The pentabox Master Integrals with the Simplified Differential Equations approach

A bstract We present the calculation of massless two-loop Master Integrals relevant to five-point amplitudes with one off-shell external leg and derive the complete set of planar Master Integrals with five on-mass-shell legs, that contribute to many 2 → 3 amplitudes of interest at the LHC, as for in...

Full description

Saved in:
Bibliographic Details
Published inThe journal of high energy physics Vol. 2016; no. 4; pp. 1 - 18
Main Authors Papadopoulos, Costas G., Tommasini, Damiano, Wever, Christopher
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2016
Subjects
Online AccessGet full text

Cover

Loading…
Abstract A bstract We present the calculation of massless two-loop Master Integrals relevant to five-point amplitudes with one off-shell external leg and derive the complete set of planar Master Integrals with five on-mass-shell legs, that contribute to many 2 → 3 amplitudes of interest at the LHC, as for instance three jet production, γ , V, H + 2 jets etc., based on the Simplified Differential Equations approach.
AbstractList A bstract We present the calculation of massless two-loop Master Integrals relevant to five-point amplitudes with one off-shell external leg and derive the complete set of planar Master Integrals with five on-mass-shell legs, that contribute to many 2 → 3 amplitudes of interest at the LHC, as for instance three jet production, γ , V, H + 2 jets etc., based on the Simplified Differential Equations approach.
We present the calculation of massless two-loop Master Integrals relevant to five-point amplitudes with one off-shell external leg and derive the complete set of planar Master Integrals with five on-mass-shell legs, that contribute to many 2 arrow right 3 amplitudes of interest at the LHC, as for instance three jet production, gamma , V, H + 2 jets etc., based on the Simplified Differential Equations approach.
Author Papadopoulos, Costas G.
Tommasini, Damiano
Wever, Christopher
Author_xml – sequence: 1
  givenname: Costas G.
  surname: Papadopoulos
  fullname: Papadopoulos, Costas G.
  email: costas.papadopoulos@cern.ch
  organization: Institute of Nuclear and Particle Physics, NCSR ‘Demokritos’, University of Debrecen and MTA-DE Particle Physics Research Group
– sequence: 2
  givenname: Damiano
  surname: Tommasini
  fullname: Tommasini, Damiano
  organization: Institute of Nuclear and Particle Physics, NCSR ‘Demokritos’
– sequence: 3
  givenname: Christopher
  surname: Wever
  fullname: Wever, Christopher
  organization: Institute of Nuclear and Particle Physics, NCSR ‘Demokritos’, Institute for Theoretical Particle Physics (TTP), Karlsruhe Institute of Technology, Institute for Nuclear Physics (IKP), Karlsruhe Institute of Technology
BookMark eNp1kDFPwzAQRi1UJNrCzOqxDKFnJ3GcEZVCi0CAKLNl0kvrKk1S2xHw73EVBhZ0w93wvTvdG5FB3dRIyCWDawaQTR8W8xdIJhyYuIJMnpAhA55HMsnywZ_5jIyc2wGwlOUwJK-rLdIWa68_mi_6pJ1HS5e1x43VlaOfxm-pD5E3s28rUxpc01tTlmgDYnRF54dOe9PUjuq2tY0utufktAwoXvz2MXm_m69mi-jx-X45u3mMigS4j3gseKoFxAkvEAQKBhqzWJSQFjkHWQBn-VqXSawlpilKKbhMtdYpX2eCx_GYTPq94eyhQ-fV3rgCq0rX2HROMQmhWCZZiE77aGEb5yyWqrVmr-23YqCO8lQvTx3lqSAvENATLiTrDVq1azpbh3_-RX4A26pyaw
CitedBy_id crossref_primary_10_1103_PhysRevLett_122_121603
crossref_primary_10_1103_PhysRevLett_122_121602
crossref_primary_10_1103_PhysRevLett_127_262001
crossref_primary_10_1103_PhysRevD_97_105014
crossref_primary_10_1103_PhysRevLett_123_041603
crossref_primary_10_21468_SciPostPhysProc_7_023
crossref_primary_10_1103_PhysRevLett_127_151602
crossref_primary_10_1103_PhysRevD_105_L051503
crossref_primary_10_21468_SciPostPhysProc_7_028
crossref_primary_10_1103_PhysRevLett_123_071601
crossref_primary_10_1103_PhysRevLett_122_082002
crossref_primary_10_1103_PhysRevLett_132_141601
crossref_primary_10_1088_1742_6596_2105_1_012009
crossref_primary_10_1103_PhysRevD_106_074016
crossref_primary_10_21468_SciPostPhysProc_7_030
crossref_primary_10_1103_PhysRevD_97_116014
crossref_primary_10_1103_PhysRevLett_121_021602
crossref_primary_10_1103_PhysRevD_109_094025
crossref_primary_10_1103_PhysRevD_109_094024
crossref_primary_10_1088_1751_8121_ac7e8e
crossref_primary_10_1103_PhysRevD_109_094023
crossref_primary_10_1103_PhysRevLett_120_092001
crossref_primary_10_1103_PhysRevD_98_025023
crossref_primary_10_21468_SciPostPhysProc_7_037
crossref_primary_10_1007_JHEP08_2016_063
crossref_primary_10_1088_1751_8121_ac0ebf
Cites_doi 10.1016/0550-3213(79)90605-9
10.1016/j.cpc.2014.10.019
10.1016/S0550-3213(03)00299-2
10.1016/S0168-9002(97)00126-5
10.1007/JHEP09(2015)128
10.1007/JHEP06(2014)032
10.1016/0550-3213(94)00488-Z
10.1007/JHEP10(2013)037
10.1016/S0550-3213(98)00138-2
10.1007/JHEP08(2013)070
10.1007/JHEP04(2012)055
10.1016/0370-2693(93)90400-C
10.4310/MRL.1998.v5.n4.a7
10.1103/PhysRevLett.116.052002
10.1016/j.nuclphysb.2006.11.012
10.1007/JHEP10(2012)026
10.1007/JHEP01(2015)072
10.1145/1277548.1277550
10.1016/0550-3213(81)90199-1
10.1016/S0550-3213(00)00223-6
10.1016/0370-2693(81)90288-4
10.1088/1126-6708/2008/07/129
10.1016/j.cpc.2012.09.020
10.1142/S0217751X08040263
10.1007/JHEP05(2014)090
10.1016/j.nuclphysb.2004.10.044
10.1016/0550-3213(94)90179-1
10.1016/0370-2693(91)90536-Y
10.1007/BF01162962
10.1140/epjc/s10052-012-2139-2
10.1016/j.physrep.2012.01.008
10.1007/JHEP09(2014)043
10.1016/S0550-3213(00)00429-6
10.1016/S0550-3213(01)00074-8
10.1016/0370-2693(91)90413-K
10.1016/j.cpc.2014.11.024
10.1007/3-540-44574-9_1
10.1142/S0217751X00000367
10.1016/j.cpc.2013.05.022
10.1088/1126-6708/2008/05/004
10.1007/JHEP12(2013)045
10.1007/BF03185566
10.1016/j.cpc.2004.12.009
10.1016/S0550-3213(01)00057-8
10.1103/PhysRevLett.116.062001
10.1016/j.nuclphysb.2003.09.003
10.1103/PhysRevLett.110.251601
10.1007/JHEP07(2014)088
10.1007/JHEP11(2011)014
10.1016/j.jsc.2009.01.002
ContentType Journal Article
Copyright The Author(s) 2016
Copyright_xml – notice: The Author(s) 2016
DBID C6C
AAYXX
CITATION
7U5
8FD
H8D
L7M
DOI 10.1007/JHEP04(2016)078
DatabaseName Springer_OA刊
CrossRef
Solid State and Superconductivity Abstracts
Technology Research Database
Aerospace Database
Advanced Technologies Database with Aerospace
DatabaseTitle CrossRef
Aerospace Database
Solid State and Superconductivity Abstracts
Technology Research Database
Advanced Technologies Database with Aerospace
DatabaseTitleList
Aerospace Database
Database_xml – sequence: 1
  dbid: C6C
  name: SpringerOpen
  url: http://www.springeropen.com/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 1029-8479
EndPage 18
ExternalDocumentID 10_1007_JHEP04_2016_078
GroupedDBID -5F
-5G
-A0
-BR
0R~
0VY
199
1N0
30V
4.4
408
40D
5GY
5VS
8FE
8FG
8TC
8UJ
95.
AAFWJ
AAKKN
AAYZJ
ACACY
ACGFS
ACHIP
ACREN
ADBBV
ADINQ
AEGXH
AENEX
AFGXO
AFKRA
AFNRJ
AFPKN
AFWTZ
AHBXF
AHBYD
AHSBF
AHYZX
AIBLX
ALMA_UNASSIGNED_HOLDINGS
AMKLP
AMTXH
ARAPS
ASPBG
ATQHT
AVWKF
AZFZN
BCNDV
BENPR
BGLVJ
C24
C6C
CCPQU
CS3
CSCUP
DU5
EBS
EJD
ER.
FEDTE
GQ6
GROUPED_DOAJ
HCIFZ
HF~
HLICF
HMJXF
HVGLF
HZ~
IHE
KOV
LAP
M~E
N5L
N9A
NB0
O93
OK1
P62
P9T
PIMPY
PROAC
R9I
RO9
RSV
S27
S3B
SOJ
SPH
T13
TUS
U2A
VC2
VSI
WK8
XPP
Z45
ZMT
02O
1JI
1PV
1WK
2VQ
5ZI
AAGCD
AAGCF
AAIAL
AAJIO
AALHV
AARHV
AATNI
AAYXX
ABEEZ
ABTEG
ACAFW
ACBXY
ACMRT
ACULB
ADKPE
ADRFC
AEFHF
AEJGL
AERVB
AFLOW
AGJBK
AHSEE
AIYBF
AKPSB
AOAED
BAPOH
BBWZM
BGNMA
CAG
CITATION
CJUJL
COF
CRLBU
EDWGO
EMSAF
EPQRW
EQZZN
H13
HAK
IJHAN
IOP
IZVLO
JCGBZ
KC5
KOT
M45
M4Y
NT-
NT.
NU0
O9-
PJBAE
Q02
R4D
RIN
RKQ
RNS
ROL
RPA
S1Z
S3P
SY9
T37
7U5
8FD
H8D
L7M
ID FETCH-LOGICAL-c402t-23625a60342ce06e610ae736f05c9208c0219daf43a8e55e886285aaa52d76233
IEDL.DBID C24
ISSN 1029-8479
IngestDate Sat Aug 17 01:29:36 EDT 2024
Thu Sep 26 19:58:25 EDT 2024
Sat Dec 16 12:03:16 EST 2023
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 4
Keywords NLO Computations
QCD Phenomenology
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c402t-23625a60342ce06e610ae736f05c9208c0219daf43a8e55e886285aaa52d76233
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
OpenAccessLink http://link.springer.com/10.1007/JHEP04(2016)078
PQID 1808081781
PQPubID 23500
PageCount 18
ParticipantIDs proquest_miscellaneous_1808081781
crossref_primary_10_1007_JHEP04_2016_078
springer_journals_10_1007_JHEP04_2016_078
PublicationCentury 2000
PublicationDate 2016-04-01
PublicationDateYYYYMMDD 2016-04-01
PublicationDate_xml – month: 04
  year: 2016
  text: 2016-04-01
  day: 01
PublicationDecade 2010
PublicationPlace Berlin/Heidelberg
PublicationPlace_xml – name: Berlin/Heidelberg
PublicationTitle The journal of high energy physics
PublicationTitleAbbrev J. High Energ. Phys
PublicationYear 2016
Publisher Springer Berlin Heidelberg
Publisher_xml – name: Springer Berlin Heidelberg
References Z. Bern, L.J. Dixon and D.A. Kosower, Dimensionally regulated one loop integrals, Phys. Lett.B 302 (1993) 299 [Erratum ibid.B 318 (1993) 649] [hep-ph/9212308] [INSPIRE].
S. Borowka, G. Heinrich, S.P. Jones, M. Kerner, J. Schlenk and T. Zirke, SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop, Comput. Phys. Commun.196 (2015) 470 [arXiv:1502.06595] [INSPIRE].
M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys.B 522 (1998) 321 [hep-ph/9711391] [INSPIRE].
SM MC Working Group, SM and NLO MULTILEG Working Group collaborations, J. Alcaraz Maestre et al., The SM and NLO Multileg and SM MC working groups: summary report, arXiv:1203.6803 [INSPIRE].
S. Laporta and E. Remiddi, Analytic treatment of the two loop equal mass sunrise graph, Nucl. Phys.B 704 (2005) 349 [hep-ph/0406160] [INSPIRE].
BorowkaSCarterJHeinrichGNumerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0Comput. Phys. Commun.20131843962013CoPhC.184..396B10.1016/j.cpc.2012.09.020[arXiv:1204.4152] [INSPIRE]
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys.A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
Caron-HuotSLarsenKJUniqueness of two-loop master contoursJHEP2012100262012JHEP...10..026C10.1007/JHEP10(2012)026[arXiv:1205.0801] [INSPIRE]
V.A. Smirnov and M. Steinhauser, Solving recurrence relations for multiloop Feynman integrals, Nucl. Phys.B 672 (2003) 199 [hep-ph/0307088] [INSPIRE].
MastroliaPOssolaGOn the integrand-reduction method for two-loop scattering amplitudesJHEP2011110142011JHEP...11..014M291330510.1007/JHEP11(2011)0141306.81357[arXiv:1107.6041] [INSPIRE]
G. ’t Hooft and M.J.G. Veltman, Scalar one loop integrals, Nucl. Phys.B 153 (1979) 365 [INSPIRE].
RemiddiEDifferential equations for Feynman graph amplitudesNuovo Cim.1997A 11014351997NCimA.110.1435R[hep-th/9711188] [INSPIRE]
BadgerSFrellesvigHZhangYA two-loop five-gluon helicity amplitude in QCDJHEP2013120452013JHEP...12..045B10.1007/JHEP12(2013)045[arXiv:1310.1051] [INSPIRE]
KosowerDALarsenKJMaximal unitarity at two loopsPhys. Rev.2012D 850450172012PhRvD..85d5017K[arXiv:1108.1180] [INSPIRE]
M. Barkatou and E. Pflügel, Computing super-irreducible forms of systems of linear differential equations via Moser-reduction: a new approach, in Proceedings of the 2007 international symposium on Symbolic and algebraic computation, ACM, U.S.A. (2007), pg. 1.
SmirnovVAApplied asymptotic expansions in momenta and massesSpringer Tracts Mod. Phys.200217712002aaem.book.....S190359610.1007/3-540-44574-9_11025.81002[INSPIRE]
P.A. Baikov, Explicit solutions of the multiloop integral recurrence relations and its application, Nucl. Instrum. Meth.A 389 (1997) 347 [hep-ph/9611449] [INSPIRE].
Analytic results for all two-loop MI in terms of Goncharov polylogarithms together with explicit numerical results, https://www.dropbox.com/s/90iiqfcazrhwtso/results.tgz?dl=0.
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys.B 435 (1995) 59 [hep-ph/9409265] [INSPIRE].
EllisRKKunsztZMelnikovKZanderighiGOne-loop calculations in quantum field theory: from Feynman diagrams to unitarity cutsPhys. Rept.20125181412012PhR...518..141E297928510.1016/j.physrep.2012.01.008[arXiv:1105.4319] [INSPIRE]
CaolaFHennJMMelnikovKSmirnovVANon-planar master integrals for the production of two off-shell vector bosons in collisions of massless partonsJHEP2014090432014JHEP...09..043C10.1007/JHEP09(2014)043[arXiv:1404.5590] [INSPIRE]
LeeRNReducing differential equations for multiloop master integralsJHEP2015041082015JHEP...04..108L335126110.1007/JHEP04(2015)108[arXiv:1411.0911] [INSPIRE]
TkachovFVA theorem on analytical calculability of four loop renormalization group functionsPhys. Lett.1981B 100651981PhLB..100...65T60764010.1016/0370-2693(81)90288-4[INSPIRE]
HennJMMelnikovKSmirnovVATwo-loop planar master integrals for the production of off-shell vector bosons in hadron collisionsJHEP2014050902014JHEP...05..090H10.1007/JHEP05(2014)090[arXiv:1402.7078] [INSPIRE]
BarkatouMPflügelEOn the Moser-and super-reduction algorithms of systems of linear differential equations and their complexityJ. Symb. Comput.2009441017252376510.1016/j.jsc.2009.01.0021183.34134
T. Gehrmann and E. Remiddi, Two loop master integrals for γ∗ → 3 jets: the planar topologies, Nucl. Phys.B 601 (2001) 248 [hep-ph/0008287] [INSPIRE].
GehrmannTvon ManteuffelATancrediLThe two-loop helicity amplitudes for qq¯′→V1V2→4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ q{\overline{q}}^{\prime}\to {V}_1{V}_2\to\ 4 $$\end{document} leptonsJHEP2015091282015JHEP...09..128G10.1007/JHEP09(2015)128[arXiv:1503.04812] [INSPIRE]
CMS collaboration, Measurement of spin correlations intt¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ t\overline{t} $$\end{document}production using the matrix element method in the muon+jets final state in pp collisions ats=8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s}=8 $$\end{document}TeV, arXiv:1511.06170 [INSPIRE].
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys.A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
HeinrichGSector decompositionInt. J. Mod. Phys.2008A 2314572008IJMPA..23.1457H240144810.1142/S0217751X080402631153.81522[arXiv:0803.4177] [INSPIRE]
GehrmannTTancrediLWeihsETwo-loop master integrals for qq¯→VV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ q\overline{q}\to VV $$\end{document}: the planar topologiesJHEP2013080702013JHEP...08..070G10.1007/JHEP08(2013)070[arXiv:1306.6344] [INSPIRE]
BorowkaSHeinrichGMassive non-planar two-loop four-point integrals with SecDec 2.1Comput. Phys. Commun.201318425522013CoPhC.184.2552B10.1016/j.cpc.2013.05.022[arXiv:1303.1157] [INSPIRE]
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys.B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
CMS collaboration, Measurement of the top quark pair production cross section in proton-proton collisions ats=13\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s}=13 $$\end{document}TeV, Phys. Rev. Lett.116 (2016) 052002 [arXiv:1510.05302] [INSPIRE].
J.R. Andersen et al., Les Houches 2013: physics at TeV colliders — standard model working group report, arXiv:1405.1067 [INSPIRE].
R. Bonciani, P. Mastrolia and E. Remiddi, Vertex diagrams for the QED form-factors at the two loop level, Nucl. Phys.B 661 (2003) 289 [Erratum ibid.B 702 (2004) 359] [hep-ph/0301170] [INSPIRE].
von ManteuffelAStuderusCMassive planar and non-planar double box integrals for light Nfcontributions to gg → ttJHEP20131003710.1007/JHEP10(2013)037[arXiv:1306.3504] [INSPIRE]
PapadopoulosCGSimplified differential equations approach for master integralsJHEP2014070882014JHEP...07..088P10.1007/JHEP07(2014)088[arXiv:1401.6057] [INSPIRE]
JantzenBSmirnovAVSmirnovVAExpansion by regions: revealing potential and Glauber regions automaticallyEur. Phys. J.2012C 7221392012EPJC...72.2139J10.1140/epjc/s10052-012-2139-2[arXiv:1206.0546] [INSPIRE]
GehrmannTHennJMLo PrestiNAAnalytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCDPhys. Rev. Lett.20161160620012016PhRvL.116f2001G10.1103/PhysRevLett.116.062001[arXiv:1511.05409] [INSPIRE]
ATLAS collaboration, Measurement of the production cross sections of a Z boson in association with jets in pp collisions ats=13\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s}=13 $$\end{document}TeV with the ATLAS detector, ATLAS-CONF-2015-041, CERN, Geneva Switzerland (2015).
J. Vollinga and S. Weinzierl, Numerical evaluation of multiple polylogarithms, Comput. Phys. Commun.167 (2005) 177 [hep-ph/0410259] [INSPIRE].
PanzerEAlgorithms for the symbolic integration of hyperlogarithms with applications to Feynman integralsComput. Phys. Commun.20141881482015CoPhC.188..148P10.1016/j.cpc.2014.10.019[arXiv:1403.3385] [INSPIRE]
GoncharovABMultiple polylogarithms, cyclotomy and modular complexesMath. Res. Lett.19985497165332010.4310/MRL.1998.v5.n4.a70961.11040[arXiv:1105.2076] [INSPIRE]
ATLAS collaboration, Measurement of four-jet differential cross sections ins=8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \sqrt{s}=8 $$\end{document}TeV proton-proton collisions using the ATLAS detector, JHEP12 (2015) 105 [arXiv:1509.07335] [INSPIRE].
GluzaJKajdaKKosowerDATowards a basis for planar two-loop integralsPhys. Rev.2011D 830450122011PhRvD..83d5012G[arXiv:1009.0472] [INSPIRE]
BoncianiRFerrogliaAGehrmannTMaîtreDStuderusCTwo-loop fermionic corrections to heavy-quark pair production: the quark-antiquark channelJHEP2008071292008JHEP...07..129B10.1088/1126-6708/2008/07/129[arXiv:0806.2301] [INSPIRE]
T. Gehrmann and E. Remiddi, Differential equations
S Badger (3725_CR17) 2013; 12
AV Kotikov (3725_CR23) 1991; B 254
3725_CR43
M Caffo (3725_CR29) 1998; A 111
3725_CR46
G Ossola (3725_CR9) 2008; 05
3725_CR47
J Moser (3725_CR55) 1960; 72
S Borowka (3725_CR60) 2013; 184
G Heinrich (3725_CR59) 2008; A 23
RK Ellis (3725_CR11) 2012; 518
DA Kosower (3725_CR13) 2012; D 85
R Bonciani (3725_CR34) 2008; 07
CG Papadopoulos (3725_CR42) 2014; 07
T Gehrmann (3725_CR49) 2016; 116
3725_CR10
3725_CR54
T Gehrmann (3725_CR41) 2015; 09
3725_CR19
3725_CR18
3725_CR7
3725_CR57
3725_CR8
KG Chetyrkin (3725_CR44) 1981; B 192
3725_CR58
3725_CR3
3725_CR4
M Barkatou (3725_CR53) 2009; 44
3725_CR5
3725_CR6
S Badger (3725_CR16) 2012; 04
3725_CR1
3725_CR2
S Caron-Huot (3725_CR14) 2012; 10
P Mastrolia (3725_CR15) 2011; 11
3725_CR64
3725_CR22
3725_CR66
3725_CR21
3725_CR65
F Caola (3725_CR39) 2014; 09
T Gehrmann (3725_CR35) 2013; 08
AB Goncharov (3725_CR20) 1998; 5
3725_CR62
RN Lee (3725_CR52) 2015; 04
AV Smirnov (3725_CR50) 2014; 189
3725_CR27
T Gehrmann (3725_CR38) 2014; 06
JM Henn (3725_CR37) 2014; 05
3725_CR25
CG Papadopoulos (3725_CR40) 2015; 01
3725_CR31
3725_CR30
AV Kotikov (3725_CR24) 1991; B 267
3725_CR33
3725_CR32
JM Henn (3725_CR51) 2015; A 48
S Borowka (3725_CR61) 2013; 184
E Remiddi (3725_CR26) 1997; A 110
A Manteuffel von (3725_CR36) 2013; 10
B Jantzen (3725_CR56) 2012; C 72
VA Smirnov (3725_CR48) 2002; 177
JM Henn (3725_CR28) 2013; 110
FV Tkachov (3725_CR45) 1981; B 100
E Panzer (3725_CR63) 2014; 188
J Gluza (3725_CR12) 2011; D 83
References_xml – ident: 3725_CR19
  doi: 10.1016/0550-3213(79)90605-9
– volume: 188
  start-page: 148
  year: 2014
  ident: 3725_CR63
  publication-title: Comput. Phys. Commun.
  doi: 10.1016/j.cpc.2014.10.019
  contributor:
    fullname: E Panzer
– ident: 3725_CR32
  doi: 10.1016/S0550-3213(03)00299-2
– ident: 3725_CR64
  doi: 10.1016/S0168-9002(97)00126-5
– volume: 09
  start-page: 128
  year: 2015
  ident: 3725_CR41
  publication-title: JHEP
  doi: 10.1007/JHEP09(2015)128
  contributor:
    fullname: T Gehrmann
– volume: 06
  start-page: 032
  year: 2014
  ident: 3725_CR38
  publication-title: JHEP
  doi: 10.1007/JHEP06(2014)032
  contributor:
    fullname: T Gehrmann
– ident: 3725_CR6
  doi: 10.1016/0550-3213(94)00488-Z
– volume: A 111
  start-page: 365
  year: 1998
  ident: 3725_CR29
  publication-title: Nuovo Cim.
  contributor:
    fullname: M Caffo
– ident: 3725_CR5
– volume: D 83
  start-page: 045012
  year: 2011
  ident: 3725_CR12
  publication-title: Phys. Rev.
  contributor:
    fullname: J Gluza
– volume: 10
  start-page: 037
  year: 2013
  ident: 3725_CR36
  publication-title: JHEP
  doi: 10.1007/JHEP10(2013)037
  contributor:
    fullname: A Manteuffel von
– ident: 3725_CR47
  doi: 10.1016/S0550-3213(98)00138-2
– volume: 08
  start-page: 070
  year: 2013
  ident: 3725_CR35
  publication-title: JHEP
  doi: 10.1007/JHEP08(2013)070
  contributor:
    fullname: T Gehrmann
– volume: 04
  start-page: 055
  year: 2012
  ident: 3725_CR16
  publication-title: JHEP
  doi: 10.1007/JHEP04(2012)055
  contributor:
    fullname: S Badger
– ident: 3725_CR22
– ident: 3725_CR25
  doi: 10.1016/0370-2693(93)90400-C
– volume: 5
  start-page: 497
  year: 1998
  ident: 3725_CR20
  publication-title: Math. Res. Lett.
  doi: 10.4310/MRL.1998.v5.n4.a7
  contributor:
    fullname: AB Goncharov
– ident: 3725_CR43
– ident: 3725_CR1
  doi: 10.1103/PhysRevLett.116.052002
– ident: 3725_CR8
  doi: 10.1016/j.nuclphysb.2006.11.012
– volume: 10
  start-page: 026
  year: 2012
  ident: 3725_CR14
  publication-title: JHEP
  doi: 10.1007/JHEP10(2012)026
  contributor:
    fullname: S Caron-Huot
– volume: 01
  start-page: 072
  year: 2015
  ident: 3725_CR40
  publication-title: JHEP
  doi: 10.1007/JHEP01(2015)072
  contributor:
    fullname: CG Papadopoulos
– ident: 3725_CR54
  doi: 10.1145/1277548.1277550
– volume: B 192
  start-page: 159
  year: 1981
  ident: 3725_CR44
  publication-title: Nucl. Phys.
  doi: 10.1016/0550-3213(81)90199-1
  contributor:
    fullname: KG Chetyrkin
– ident: 3725_CR27
  doi: 10.1016/S0550-3213(00)00223-6
– volume: B 100
  start-page: 65
  year: 1981
  ident: 3725_CR45
  publication-title: Phys. Lett.
  doi: 10.1016/0370-2693(81)90288-4
  contributor:
    fullname: FV Tkachov
– volume: 07
  start-page: 129
  year: 2008
  ident: 3725_CR34
  publication-title: JHEP
  doi: 10.1088/1126-6708/2008/07/129
  contributor:
    fullname: R Bonciani
– volume: 184
  start-page: 396
  year: 2013
  ident: 3725_CR60
  publication-title: Comput. Phys. Commun.
  doi: 10.1016/j.cpc.2012.09.020
  contributor:
    fullname: S Borowka
– volume: A 23
  start-page: 1457
  year: 2008
  ident: 3725_CR59
  publication-title: Int. J. Mod. Phys.
  doi: 10.1142/S0217751X08040263
  contributor:
    fullname: G Heinrich
– volume: A 48
  start-page: 153001
  year: 2015
  ident: 3725_CR51
  publication-title: J. Phys.
  contributor:
    fullname: JM Henn
– ident: 3725_CR2
– volume: 05
  start-page: 090
  year: 2014
  ident: 3725_CR37
  publication-title: JHEP
  doi: 10.1007/JHEP05(2014)090
  contributor:
    fullname: JM Henn
– ident: 3725_CR33
  doi: 10.1016/j.nuclphysb.2004.10.044
– ident: 3725_CR7
  doi: 10.1016/0550-3213(94)90179-1
– volume: B 267
  start-page: 123
  year: 1991
  ident: 3725_CR24
  publication-title: Phys. Lett.
  doi: 10.1016/0370-2693(91)90536-Y
  contributor:
    fullname: AV Kotikov
– volume: 72
  start-page: 379
  year: 1960
  ident: 3725_CR55
  publication-title: Math. Zeitschr.
  doi: 10.1007/BF01162962
  contributor:
    fullname: J Moser
– volume: C 72
  start-page: 2139
  year: 2012
  ident: 3725_CR56
  publication-title: Eur. Phys. J.
  doi: 10.1140/epjc/s10052-012-2139-2
  contributor:
    fullname: B Jantzen
– ident: 3725_CR46
– volume: 518
  start-page: 141
  year: 2012
  ident: 3725_CR11
  publication-title: Phys. Rept.
  doi: 10.1016/j.physrep.2012.01.008
  contributor:
    fullname: RK Ellis
– ident: 3725_CR62
– ident: 3725_CR66
– volume: 09
  start-page: 043
  year: 2014
  ident: 3725_CR39
  publication-title: JHEP
  doi: 10.1007/JHEP09(2014)043
  contributor:
    fullname: F Caola
– ident: 3725_CR58
  doi: 10.1016/S0550-3213(00)00429-6
– ident: 3725_CR31
  doi: 10.1016/S0550-3213(01)00074-8
– volume: D 85
  start-page: 045017
  year: 2012
  ident: 3725_CR13
  publication-title: Phys. Rev.
  contributor:
    fullname: DA Kosower
– volume: B 254
  start-page: 158
  year: 1991
  ident: 3725_CR23
  publication-title: Phys. Lett.
  doi: 10.1016/0370-2693(91)90413-K
  contributor:
    fullname: AV Kotikov
– ident: 3725_CR10
– ident: 3725_CR3
– volume: 189
  start-page: 182
  year: 2014
  ident: 3725_CR50
  publication-title: Comput. Phys. Commun.
  doi: 10.1016/j.cpc.2014.11.024
  contributor:
    fullname: AV Smirnov
– volume: 177
  start-page: 1
  year: 2002
  ident: 3725_CR48
  publication-title: Springer Tracts Mod. Phys.
  doi: 10.1007/3-540-44574-9_1
  contributor:
    fullname: VA Smirnov
– ident: 3725_CR18
– ident: 3725_CR21
  doi: 10.1142/S0217751X00000367
– volume: 184
  start-page: 2552
  year: 2013
  ident: 3725_CR61
  publication-title: Comput. Phys. Commun.
  doi: 10.1016/j.cpc.2013.05.022
  contributor:
    fullname: S Borowka
– volume: 05
  start-page: 004
  year: 2008
  ident: 3725_CR9
  publication-title: JHEP
  doi: 10.1088/1126-6708/2008/05/004
  contributor:
    fullname: G Ossola
– volume: 12
  start-page: 045
  year: 2013
  ident: 3725_CR17
  publication-title: JHEP
  doi: 10.1007/JHEP12(2013)045
  contributor:
    fullname: S Badger
– volume: A 110
  start-page: 1435
  year: 1997
  ident: 3725_CR26
  publication-title: Nuovo Cim.
  doi: 10.1007/BF03185566
  contributor:
    fullname: E Remiddi
– ident: 3725_CR57
  doi: 10.1016/j.cpc.2004.12.009
– ident: 3725_CR30
  doi: 10.1016/S0550-3213(01)00057-8
– volume: 116
  start-page: 062001
  year: 2016
  ident: 3725_CR49
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.116.062001
  contributor:
    fullname: T Gehrmann
– ident: 3725_CR65
  doi: 10.1016/j.nuclphysb.2003.09.003
– volume: 04
  start-page: 108
  year: 2015
  ident: 3725_CR52
  publication-title: JHEP
  contributor:
    fullname: RN Lee
– volume: 110
  start-page: 251601
  year: 2013
  ident: 3725_CR28
  publication-title: Phys. Rev. Lett.
  doi: 10.1103/PhysRevLett.110.251601
  contributor:
    fullname: JM Henn
– volume: 07
  start-page: 088
  year: 2014
  ident: 3725_CR42
  publication-title: JHEP
  doi: 10.1007/JHEP07(2014)088
  contributor:
    fullname: CG Papadopoulos
– volume: 11
  start-page: 014
  year: 2011
  ident: 3725_CR15
  publication-title: JHEP
  doi: 10.1007/JHEP11(2011)014
  contributor:
    fullname: P Mastrolia
– volume: 44
  start-page: 1017
  year: 2009
  ident: 3725_CR53
  publication-title: J. Symb. Comput.
  doi: 10.1016/j.jsc.2009.01.002
  contributor:
    fullname: M Barkatou
– ident: 3725_CR4
SSID ssj0015190
Score 2.5916631
Snippet A bstract We present the calculation of massless two-loop Master Integrals relevant to five-point amplitudes with one off-shell external leg and derive the...
We present the calculation of massless two-loop Master Integrals relevant to five-point amplitudes with one off-shell external leg and derive the complete set...
SourceID proquest
crossref
springer
SourceType Aggregation Database
Publisher
StartPage 1
SubjectTerms Amplitudes
Classical and Quantum Gravitation
Differential equations
Elementary Particles
Integrals
Legs
Mathematical analysis
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Title The pentabox Master Integrals with the Simplified Differential Equations approach
URI https://link.springer.com/article/10.1007/JHEP04(2016)078
https://search.proquest.com/docview/1808081781
Volume 2016
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3JTsMwEB11ERIXxCrKEhmJQ3sIchZnOZbSUiq1Kkul3iIncSRElRbSSnw-M1lAgDhwsXKwcxiP_Z49M88Al5YUPIxsS49JZ8jmttRljOtRGUkYIl32vZCKk8cTZzizR3MxrwH_vLpIX66qiGS-UVe1bqNhf8rtNuKV00FYq0OTmAP5dI_qG8q4AfIRXgn4_B70HXu-COWPGGgOLYNd2Ck5IesWk7gHNZXuw1aemxllB3CPU8lWlOMdLt_ZWJK0AbsrZB4WGaObVIY0jj0-U3Z4gpyS3ZTPnuDyXbD-ayHnnbFKQPwQZoP-U2-oly8h6BGe79a6iTAjpENyfZHijkLOI5VrOQkXkW9yL0Kk9mOZ2Jb0lBDK86gyUkopzBh3O8s6gka6TNUxsEQZkiem6QokEtRJ-Y6QEZJsqWw3li1oVzYKVoXgRVBJGxfmDMicAZqzBReVDQN0Soo0yFQtN1lgkFqlZ7ie0YJOZdygXB3ZX_87-UffU9imzyKH5gwa67eNOkd6sA41qHuDWw2a1_3J9EHL_YNap6flB25sZ2b3A7R2uNE
link.rule.ids 315,786,790,870,27955,27956,33407,33778,41152,41153,41556,42221,42222,42625,51609,52266,52267
linkProvider Springer Nature
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8NAEF60InoRn1ifK3hoD8HNY_M4Sm1Ja1sUW-htmSQbEEpaTQv-fGeaRLHiwWvY5PDtzn5fdma-ZezWBimi2LGNhHyGHOGAAQnGozbTKEK5HPgRNScPhm44dnoTOSlNkqgXZi1_f9cL20_CaSBNuU1ks022RWcWdFVBy219pQtQhojKt-f3Sz8p51tHrqU-V4zS2Wd7pRTk98XcHbANnR2y7VVJZpwfsWecQT6n0u5o9sEHQI4GvFu4O0xzTgeoHNUbf3mlovAUpSR_KG87waid8vZb4eKd88o3_JiNO-1RKzTKCxCMGH_rFoaF7CLBJZe-WAtXo9QB7dluKmQcWMKPkaCDBFLHBl9LqX2fGiIBQFoJbnK2fcJq2SzTp4yn2gSRWpYnUT_QIB24EmLU1qAdL4E6a1QYqXnhc6EqR-MCTkVwKoSzzm4qDBWuRUowQKZny1yZZFLpm55v1lmzAleVQZH_9b2zf4y9ZjvhaNBX_e7w8Zzt0uOijOaC1RbvS32JCmERXa1Wxyez-7MG
linkToPdf http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8NAEB60ongRn1ifK3hoD6Gbx-ZxLLalrbZUtNBb2CQbEEpaTQr-fGearKLiwWvY5DA7k-9L5ptvAW5tKXgUO7aRkM-Qwx1pyATrUZlpFCFdDvyIhpNHY7c_dYYzMau0OblWu-uWZDnTQC5NWdFaJqnu6reG_e6EOw0EL7eJGLcJW4SLlOBTq_3ZREBywrWbz--bvgPRF7v80RBd40xvH_Yqgsja5Y4ewIbKDmF7LdSM8yN4xH1lSxJ8R4t3NpLkc8AGpefDPGf0W5Uhp2NPLyQVT5Fgsk51BgrW8px1X0tv75xpN_FjmPa6z3d9ozoWwYjxY68wLMQcIV3y7osVdxUSIKk82025iAOL-zHCdpDI1LGlr4RQvk9jklJKYSX46rPtE6hli0ydAkuVKXlqWZ5AVkGLVOAKGSPjlsrxElmHho5RuCzdL0Ltc1yGM6RwhhjOOtzoGIaYodR2kJlarPLQJOtK3_R8sw5NHdywKpX8r-ed_WPtNexMOr3wYTC-P4ddulpqay6gVryt1CXShiK6WifHB7wEu3U
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The+pentabox+Master+Integrals+with+the+Simplified+Differential+Equations+approach&rft.jtitle=The+journal+of+high+energy+physics&rft.au=Papadopoulos%2C+Costas+G.&rft.au=Tommasini%2C+Damiano&rft.au=Wever%2C+Christopher&rft.date=2016-04-01&rft.pub=Springer+Berlin+Heidelberg&rft.eissn=1029-8479&rft.volume=2016&rft.issue=4&rft_id=info:doi/10.1007%2FJHEP04%282016%29078&rft.externalDocID=10_1007_JHEP04_2016_078
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1029-8479&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1029-8479&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1029-8479&client=summon