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Volumn 2011, Issue 11, 2011, Pages

On the integrand-reduction method for two-loop cattering amplitudes

Author keywords

NLO computations; QCD; Standard model

Indexed keywords


EID: 81255169889     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP11(2011)014     Document Type: Article
Times cited : (143)

References (125)
  • 1
    • 23044434458 scopus 로고    scopus 로고
    • MHV vertices and tree amplitudes in gauge theory
    • [hep-th/0403047]
    • F. Cachazo, P. Svrček and E. Witten, MHV vertices and tree amplitudes in gauge theory, JHEP 09 (2004) 006 [hep-th/0403047]
    • (2004) JHEP , vol.9 , pp. 006
    • Cachazo, F.1    Svrček, P.2    Witten, E.3
  • 2
    • 17544366149 scopus 로고    scopus 로고
    • New recursion relations for tree amplitudes of gluons
    • [hep-th/0412308]
    • R. Britto, F. Cachazo and B. Feng, New recursion relations for tree amplitudes of gluons, Nucl. Phys. B 715 (2005) 499 [hep-th/0412308]
    • (2005) Nucl. Phys. B , vol.715 , pp. 499
    • Britto, R.1    Cachazo, F.2    Feng, B.3
  • 3
    • 27144442779 scopus 로고    scopus 로고
    • Direct proof of tree-level recursion relation in Yang-Mills theory
    • [hep-th/0501052]
    • R. Britto, F. Cachazo, B. Feng and E. Witten, Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett. 94 (2005) 181602 [hep-th/0501052]
    • (2005) Phys. Rev. Lett. , vol.94 , pp. 181602
    • Britto, R.1    Cachazo, F.2    Feng, B.3    Witten, E.4
  • 4
    • 0000632007 scopus 로고
    • One loop n point gauge theory amplitudes, unitarity and collinear limits
    • [hep-ph/9403226]
    • 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]
    • (1994) Nucl. Phys. B , vol.425 , pp. 217
    • Bern, Z.1    Dixon, L.J.2    Dunbar, D.C.3    Kosower, D.A.4
  • 5
    • 0003149712 scopus 로고
    • Fusing gauge theory tree amplitudes into loop amplitudes
    • [hep-ph/9409265]
    • 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]
    • (1995) Nucl. Phys. B , vol.435 , pp. 59
    • Bern, Z.1    Dixon, L.J.2    Dunbar, D.C.3    Kosower, D.A.4
  • 6
    • 24344485193 scopus 로고    scopus 로고
    • Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills
    • [hep-th/0412103]
    • R. Britto, F. Cachazo and B. Feng, Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys. B 725 (2005) 275 [hep-th/0412103]
    • (2005) Nucl. Phys. B , vol.725 , pp. 275
    • Britto, R.1    Cachazo, F.2    Feng, B.3
  • 7
    • 0000267440 scopus 로고
    • On analytic properties of vertex parts in quantum field theory
    • L.D. Landau, On analytic properties of vertex parts in quantum field theory, Nucl. Phys. 13 (1959) 181
    • (1959) Nucl. Phys. , vol.13 , pp. 181
    • Landau, L.D.1
  • 8
    • 0000223693 scopus 로고
    • Determination of the pion-nucleon scattering amplitude from dispersion relations and unitarity. General theory
    • S. Mandelstam, Determination of the pion-nucleon scattering amplitude from dispersion relations and unitarity. General theory, Phys. Rev. 112 (1958) 1344
    • (1958) Phys. Rev. , vol.112 , pp. 1344
    • Mandelstam, S.1
  • 9
    • 0001538901 scopus 로고
    • Analytic properties of transition amplitudes in perturbation theory
    • S. Mandelstam, Analytic properties of transition amplitudes in perturbation theory, Phys. Rev. 115 (1959) 1741
    • (1959) Phys. Rev. , vol.115 , pp. 1741
    • Mandelstam, S.1
  • 10
    • 29744468057 scopus 로고
    • Singularities and discontinuities of Feynman amplitudes
    • R.E. Cutkosky, Singularities and discontinuities of Feynman amplitudes, J. Math. Phys. 1 (1960) 429
    • (1960) J. Math. Phys. , vol.1 , pp. 429
    • Cutkosky, R.E.1
  • 12
    • 0000065089 scopus 로고
    • Unitarity and causality in a renormalizable field theory with unstable particles
    • M.G.J. Veltman, Unitarity and causality in a renormalizable field theory with unstable particles, Physica 29 (1963) 186
    • (1963) Physica , vol.29 , pp. 186
    • Veltman, M.G.J.1
  • 13
    • 33644655551 scopus 로고
    • Dispersion relations for Feynman graphs
    • E. Remiddi, Dispersion relations for Feynman graphs, Helv. Phys. Acta 54 (1982) 364
    • (1982) Helv. Phys. Acta , vol.54 , pp. 364
    • Remiddi, E.1
  • 14
    • 23044502540 scopus 로고    scopus 로고
    • Recursive numerical calculus of one-loop tensor integrals
    • [hep-ph/0404120]
    • F. del Aguila and R. Pittau, Recursive numerical calculus of one-loop tensor integrals, JHEP 07 (2004) 017 [hep-ph/0404120]
    • (2004) JHEP , vol.7 , pp. 017
    • Del Aguila, F.1    Pittau, R.2
  • 15
    • 33846011109 scopus 로고    scopus 로고
    • Reducing full one-loop amplitudes to scalar integrals at the integrand level
    • [hep-ph/0609007]
    • G. Ossola, C.G. Papadopoulos and R. Pittau, Reducing full one-loop amplitudes to scalar integrals at the integrand level, Nucl. Phys. B 763 (2007) 147 [hep-ph/0609007]
    • (2007) Nucl. Phys. B , vol.763 , pp. 147
    • Ossola, G.1    Papadopoulos, C.G.2    Pittau, R.3
  • 16
    • 34547665038 scopus 로고    scopus 로고
    • Numerical evaluation of six-photon amplitudes
    • [arXiv:0704.1271]
    • G. Ossola, C.G. Papadopoulos and R. Pittau, Numerical evaluation of six-photon amplitudes, JHEP 07 (2007) 085 [arXiv:0704.1271]
    • (2007) JHEP , vol.7 , pp. 085
    • Ossola, G.1    Papadopoulos, C.G.2    Pittau, R.3
  • 17
    • 47249115748 scopus 로고    scopus 로고
    • On the rational terms of the one-loop amplitudes
    • [arXiv:0802. 1876]
    • G. Ossola, C.G. Papadopoulos and R. Pittau, On the rational terms of the one-loop amplitudes, JHEP 05 (2008) 004 [arXiv:0802.1876]
    • (2008) JHEP , vol.5 , pp. 004
    • Ossola, G.1    Papadopoulos, C.G.2    Pittau, R.3
  • 18
    • 11244344133 scopus 로고    scopus 로고
    • Perturbative gauge theory as a string theory in twistor space
    • [hep-th/0312171]
    • E. Witten, Perturbative gauge theory as a string theory in twistor space, Commun. Math. Phys. 252 (2004) 189 [hep-th/0312171]
    • (2004) Commun. Math. Phys. , vol.252 , pp. 189
    • Witten, E.1
  • 19
    • 33947628733 scopus 로고    scopus 로고
    • Magic identities for conformal four-point integrals
    • [hep-th/0607160]
    • J.M. Drummond, J. Henn, V.A. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP 01 (2007) 064 [hep-th/0607160]
    • (2007) JHEP , vol.1 , pp. 064
    • Drummond, J.M.1    Henn, J.2    Smirnov, V.A.3    Sokatchev, E.4
  • 20
    • 34249282692 scopus 로고    scopus 로고
    • The four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory
    • [hep-th/0610248]
    • Z. Bern, M. Czakon, L.J. Dixon, D.A. Kosower and V.A. Smirnov, The four-loop planar amplitude and cusp anomalous dimension in maximally supersymmetric Yang-Mills theory, Phys. Rev. D 75 (2007) 085010 [hep-th/0610248]
    • (2007) Phys. Rev.D , vol.75 , pp. 085010
    • Bern, Z.1    Czakon, M.2    Dixon, L.J.3    Kosower, D.A.4    Smirnov, V.A.5
  • 21
    • 72149096509 scopus 로고    scopus 로고
    • Dual superconformal symmetry of scattering amplitudes in N = 4 super-Yang-Mills theory
    • [arXiv:0807.1095]
    • J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Dual superconformal symmetry of scattering amplitudes in N = 4 super-Yang-Mills theory, Nucl. Phys. B 828 (2010) 317 [arXiv:0807.1095]
    • (2010) Nucl. Phys. B , vol.828 , pp. 317
    • Drummond, J.M.1    Henn, J.2    Korchemsky, G.P.3    Sokatchev, E.4
  • 22
    • 57749207942 scopus 로고    scopus 로고
    • A note on dual superconformal symmetry of the N = 4 super Yang-Mills S-matrix
    • [arXiv:0807.4097]
    • A. Brandhuber, P. Heslop and G. Travaglini, A note on dual superconformal symmetry of the N = 4 super Yang-Mills S-matrix, Phys. Rev. D 78 (2008) 125005 [arXiv:0807.4097]
    • (2008) Phys. Rev.D , vol.78 , pp. 125005
    • Brandhuber, A.1    Heslop, P.2    Travaglini, G.3
  • 23
  • 24
    • 70549088009 scopus 로고    scopus 로고
    • Dual superconformal invariance momentum twistors and Grassmannians
    • [arXiv:0909.0250]
    • L.J. Mason and D. Skinner, Dual superconformal invariance, momentum twistors and Grassmannians, JHEP 11 (2009) 045 [arXiv:0909.0250]
    • (2009) JHEP , vol.11 , pp. 045
    • Mason, L.J.1    Skinner, D.2
  • 25
    • 77954940831 scopus 로고    scopus 로고
    • The Grassmannian origin of dual superconformal invariance
    • [arXiv:0909.0483]
    • N. Arkani-Hamed, F. Cachazo and C. Cheung, The Grassmannian origin of dual superconformal invariance, JHEP 03 (2010) 036 [arXiv:0909.0483]
    • (2010) JHEP , vol.3 , pp. 036
    • Arkani-Hamed, N.1    Cachazo, F.2    Cheung, C.3
  • 26
    • 34547681641 scopus 로고    scopus 로고
    • Gluon scattering amplitudes at strong coupling
    • [arXiv:0705.0303]
    • L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303]
    • (2007) JHEP , vol.6 , pp. 064
    • Alday, L.F.1    Maldacena, J.M.2
  • 27
    • 55349119167 scopus 로고    scopus 로고
    • New relations for gauge-theory amplitudes
    • [arXiv:0805.3993]
    • Z. Bern, J.J.M. Carrasco and H. Johansson, New relations for gauge-theory amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993]
    • (2008) Phys. Rev.D , vol.78 , pp. 085011
    • Bern, Z.1    Carrasco, J.J.M.2    Johansson, H.3
  • 28
    • 77955335870 scopus 로고    scopus 로고
    • Perturbative quantum gravity as a double copy of gauge theory
    • [arXiv:1004.0476]
    • Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative quantum gravity as a double copy of gauge theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476]
    • (2010) Phys. Rev. Lett. , vol.105 , pp. 061602
    • Bern, Z.1    Carrasco, J.J.M.2    Johansson, H.3
  • 29
    • 23844446449 scopus 로고    scopus 로고
    • Recursion relations for gauge theory amplitudes with massive particles
    • [hep-th/0504159]
    • S.D. Badger, E.W.N. Glover, V.V. Khoze and P. Svrček, Recursion relations for gauge theory amplitudes with massive particles, JHEP 07 (2005) 025 [hep-th/0504159]
    • (2005) JHEP , vol.7 , pp. 025
    • Badger, S.D.1    Glover, E.W.N.2    Khoze, V.V.3    Svrček, P.4
  • 30
    • 33644893319 scopus 로고    scopus 로고
    • Bootstrapping multi-parton loop amplitudes in QCD
    • [hep-ph/0507005]
    • Z. Bern, L.J. Dixon and D.A. Kosower, Bootstrapping multi-parton loop amplitudes in QCD, Phys. Rev. D 73 (2006) 065013 [hep-ph/0507005]
    • (2006) Phys. Rev.D , vol.73 , pp. 065013
    • Bern, Z.1    Dixon, L.J.2    Kosower, D.A.3
  • 31
    • 0030594543 scopus 로고    scopus 로고
    • Massive loop amplitudes from unitarity
    • [hep-ph/9511336]
    • Z. Bern and A.G. Morgan, Massive loop amplitudes from unitarity, Nucl. Phys. B 467 (1996) 479 [hep-ph/9511336]
    • (1996) Nucl. Phys. B , vol.467 , pp. 479
    • Bern, Z.1    Morgan, A.G.2
  • 32
    • 29744435862 scopus 로고    scopus 로고
    • One-loop amplitudes of gluons in SQCD
    • [hep-ph/0503132]
    • R. Britto, E. Buchbinder, F. Cachazo and B. Feng, One-loop amplitudes of gluons in SQCD, Phys. Rev. D 72 (2005) 065012 [hep-ph/0503132]
    • (2005) Phys. Rev. D , vol.72 , pp. 065012
    • Britto, R.1    Buchbinder, E.2    Cachazo, F.3    Feng, B.4
  • 33
    • 33646378186 scopus 로고    scopus 로고
    • The cut-constructible part of QCD amplitudes
    • [hep-ph/0602178]
    • R. Britto, B. Feng and P. Mastrolia, The cut-constructible part of QCD amplitudes, Phys. Rev. D 73 (2006) 105004 [hep-ph/0602178]
    • (2006) Phys. Rev. D , vol.73 , pp. 105004
    • Britto, R.1    Feng, B.2    Mastrolia, P.3
  • 34
    • 48749091449 scopus 로고    scopus 로고
    • Closed-form decomposition of one-loop massive amplitudes
    • [arXiv:0803. 1989]
    • R. Britto, B. Feng and P. Mastrolia, Closed-form decomposition of one-loop massive amplitudes, Phys. Rev. D 78 (2008) 025031 [arXiv:0803.1989]
    • (2008) Phys. Rev. D , vol.78 , pp. 025031
    • Britto, R.1    Feng, B.2    Mastrolia, P.3
  • 35
    • 67649240143 scopus 로고    scopus 로고
    • Double-cut of scattering amplitudes and Stokes' theorem
    • [arXiv:0905.2909]
    • P. Mastrolia, Double-cut of scattering amplitudes and Stokes' theorem, Phys. Lett. B 678 (2009) 246 [arXiv:0905.2909]
    • (2009) Phys. Lett. B , vol.678 , pp. 246
    • Mastrolia, P.1
  • 36
    • 44449151245 scopus 로고    scopus 로고
    • Analytic structure of three-mass triangle coefficients
    • [arXiv:0709.2086]
    • N.E.J. Bjerrum-Bohr, D.C. Dunbar and W.B. Perkins, Analytic structure of three-mass triangle coefficients, JHEP 04 (2008) 038 [arXiv:0709.2086]
    • (2008) JHEP , vol.4 , pp. 038
    • Bjerrum-Bohr, N.E.J.1    Dunbar, D.C.2    Perkins, W.B.3
  • 37
    • 33845628572 scopus 로고    scopus 로고
    • On triple-cut of scattering amplitudes
    • [hep-th/0611091]
    • P. Mastrolia, On triple-cut of scattering amplitudes, Phys. Lett. B 644 (2007) 272 [hep-th/0611091]
    • (2007) Phys. Lett. B , vol.644 , pp. 272
    • Mastrolia, P.1
  • 38
    • 34347379293 scopus 로고    scopus 로고
    • Direct extraction of one-loop integral coefficients
    • [arXiv:0704. 1835]
    • D. Forde, Direct extraction of one-loop integral coefficients, Phys. Rev. D 75 (2007) 125019 [arXiv:0704.1835]
    • Phys. Rev.D , vol.75 , Issue.2007 , pp. 125019
    • Forde, D.1
  • 39
    • 70350032294 scopus 로고    scopus 로고
    • One-loop gluonic amplitudes from single unitarity cuts
    • [arXiv:0810.2964]
    • E.W.N. Glover and C. Williams, One-loop gluonic amplitudes from single unitarity cuts, JHEP 12 (2008) 067 [arXiv:0810.2964]
    • (2008) JHEP , vol.12 , pp. 067
    • Glover, E.W.N.1    Williams, C.2
  • 40
    • 74249101498 scopus 로고    scopus 로고
    • Solving for tadpole coefficients in one-loop amplitudes
    • [arXiv:0904.2766]
    • R. Britto and B. Feng, Solving for tadpole coefficients in one-loop amplitudes, Phys. Lett. B 681 (2009) 376 [arXiv:0904.2766]
    • (2009) Phys. Lett. B , vol.681 , pp. 376
    • Britto, R.1    Feng, B.2
  • 41
    • 80053129623 scopus 로고    scopus 로고
    • Single cut integration
    • [arXiv:1011.2344]
    • R. Britto and E. Mirabella, Single cut integration, JHEP 01 (2011) 135 [arXiv:1011.2344]
    • (2011) JHEP , vol.1 , pp. 135
    • Britto, R.1    Mirabella, E.2
  • 42
    • 27544511311 scopus 로고    scopus 로고
    • Loop amplitudes in pure Yang-Mills from generalised unitarity
    • [hep-th/0506068]
    • A. Brandhuber, S. McNamara, B.J. Spence and G. Travaglini, Loop amplitudes in pure Yang-Mills from generalised unitarity, JHEP 10 (2005) 011 [hep-th/0506068]
    • (2005) JHEP , vol.10 , pp. 011
    • Brandhuber, A.1    McNamara, S.2    Spence, B.J.3    Travaglini, G.4
  • 44
    • 33947663599 scopus 로고    scopus 로고
    • Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes
    • [hep-ph/0612277]
    • C. Anastasiou, R. Britto, B. Feng, Z. Kunszt and P. Mastrolia, Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes, JHEP 03 (2007) 111 [hep-ph/0612277]
    • (2007) JHEP , vol.3 , pp. 111
    • Anastasiou, C.1    Britto, R.2    Feng, B.3    Kunszt, Z.4    Mastrolia, P.5
  • 45
    • 63649120173 scopus 로고    scopus 로고
    • Direct extraction of one loop rational terms
    • [arXiv:0806.4600]
    • S.D. Badger, Direct extraction of one loop rational terms, JHEP 01 (2009) 049 [arXiv:0806.4600]
    • (2009) JHEP , vol.1 , pp. 049
    • Badger, S.D.1
  • 47
    • 18444410373 scopus 로고
    • Scalar one loop integrals
    • G. 't Hooft and M. Veltman, Scalar one loop integrals, Nucl. Phys. B 153 (1979) 365
    • (1979) Nucl. Phys. B , vol.153 , pp. 365
    • 'T Hooft, G.1    Veltman, M.2
  • 49
    • 0026187452 scopus 로고
    • FF: A package to evaluate one loop Feynman diagrams
    • G.J. van Oldenborgh, FF: a package to evaluate one loop Feynman diagrams, Comput. Phys. Commun. 66 (1991) 1
    • (1991) Comput. Phys. Commun , vol.66 , pp. 1
    • Van Oldenborgh, G.J.1
  • 50
    • 40549123371 scopus 로고    scopus 로고
    • Scalar one-loop integrals for QCD
    • [arXiv:0712 1851]
    • R.K. Ellis and G. Zanderighi, Scalar one-loop integrals for QCD, JHEP 02 (2008) 002 [arXiv:0712.1851]
    • (2008) JHEP , vol.2 , pp. 002
    • Ellis, R.K.1    Zanderighi, G.2
  • 51
    • 70149099971 scopus 로고    scopus 로고
    • Golem95: A numerical program to calculate one-loop tensor integrals with up to six external legs
    • [arXiv:0810.0992]
    • T. Binoth, J.P. Guillet, G. Heinrich, E. Pilon and T. Reiter, Golem95: a numerical program to calculate one-loop tensor integrals with up to six external legs, Comput. Phys. Commun. 180 (2009) 2317 [arXiv:0810.0992]
    • (2009) Comput. Phys. Commun. , vol.180 , pp. 2317
    • Binoth, T.1    Guillet, J.P.2    Heinrich, G.3    Pilon, E.4    Reiter, T.5
  • 52
    • 79961022057 scopus 로고    scopus 로고
    • OneLOop: For the evaluation of one-loop scalar functions
    • [arXiv:1007.4716]
    • A. van Hameren, OneLOop: for the evaluation of one-loop scalar functions, Comput. Phys. Commun. 182 (2011) 2427 [arXiv:1007.4716]
    • (2011) Comput. Phys. Commun. , vol.182 , pp. 2427
    • Van Hameren, A.1
  • 53
    • 33645910547 scopus 로고    scopus 로고
    • News from formcalc and looptools
    • [hep-ph/0601248]
    • T. Hahn and M. Rauch, News from FormCalc and LoopTools, Nucl. Phys. Proc. Suppl. 157 (2006) 236 [hep-ph/0601248]
    • (2006) Nucl. Phys. Proc. Suppl. , vol.157 , pp. 236
    • Hahn, T.1    Rauch, M.2
  • 54
    • 78649903578 scopus 로고    scopus 로고
    • Scalar one-loop 4-point integrals
    • [arXiv:1005.2076]
    • A. Denner and S. Dittmaier, Scalar one-loop 4-point integrals, Nucl. Phys. B 844 (2011) 199 [arXiv:1005.2076]
    • (2011) Nucl. Phys. B , vol.844 , pp. 199
    • Denner, A.1    Dittmaier, S.2
  • 55
    • 79960044000 scopus 로고    scopus 로고
    • Golem95C: A library for one-loop integrals with complex masses
    • [arXiv:1101.5595]
    • G. Cullen et al., Golem95C: a library for one-loop integrals with complex masses, Comput. Phys. Commun. 182 (2011) 2276 [arXiv:1101.5595]
    • (2011) Comput. Phys. Commun. , vol.182 , pp. 2276
    • Cullen, G.1
  • 56
    • 27544452373 scopus 로고    scopus 로고
    • An algebraic/numerical formalism for one-loop multi-leg amplitudes
    • [hep-ph/0504267]
    • T. Binoth, J.P. Guillet, G. Heinrich, E. Pilon and C. Schubert, An algebraic/numerical formalism for one-loop multi-leg amplitudes, JHEP 10 (2005) 015 [hep-ph/0504267]
    • (2005) JHEP , vol.10 , pp. 015
    • Binoth, T.1    Guillet, J.P.2    Heinrich, G.3    Pilon, E.4    Schubert, C.5
  • 57
    • 29544438846 scopus 로고    scopus 로고
    • Reduction schemes for one-loop tensor integrals
    • [hep-ph/0509141]
    • A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys. B 734 (2006) 62 [hep-ph/0509141]
    • (2006) Nucl. Phys. B , vol.734 , pp. 62
    • Denner, A.1    Dittmaier, S.2
  • 58
    • 84864029640 scopus 로고    scopus 로고
    • Numerical evaluation of tensor Feynman integrals in Euclidean kinematics
    • [arXiv:1010.1667]
    • J. Gluza, K. Kajda, T. Riemann and V. Yundin, Numerical evaluation of tensor Feynman integrals in Euclidean kinematics, Eur. Phys. J. C 71 (2011) 1516 [arXiv:1010.1667]
    • (2011) Eur. Phys. J. C , vol.71 , pp. 1516
    • Gluza, J.1    Kajda, K.2    Riemann, T.3    Yundin, V.4
  • 60
    • 18244402647 scopus 로고    scopus 로고
    • Techniques for QCD calculations by numerical integration
    • [hep-ph/9910292]
    • D.E. Soper, Techniques for QCD calculations by numerical integration, Phys. Rev. D 62 (2000) 014009 [hep-ph/9910292]
    • (2000) Phys. Rev.D , vol.62 , pp. 014009
    • Soper, D.E.1
  • 61
    • 33751178614 scopus 로고    scopus 로고
    • Numerical integration of one-loop Feynman diagrams for N-photon amplitudes
    • [hep-ph/0610028]
    • Z. Nagy and D.E. Soper, Numerical integration of one-loop Feynman diagrams for N-photon amplitudes, Phys. Rev. D 74 (2006) 093006 [hep-ph/0610028]
    • (2006) Phys. Rev. D , vol.74 , pp. 093006
    • Nagy, Z.1    Soper, D.E.2
  • 62
    • 43049083695 scopus 로고    scopus 로고
    • A numerical unitarity formalism for evaluating one-loop amplitudes
    • [arXiv:0708.2398]
    • R.K. Ellis, W.T. Giele and Z. Kunszt, A numerical unitarity formalism for evaluating one-loop amplitudes, JHEP 03 (2008) 003 [arXiv:0708.2398]
    • (2008) JHEP , vol.3 , pp. 003
    • Ellis, R.K.1    Giele, W.T.2    Kunszt, Z.3
  • 63
    • 44449166767 scopus 로고    scopus 로고
    • Full one-loop amplitudes from tree amplitudes
    • [arXiv:0801.2237]
    • W.T. Giele, Z. Kunszt and K. Melnikov, Full one-loop amplitudes from tree amplitudes, JHEP 04 (2008) 049 [arXiv:0801.2237]
    • (2008) JHEP , vol.4 , pp. 049
    • Giele, W.T.1    Kunszt, Z.2    Melnikov, K.3
  • 64
    • 69249218910 scopus 로고    scopus 로고
    • Masses, fermions and generalized D-dimensional unitarity
    • [arXiv:0806.3467]
    • R.K. Ellis, W.T. Giele, Z. Kunszt and K. Melnikov, Masses, fermions and generalized D-dimensional unitarity, Nucl. Phys. B 822 (2009) 270 [arXiv:0806.3467]
    • (2009) Nucl. Phys. B , vol.822 , pp. 270
    • Ellis, R.K.1    Giele, W.T.2    Kunszt, Z.3    Melnikov, K.4
  • 65
    • 77955884962 scopus 로고    scopus 로고
    • Scattering amplitudes from unitarity-based reduction algorithm at the integrand-level
    • [arXiv:1006.0710]
    • P. Mastrolia, G. Ossola, T. Reiter and F. Tramontano, Scattering amplitudes from unitarity-based reduction algorithm at the integrand-level, JHEP 08 (2010) 080 [arXiv:1006.0710]
    • (2010) JHEP , vol.8 , pp. 080
    • Mastrolia, P.1    Ossola, G.2    Reiter, T.3    Tramontano, F.4
  • 66
    • 78649704626 scopus 로고    scopus 로고
    • Tensorial reconstruction at the integrand level
    • [arXiv:1008.2441]
    • G. Heinrich, G. Ossola, T. Reiter and F. Tramontano, Tensorial reconstruction at the integrand level, JHEP 10 (2010) 105 [arXiv:1008.2441]
    • (2010) JHEP , vol.10 , pp. 105
    • Heinrich, G.1    Ossola, G.2    Reiter, T.3    Tramontano, F.4
  • 67
    • 43049151516 scopus 로고    scopus 로고
    • CutTools: A program implementing the OPP reduction method to compute one-loop amplitudes
    • [arXiv:0711.3596]
    • G. Ossola, C.G. Papadopoulos and R. Pittau, CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes, JHEP 03 (2008) 042 [arXiv:0711.3596]
    • (2008) JHEP , vol.3 , pp. 042
    • Ossola, G.1    Papadopoulos, C.G.2    Pittau, R.3
  • 68
    • 49749113761 scopus 로고    scopus 로고
    • An automated implementation of on-shell methods for one-loop amplitudes
    • [arXiv:0803.4180]
    • C.F. Berger et al., An automated implementation of on-shell methods for one-loop amplitudes, Phys. Rev. D 78 (2008) 036003 [arXiv:0803.4180]
    • (2008) Phys. Rev. D , vol.78 , pp. 036003
    • Berger, C.F.1
  • 69
    • 47249113006 scopus 로고    scopus 로고
    • On the numerical evaluation of one-loop amplitudes: The gluonic case
    • [arXiv:0805.2152]
    • W.T. Giele and G. Zanderighi, On the numerical evaluation of one-loop amplitudes: the gluonic case, JHEP 06 (2008) 038 [arXiv:0805.2152]
    • (2008) JHEP , pp. 8
    • Giele, W.T.1    Zanderighi, G.2
  • 71
    • 81255182576 scopus 로고    scopus 로고
    • Ynman diagram calculations with Feynarts, Formcalc and Looptools
    • rXiv:1006.2231]
    • T. Hahn, Feynman diagram calculations with FeynArts, FormCalc and LoopTools, PoS(ACAT2010)078 [arXiv:1006.2231]
    • PoS(ACAT2010)078
    • Hahn, T.1
  • 72
    • 70350043452 scopus 로고    scopus 로고
    • Automated one-loop calculations: A proof of concept
    • [arXiv:0903.4665]
    • A. van Hameren, C.G. Papadopoulos and R. Pittau, Automated one-loop calculations: a proof of concept, JHEP 09 (2009) 106 [arXiv:0903.4665]
    • (2009) JHEP , pp. 6
    • Vn Hameren, A.1    Papadopoulos, C.G.2    Pittau, R.3
  • 73
    • 78449265403 scopus 로고    scopus 로고
    • NLO QCD calculations with HELAC-NLO
    • [arXiv:1007.4918]
    • G. Bevilacqua et al., NLO QCD calculations with HELAC-NLO, Nucl. Phys. Proc. Suppl. 205-206 (2010) 211 [arXiv:1007.4918]
    • (2010) Nucl. Phys. Proc. Suppl. , vol.205-206 , pp. 211
    • Bevilacqua, G.1
  • 75
    • 80053149864 scopus 로고    scopus 로고
    • Automation of one-loop QCD corrections
    • [arXiv:1103.0621]
    • V. Hirschi et al., Automation of one-loop QCD corrections, JHEP 05 (2011) 044 [arXiv:1103.0621]
    • (2011) JHEP , vol.5 , pp. 044
    • Hirschi, V.1
  • 76
    • 81255182574 scopus 로고    scopus 로고
    • preparation.
    • G. Cullen et al., GoSam, in preparation.
    • GoSam
    • Cullen, G.1
  • 78
    • 0034736523 scopus 로고    scopus 로고
    • High precision calculation of multiloop Feynman integrals by difference equations
    • [hep-ph/0102033]
    • S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033]
    • (2000) Int. J. Mod. Phys. A , vol.15 , pp. 5087
    • Laporta, S.1
  • 79
    • 0035810304 scopus 로고    scopus 로고
    • Lculation of master integrals by difference equations
    • [hep-ph/0102032]
    • S. Laporta, Calculation of master integrals by difference equations, Phys. Lett. B 504 (2001) 188 [hep-ph/0102032]
    • (2001) Ys. Lett. B , vol.504 , pp. 188
    • Laporta, S.1
  • 80
    • 0002872832 scopus 로고
    • A theorem on analytical calculability of four loop renormalization group functions
    • F.V. Tkachov, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett. B 100 (1981) 65
    • (1981) Phys. Lett. B , vol.100 , pp. 65
    • Tkachov, F.V.1
  • 81
    • 0000312317 scopus 로고
    • Integration by parts: The algorithm to calculate β-functions in 4 loops
    • K.G. Chetyrkin and F.V. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys. B 192 (1981) 159
    • (1981) Nucl. Phys. B , vol.192 , pp. 159
    • Chetyrkin, K.G.1    Tkachov, F.V.2
  • 82
    • 78449232514 scopus 로고    scopus 로고
    • Dimensional recurrence relations: An easy way to evaluate higher orders of expansion in ?
    • [arXiv:1005.0362]
    • R.N. Lee, A.V. Smirnov and V.A. Smirnov, Dimensional recurrence relations: an easy way to evaluate higher orders of expansion in ?, Nucl. Phys. Proc. Suppl. 205-206 (2010) 308 [arXiv:1005.0362]
    • (2010) Nucl. Phys. Proc. Suppl. , vol.205-206 , pp. 308
    • Lee, R.N.1    Smirnov, A.V.2    Smirnov, V.A.3
  • 83
    • 0042410077 scopus 로고
    • Differential equation method: The calculation of N point Feynman diagrams
    • A.V. Kotikov, Differential equation method: the calculation of N point Feynman diagrams, Phys. Lett. B 267 (1991) 123
    • (1991) Phys. Lett. B , vol.267 , pp. 123
    • Kotikov, A.V.1
  • 84
    • 0040054123 scopus 로고    scopus 로고
    • Differential equations for Feynman graph amplitudes
    • [hep-th/9711188]
    • E. Remiddi, Differential equations for Feynman graph amplitudes, Nuovo Cim. A 110 (1997) 1435 [hep-th/9711188]
    • (1997) Nuovo Cim. A , vol.110 , pp. 1435
    • Remiddi, E.1
  • 85
    • 0034288937 scopus 로고    scopus 로고
    • Using differential equations to compute two loop box integrals
    • [hep-ph/0005232]
    • T. Gehrmann and E. Remiddi, Using differential equations to compute two loop box integrals, Nucl. Phys. Proc. Suppl. 89 (2000) 251 [hep-ph/0005232]
    • (2000) Nucl. Phys. Proc. Suppl. , vol.89 , pp. 251
    • Gehrmann, T.1    Remiddi, E.2
  • 86
    • 0035821473 scopus 로고    scopus 로고
    • Two loop master integrals for γ 3 jets: The planar topologies
    • [hep-ph/0008287]
    • 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]
    • (2001) Nucl. Phys. B , vol.601 , pp. 248
    • Gehrmann, T.1    Remiddi, E.2
  • 87
    • 0035821478 scopus 로고    scopus 로고
    • Two loop master integrals for γ 3 jets: The nonplanar topologies
    • [hep-ph/0101124]
    • T. Gehrmann and E. Remiddi, Two loop master integrals for γ 3 jets: the nonplanar topologies, Nucl. Phys. B 601 (2001) 287 [hep-ph/0101124]
    • (2001) Nucl. Phys. B , vol.601 , pp. 287
    • Gehrmann, T.1    Remiddi, E.2
  • 88
    • 0042174965 scopus 로고    scopus 로고
    • Vertex diagrams for the QED form-factors at the two loop level
    • [Erratum ibid. B 702 (2004 359] [hep-ph/0301170]
    • 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]
    • (2003) Nucl. Phys. B , vol.661 , pp. 289
    • Bonciani, R.1    Mastrolia, P.2    Remiddi, E.3
  • 89
    • 35148834667 scopus 로고    scopus 로고
    • Feynman diagrams and differential equations
    • [arXiv:0707.4037]
    • M. Argeri and P. Mastrolia, Feynman diagrams and differential equations, Int. J. Mod. Phys. A 22 (2007) 4375 [arXiv:0707.4037]
    • (2007) Int. J. Mod. Phys. A , vol.22 , pp. 4375
    • Argeri, M.1    Mastrolia, P.2
  • 90
    • 0031120971 scopus 로고    scopus 로고
    • Algebraic algorithms for multiloop calculations. The first 15 years. What's next?
    • [hep-ph/9609429]
    • F.V. Tkachov, Algebraic algorithms for multiloop calculations. The first 15 years. What's next?, Nucl. Instrum. Meth. A 389 (1997) 309 [hep-ph/9609429]
    • (1997) Nucl. Instrum. Meth. A , vol.389 , pp. 309
    • Tkachov, F.V.1
  • 91
    • 0001620260 scopus 로고
    • The analytic continuation of generalized functions with respect to a parameter
    • I.N. Bernstein, The analytic continuation of generalized functions with respect to a parameter, Funct. Anal. Appl. 6 (1972) 273.
    • (1972) Funct. Anal. Appl. , vol.6 , pp. 273
    • Bernstein, I.N.1
  • 92
    • 0037415267 scopus 로고    scopus 로고
    • All purpose numerical evaluation of one loop multileg Feynman diagrams
    • [hep-ph/0209219]
    • A. Ferroglia, M. Passera, G. Passarino and S. Uccirati, All purpose numerical evaluation of one loop multileg Feynman diagrams, Nucl. Phys. B 650 (2003) 162 [hep-ph/0209219]
    • (2003) Nucl. Phys. B , vol.650 , pp. 162
    • Ferroglia, A.1    Passera, M.2    Passarino, G.3    Uccirati, S.4
  • 94
    • 0000396827 scopus 로고    scopus 로고
    • Analytical result for dimensionally regularized massless on shell double box
    • [hep-ph/9905323]
    • V.A. Smirnov, Analytical result for dimensionally regularized massless on shell double box, Phys. Lett. B 460 (1999) 397 [hep-ph/9905323]
    • (1999) Phys. Lett. B , vol.460 , pp. 397
    • Smirnov, V.A.1
  • 95
    • 0001718629 scopus 로고    scopus 로고
    • Nonplanar massless two loop Feynman diagrams with four on-shell legs
    • [hep-ph/9909506]
    • J.B. Tausk, Nonplanar massless two loop Feynman diagrams with four on-shell legs, Phys. Lett. B 469 (1999) 225 [hep-ph/9909506]
    • (1999) Phys. Lett. B , vol.469 , pp. 225
    • Tausk, J.B.1
  • 96
    • 33748798230 scopus 로고    scopus 로고
    • Automatized analytic continuation of Mellin-Barnes integrals
    • [hep-ph/0511200]
    • M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals, Comput. Phys. Commun. 175 (2006) 559 [hep-ph/0511200]
    • (2006) Comput. Phys. Commun. , vol.175 , pp. 559
    • Czakon, M.1
  • 97
    • 67650021587 scopus 로고    scopus 로고
    • On the resolution of singularities of multiple Mellin-Barnes integrals
    • [arXiv:0901.0386]
    • A.V. Smirnov and V.A. Smirnov, On the resolution of singularities of multiple Mellin-Barnes integrals, Eur. Phys. J. C 62 (2009) 445 [arXiv:0901.0386]
    • (2009) Eur. Phys. J. C , vol.62 , pp. 445
    • Smirnov, A.V.1    Smirnov, V.A.2
  • 98
    • 0032577752 scopus 로고    scopus 로고
    • Asymptotic expansion of Feynman integrals near threshold
    • [hep-ph/9711391]
    • M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522 (1998) 321 [hep-ph/9711391]
    • (1998) Nucl. Phys. B , vol.522 , pp. 321
    • Beneke, M.1    Smirnov, V.A.2
  • 99
    • 0001175264 scopus 로고
    • Asymptotic expansions in limits of large momenta and masses
    • V.A. Smirnov, Asymptotic expansions in limits of large momenta and masses, Commun. Math. Phys. 134 (1990) 109
    • (1990) Commun. Math. Phys. , vol.134 , pp. 109
    • Smirnov, V.A.1
  • 101
    • 0005952131 scopus 로고    scopus 로고
    • An automatized algorithm to compute infrared divergent multiloop integrals
    • [hep-ph/0004013]
    • T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multiloop integrals, Nucl. Phys. B 585 (2000) 741 [hep-ph/0004013]
    • (2000) Nucl. Phys. B , vol.585 , pp. 741
    • Binoth, T.1    Heinrich, G.2
  • 102
    • 0742320151 scopus 로고    scopus 로고
    • Numerical evaluation of multiloop integrals by sector decomposition
    • [hep-ph/0305234]
    • T. Binoth and G. Heinrich, Numerical evaluation of multiloop integrals by sector decomposition, Nucl. Phys. B 680 (2004) 375 [hep-ph/0305234]
    • (2004) Nucl. Phys. B , vol.680 , pp. 375
    • Binoth, T.1    Heinrich, G.2
  • 103
    • 40849100263 scopus 로고    scopus 로고
    • Resolution of singularities for multi-loop integrals
    • [arXiv:0709.4092]
    • C. Bogner and S. Weinzierl, Resolution of singularities for multi-loop integrals, Comput. Phys. Commun. 178 (2008) 596 [arXiv:0709.4092]
    • (2008) Comput. Phys. Commun. , vol.178 , pp. 596
    • Bogner, C.1    Weinzierl, S.2
  • 104
    • 43949137601 scopus 로고    scopus 로고
    • Sector decomposition
    • [arXiv:0803.4177]
    • G. Heinrich, Sector decomposition, Int. J. Mod. Phys. A 23 (2008) 1457 [arXiv:0803.4177]
    • (2008) Int. J. Mod. Phys. A , vol.23 , pp. 1457
    • Heinrich, G.1
  • 105
    • 78650733121 scopus 로고    scopus 로고
    • FIESTA 2: Parallelizeable multiloop numerical calculations
    • [arXiv:0912.0158]
    • A.V. Smirnov, V.A. Smirnov and M. Tentyukov, FIESTA 2: parallelizeable multiloop numerical calculations, Comput. Phys. Commun. 182 (2011) 790 [arXiv:0912.0158]
    • (2011) Comput. Phys. Commun. , vol.182 , pp. 790
    • Smirnov, A.V.1    Smirnov, V.A.2    Tentyukov, M.3
  • 106
    • 79955555731 scopus 로고    scopus 로고
    • SecDec: A general program for sector decomposition
    • [arXiv:1011.5493]
    • J. Carter and G. Heinrich, SecDec: a general program for sector decomposition, Comput. Phys. Commun. 182 (2011) 1566 [arXiv:1011.5493]
    • (2011) Comput. Phys. Commun. , vol.182 , pp. 1566
    • Carter, J.1    Heinrich, G.2
  • 107
    • 34547609092 scopus 로고    scopus 로고
    • Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically
    • [hep-ph/0703282]
    • C. Anastasiou, S. Beerli and A. Daleo, Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically, JHEP 05 (2007) 071 [hep-ph/0703282]
    • (2007) JHEP , vol.5 , pp. 071
    • Anastasiou, C.1    Beerli, S.2    Daleo, A.3
  • 108
    • 77952951796 scopus 로고    scopus 로고
    • Higgs pseudo-observables, second Riemann sheet and all that
    • [arXiv:1001.3360]
    • G. Passarino, C. Sturm and S. Uccirati, Higgs pseudo-observables, second Riemann sheet and all that, Nucl. Phys. B 834 (2010) 77 [arXiv:1001.3360]
    • (2010) Nucl. Phys. B , vol.834 , pp. 77
    • Passarino, G.1    Sturm, C.2    Uccirati, S.3
  • 109
    • 79960947107 scopus 로고    scopus 로고
    • Counting master integrals: Integration by parts versus differential reduction
    • [arXiv:1105.5319]
    • M.Y. Kalmykov and B.A. Kniehl, Counting master integrals: integration by parts versus differential reduction, Phys. Lett. B 702 (2011) 268 [arXiv:1105.5319]
    • (2011) Phys. Lett. B , vol.702 , pp. 268
    • Kalmykov, M.Y.1    Kniehl, B.A.2
  • 110
    • 79956133881 scopus 로고    scopus 로고
    • The number of master integrals is finite
    • [arXiv:1004.4199]
    • A.V. Smirnov and A.V. Petukhov, The number of master integrals is finite, Lett. Math. Phys. 97 (2011) 37 [arXiv:1004.4199]
    • (2011) Lett. Math. Phys. , vol.97 , pp. 37
    • Smirnov, A.V.1    Petukhov, A.V.2
  • 111
    • 33144480078 scopus 로고    scopus 로고
    • A practical criterion of irreducibility of multi-loop Feynman integrals
    • [hep-ph/0507053]
    • P.A. Baikov, A practical criterion of irreducibility of multi-loop Feynman integrals, Phys. Lett. B 634 (2006) 325 [hep-ph/0507053]
    • (2006) Phys. Lett. B , vol.634 , pp. 325
    • Baikov, P.A.1
  • 112
    • 0034677428 scopus 로고    scopus 로고
    • The criterion of irreducibility of multiloop Feynman integrals
    • [hep-ph/9912421]
    • P.A. Baikov, The criterion of irreducibility of multiloop Feynman integrals, Phys. Lett. B 474 (2000) 385 [hep-ph/9912421]
    • (2000) Phys. Lett. B , vol.474 , pp. 385
    • Baikov, P.A.1
  • 113
    • 79952211280 scopus 로고    scopus 로고
    • Towards a basis for planar two-loop integrals
    • [arXiv:1009.0472]
    • J. Gluza, K. Kajda and D.A. Kosower, Towards a basis for planar two-loop integrals, Phys. Rev. D 83 (2011) 045012 [arXiv:1009.0472]
    • (2011) Phys. Rev. D , vol.83 , pp. 045012
    • Gluza, J.1    Kajda, K.2    Kosower, D.A.3
  • 114
    • 0041438181 scopus 로고    scopus 로고
    • Two loop four gluon amplitudes in N = 4 super Yang-Mills
    • [hep-ph/9702424]
    • Z. Bern, J.S. Rozowsky and B. Yan, Two loop four gluon amplitudes in N = 4 super Yang-Mills, Phys. Lett. B 401 (1997) 273 [hep-ph/9702424]
    • (1997) Phys. Lett. B , vol.401 , pp. 273
    • Bern, Z.1    Rozowsky, J.S.2    Yan, B.3
  • 115
    • 0032511717 scopus 로고    scopus 로고
    • On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences
    • [hep-th/9802162]
    • Z. Bern, L.J. Dixon, D.C. Dunbar, M. Perelstein and J.S. Rozowsky, On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences, Nucl. Phys. B 530 (1998) 401 [hep-th/9802162]
    • (1998) Nucl. Phys. B , vol.530 , pp. 401
    • Bern, Z.1    Dixon, L.J.2    Dunbar, D.C.3    Perelstein, M.4    Rozowsky, J.S.5
  • 116
    • 7444227086 scopus 로고    scopus 로고
    • A two loop four gluon helicity amplitude in QCD
    • [hep-ph/0001001]
    • Z. Bern, L.J. Dixon and D.A. Kosower, A two loop four gluon helicity amplitude in QCD, JHEP 01 (2000) 027 [hep-ph/0001001]
    • (2000) JHEP , vol.1 , pp. 027
    • Bern, Z.1    Dixon, L.J.2    Kosower, D.A.3
  • 117
    • 33645503640 scopus 로고    scopus 로고
    • Two-loop amplitudes of gluons and octa-cuts in N = 4 super Yang-Mills
    • [hep-th/0506126]
    • E.I. Buchbinder and F. Cachazo, Two-loop amplitudes of gluons and octa-cuts in N = 4 super Yang-Mills, JHEP 11 (2005) 036 [hep-th/0506126]
    • (2005) JHEP , vol.11 , pp. 036
    • Buchbinder, E.I.1    Cachazo, F.2
  • 119
    • 37349078996 scopus 로고    scopus 로고
    • Maximally supersymmetric planar Yang-Mills amplitudes at five loops
    • [arXiv:0705. 1864]
    • Z. Bern, J.J.M. Carrasco, H. Johansson and D.A. Kosower, Maximally supersymmetric planar Yang-Mills amplitudes at five loops, Phys. Rev. D 76 (2007) 125020 [arXiv:0705.1864]
    • (2007) Phys. Rev. D , vol.76 , pp. 125020
    • Bern, Z.1    Carrasco, J.J.M.2    Johansson, H.3    Kosower, D.A.4
  • 120
    • 57149142775 scopus 로고    scopus 로고
    • Manifest ultraviolet behavior for the three-loop four-point amplitude of N = 8 supergravity
    • [arXiv:0808.4112]
    • Z. Bern, J.J.M. Carrasco, L.J. Dixon, H. Johansson and R. Roiban, Manifest ultraviolet behavior for the three-loop four-point amplitude of N = 8 supergravity, Phys. Rev. D 78 (2008) 105019 [arXiv:0808.4112]
    • (2008) Phys. Rev. D , vol.78 , pp. 105019
    • Bern, Z.1    Carrasco, J.J.M.2    Dixon, L.J.3    Johansson, H.4    Roiban, R.5
  • 121
    • 77955335870 scopus 로고    scopus 로고
    • Perturbative quantum gravity as a double copy of gauge theory
    • [arXiv:1004.0476]
    • Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative quantum gravity as a double copy of gauge theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476]
    • Phys. Rev. Lett. , vol.105 , Issue.2010 , pp. 061602
    • Bern, Z.1    Carrasco, J.J.M.2    Johansson, H.3
  • 122
    • 47249096199 scopus 로고    scopus 로고
    • Optimizing the reduction of one-loop amplitudes
    • [arXiv:0803.3964]
    • P. Mastrolia, G. Ossola, C.G. Papadopoulos and R. Pittau, Optimizing the reduction of one-loop amplitudes, JHEP 06 (2008) 030 [arXiv:0803.3964]
    • (2008) JHEP , vol.6 , pp. 030
    • Mastrolia, P.1    Ossola, G.2    Papadopoulos, C.G.3    Pittau, R.4
  • 123
    • 50849141082 scopus 로고    scopus 로고
    • SatM, a Mathematica implementation of the spinor-helicity formalism
    • [arXiv:0710.5559]
    • D. Maî?tre and P. Mastrolia, S@M, a Mathematica implementation of the spinor-helicity formalism, Comput. Phys. Commun. 179 (2008) 501 [arXiv:0710.5559]
    • (2008) Comput. Phys. Commun. , vol.179 , pp. 501
    • Maître, D.1    Mastrolia, P.2
  • 125
    • 33750598337 scopus 로고    scopus 로고
    • Two-loop iteration of five-point N = 4 super-Yang-Mills amplitudes
    • [hep-th/0604074]
    • Z. Bern, M. Czakon, D.A. Kosower, R. Roiban and V.A. Smirnov, Two-loop iteration of five-point N = 4 super-Yang-Mills amplitudes, Phys. Rev. Lett. 97 (2006) 181601 [hep-th/0604074]
    • (2006) Phys. Rev. Lett. , vol.97 , pp. 181601
    • Bern, Z.1    Czakon, M.2    Kosower, D.A.3    Roiban, R.4    Smirnov, V.A.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.