doi.org/10.1007/BF03185566	journal	December 1997

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