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Real-virtual corrections for gluon scattering at NNLO. (English) Zbl 1309.81285

Summary: We use the antenna subtraction method to isolate the mixed real-virtual infrared singularities present in gluonic scattering amplitudes at next-to-next-to-leading order. In a previous paper, we derived the subtraction term that rendered the double real radiation tree-level process finite in the single and double unresolved regions of the phase space. Here, we show how to construct the real-virtual subtraction term using antenna functions with both initial- and final-state partons which removes the explicit infrared poles present in the one-loop amplitude, as well as the implicit singularities that occur in the soft and collinear limits. As an explicit example, we write down the subtraction term that describes the single unresolved contributions from the five-gluon one-loop process. The infrared poles are explicitly and locally cancelled in all regions of phase space prior to integration, leaving a finite remainder that can be safely evaluated numerically in four-dimensions. We show numerically that the subtraction term correctly approximates the matrix elements in the various single unresolved configurations.

MSC:

81V05 Strong interaction, including quantum chromodynamics
81U05 \(2\)-body potential quantum scattering theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T18 Feynman diagrams
81T80 Simulation and numerical modelling (quantum field theory) (MSC2010)

Software:

NGluon; SecDec; CHAPLIN
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Full Text: DOI arXiv

References:

[1] S.D. Ellis, Z. Kunszt and D.E. Soper, The one jet inclusive cross-section at order \(\alpha_S^3 \): gluons only, Phys. Rev. Lett.62 (1989) 726 [INSPIRE]. · doi:10.1103/PhysRevLett.62.726
[2] S.D. Ellis, Z. Kunszt and D.E. Soper, The one jet inclusive cross-section at order\)
( \alpha_s^3\) quarks and gluons, Phys. Rev. Lett.64 (1990) 2121 [INSPIRE]. · doi:10.1103/PhysRevLett.64.2121
[3] S.D. Ellis, Z. Kunszt and D.E. Soper, Two jet production in hadron collisions at order \(\alpha_S^3\) in QCD, Phys. Rev. Lett.69 (1992) 1496 [INSPIRE]. · doi:10.1103/PhysRevLett.69.1496
[4] W. Giele, E. Glover and D.A. Kosower, Higher order corrections to jet cross-sections in hadron colliders, Nucl. Phys.B 403 (1993) 633 [hep-ph/9302225] [INSPIRE]. · doi:10.1016/0550-3213(93)90365-V
[5] W. Giele, E. Glover and D.A. Kosower, The two-jet differential cross section at \(\mathcal{O}\left( {\alpha_s^3} \right)\) in hadron collisions, Phys. Rev. Lett.73 (1994) 2019 [hep-ph/9403347] [INSPIRE]. · doi:10.1103/PhysRevLett.73.2019
[6] Z. Nagy, Three jet cross-sections in hadron hadron collisions at next-to-leading order, Phys. Rev. Lett.88 (2002) 122003 [hep-ph/0110315] [INSPIRE]. · doi:10.1103/PhysRevLett.88.122003
[7] CDF-Run II collaboration, A. Abulencia et al., Measurement of the inclusive jet cross section using the kTalgorithmin p \(\overline p\) collisions at \(\sqrt{s} = 1.96\) TeV with the CDF II detector, Phys. Rev.D 75 (2007) 092006 [Erratum ibid.D 75 (2007) 119901] [hep-ex/0701051] [INSPIRE].
[8] D0 collaboration, V. Abazov et al., Measurement of the inclusive jet cross-section in p \(\overline p\) collisions at s(1/2) = 1.96 TeV, Phys. Rev. Lett.101 (2008) 062001 [arXiv:0802.2400] [INSPIRE]. · doi:10.1103/PhysRevLett.101.062001
[9] CDF collaboration, T. Aaltonen et al., Measurement of the inclusive jet cross section at the Fermilab Tevatron p \(\overline p\) collider using a cone-based jet algorithm, Phys. Rev.D 78 (2008) 052006 [Erratum ibid.D 79 (2009) 119902] [arXiv:0807.2204] [INSPIRE].
[10] ATLAS collaboration, G. Aad et al., Measurement of inclusive jet and dijet cross sections in proton-proton collisions at 7 TeV centre-of-mass energy with the ATLAS detector, Eur. Phys. J.C 71 (2011) 1512 [arXiv:1009.5908] [INSPIRE].
[11] CMS collaboration, S. Chatrchyan et al., Measurement of the inclusive jet cross section in pp collisions at \(\sqrt{s} = 7\) TeV, Phys. Rev. Lett.107 (2011) 132001 [arXiv:1106.0208] [INSPIRE]. · doi:10.1103/PhysRevLett.107.132001
[12] W. Giele, E. Glover and J. Yu, The determination of αsat hadron colliders, Phys. Rev.D 53 (1996) 120 [hep-ph/9506442] [INSPIRE].
[13] CDF collaboration, T. Affolder et al., Measurement of the strong coupling constant from inclusive jet production at the Tevatron \(\overline p\) p collider, Phys. Rev. Lett.88 (2002) 042001 [hep-ex/0108034] [INSPIRE]. · doi:10.1103/PhysRevLett.88.042001
[14] D0 collaboration, V. Abazov et al., Determination of the strong coupling constant from the inclusive jet cross section in ppbar collisions at \(\sqrt{s} = 1.96\) TeV, Phys. Rev.D 80 (2009) 111107 [arXiv:0911.2710] [INSPIRE].
[15] E. Glover, Progress in NNLO calculations for scattering processes, Nucl. Phys. Proc. Suppl.116 (2003) 3 [hep-ph/0211412] [INSPIRE]. · doi:10.1016/S0920-5632(03)80133-0
[16] S. Catani and M. Seymour, A general algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys.B 485 (1997) 291 [Erratum ibid.B 510 (1998) 503-504] [hep-ph/9605323] [INSPIRE].
[17] S. Frixione, Z. Kunszt and A. Signer, Three jet cross-sections to next-to-leading order, Nucl. Phys.B 467 (1996) 399 [hep-ph/9512328] [INSPIRE]. · doi:10.1016/0550-3213(96)00110-1
[18] Z. Nagy and Z. Trócsányi, Calculation of QCD jet cross-sections at next-to-leading order, Nucl. Phys.B 486 (1997) 189 [hep-ph/9610498] [INSPIRE]. · doi:10.1016/S0550-3213(96)00657-8
[19] S. Frixione, A general approach to jet cross-sections in QCD, Nucl. Phys.B 507 (1997) 295 [hep-ph/9706545] [INSPIRE]. · doi:10.1016/S0550-3213(97)00574-9
[20] G. Somogyi and Z. Trócsányi, A new subtraction scheme for computing QCD jet cross sections at next-to-leading order accuracy, hep-ph/0609041 [INSPIRE]. · Zbl 1214.81293
[21] A. Gehrmann-De Ridder, T. Gehrmann and E. Glover, Antenna subtraction at NNLO, JHEP09 (2005) 056 [hep-ph/0505111] [INSPIRE]. · doi:10.1088/1126-6708/2005/09/056
[22] S. Weinzierl, Subtraction terms at NNLO, JHEP03 (2003) 062 [hep-ph/0302180] [INSPIRE]. · doi:10.1088/1126-6708/2003/03/062
[23] W.B. Kilgore, Subtraction terms for hadronic production processes at next-to-next-to-leading order, Phys. Rev.D 70 (2004) 031501 [hep-ph/0403128] [INSPIRE].
[24] S. Frixione and M. Grazzini, Subtraction at NNLO, JHEP06 (2005) 010 [hep-ph/0411399] [INSPIRE]. · doi:10.1088/1126-6708/2005/06/010
[25] G. Somogyi, Z. Trócsányi and V. Del Duca, Matching of singly- and doubly-unresolved limits of tree-level QCD squared matrix elements, JHEP06 (2005) 024 [hep-ph/0502226] [INSPIRE]. · doi:10.1088/1126-6708/2005/06/024
[26] G. Somogyi, Z. Trócsányi and V. Del Duca, A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of doubly-real emissions, JHEP01 (2007) 070 [hep-ph/0609042] [INSPIRE]. · doi:10.1088/1126-6708/2007/01/070
[27] G. Somogyi and Z. Trócsányi, A Subtraction scheme for computing QCD jet cross sections at NNLO: regularization of real-virtual emission, JHEP01 (2007) 052 [hep-ph/0609043] [INSPIRE]. · doi:10.1088/1126-6708/2007/01/052
[28] G. Somogyi and Z. Trócsányi, A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the subtraction terms. I, JHEP08 (2008) 042 [arXiv:0807.0509] [INSPIRE]. · doi:10.1088/1126-6708/2008/08/042
[29] U. Aglietti, V. Del Duca, C. Duhr, G. Somogyi and Z. Trócsányi, Analytic integration of real-virtual counterterms in NNLO jet cross sections. I, JHEP09 (2008) 107 [arXiv:0807.0514] [INSPIRE]. · doi:10.1088/1126-6708/2008/09/107
[30] G. Somogyi, Subtraction with hadronic initial states at NLO: An NNLO-compatible scheme, JHEP05 (2009) 016 [arXiv:0903.1218] [INSPIRE]. · doi:10.1088/1126-6708/2009/05/016
[31] P. Bolzoni, S.-O. Moch, G. Somogyi and Z. Trócsányi, Analytic integration of real-virtual counterterms in NNLO jet cross sections. II., JHEP08 (2009) 079 [arXiv:0905.4390] [INSPIRE]. · doi:10.1088/1126-6708/2009/08/079
[32] P. Bolzoni, G. Somogyi and Z. Trócsányi, A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the iterated singly-unresolved subtraction terms, JHEP01 (2011) 059 [arXiv:1011.1909] [INSPIRE]. · Zbl 1214.81293 · doi:10.1007/JHEP01(2011)059
[33] M. Czakon, A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett.B 693 (2010) 259 [arXiv:1005.0274] [INSPIRE].
[34] C. Anastasiou, F. Herzog and A. Lazopoulos, On the factorization of overlapping singularities at NNLO, JHEP03 (2011) 038 [arXiv:1011.4867] [INSPIRE]. · Zbl 1301.81284 · doi:10.1007/JHEP03(2011)038
[35] M. Czakon, Double-real radiation in hadronic top quark pair production as a proof of a certain concept, Nucl. Phys.B 849 (2011) 250 [arXiv:1101.0642] [INSPIRE]. · Zbl 1215.81117 · doi:10.1016/j.nuclphysb.2011.03.020
[36] C. Anastasiou, F. Herzog and A. Lazopoulos, The fully differential decay rate of a Higgs boson to bottom-quarks at NNLO in QCD, arXiv:1110.2368 [INSPIRE]. · Zbl 1309.81257
[37] R. Boughezal, K. Melnikov and F. Petriello, A subtraction scheme for NNLO computations, arXiv:1111.7041 [INSPIRE].
[38] S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett.98 (2007) 222002 [hep-ph/0703012] [INSPIRE]. · doi:10.1103/PhysRevLett.98.222002
[39] M. Grazzini, NNLO predictions for the Higgs boson signal in the H → W W → lνlν and H →ZZ →4l decay channels, JHEP02 (2008) 043 [arXiv:0801.3232] [INSPIRE]. · doi:10.1088/1126-6708/2008/02/043
[40] S. Catani, L. Cieri, G. Ferrera, D. de Florian and M. Grazzini, Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett.103 (2009) 082001 [arXiv:0903.2120] [INSPIRE]. · doi:10.1103/PhysRevLett.103.082001
[41] S. Catani, G. Ferrera and M. Grazzini, W boson production at hadron colliders: the lepton charge asymmetry in NNLO QCD, JHEP05 (2010) 006 [arXiv:1002.3115] [INSPIRE]. · doi:10.1007/JHEP05(2010)006
[42] G. Ferrera, M. Grazzini and F. Tramontano, Associated WH production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett.107 (2011) 152003 [arXiv:1107.1164] [INSPIRE]. · doi:10.1103/PhysRevLett.107.152003
[43] S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Diphoton production at hadron colliders: a fully-differential QCD calculation at NNLO, arXiv:1110.2375 [INSPIRE]. · Zbl 1284.81281
[44] T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multiloop integrals, Nucl. Phys.B 585 (2000) 741 [hep-ph/0004013] [INSPIRE]. · Zbl 1042.81565 · doi:10.1016/S0550-3213(00)00429-6
[45] T. Binoth and G. Heinrich, Numerical evaluation of multiloop integrals by sector decomposition, Nucl. Phys.B 680 (2004) 375 [hep-ph/0305234] [INSPIRE]. · Zbl 1043.81630 · doi:10.1016/j.nuclphysb.2003.12.023
[46] G. Heinrich, Sector decomposition, Int. J. Mod. Phys.A 23 (2008) 1457 [arXiv:0803.4177] [INSPIRE]. · Zbl 1153.81522
[47] J. Carter and G. Heinrich, SecDec: a general program for sector decomposition, Comput. Phys. Commun.182 (2011) 1566 [arXiv:1011.5493] [INSPIRE]. · Zbl 1262.81119 · doi:10.1016/j.cpc.2011.03.026
[48] G. Heinrich, A numerical method for NNLO calculations, Nucl. Phys. Proc. Suppl.116 (2003) 368 [hep-ph/0211144] [INSPIRE]. · Zbl 1037.81585 · doi:10.1016/S0920-5632(03)80201-3
[49] C. Anastasiou, K. Melnikov and F. Petriello, A new method for real radiation at NNLO, Phys. Rev.D 69 (2004) 076010 [hep-ph/0311311] [INSPIRE].
[50] T. Binoth and G. Heinrich, Numerical evaluation of phase space integrals by sector decomposition, Nucl. Phys.B 693 (2004) 134 [hep-ph/0402265] [INSPIRE]. · Zbl 1151.81352 · doi:10.1016/j.nuclphysb.2004.06.005
[51] G. Heinrich, The sector decomposition approach to real radiation at NNLO, Nucl. Phys. Proc. Suppl.157 (2006) 43 [hep-ph/0601232] [INSPIRE]. · doi:10.1016/j.nuclphysbps.2006.03.034
[52] C. Anastasiou, K. Melnikov and F. Petriello, Real radiation at NNLO: e+e− → 2 jets through \(O\left( {\alpha_s^2} \right) \), Phys. Rev. Lett.93 (2004) 032002 [hep-ph/0402280] [INSPIRE]. · doi:10.1103/PhysRevLett.93.032002
[53] C. Anastasiou, K. Melnikov and F. Petriello, Higgs boson production at hadron colliders: differential cross sections through next-to-next-to-leading order, Phys. Rev. Lett.93 (2004) 262002 [hep-ph/0409088] [INSPIRE]. · doi:10.1103/PhysRevLett.93.262002
[54] C. Anastasiou, K. Melnikov and F. Petriello, Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order, Nucl. Phys.B 724 (2005) 197 [hep-ph/0501130] [INSPIRE]. · doi:10.1016/j.nuclphysb.2005.06.036
[55] K. Melnikov and F. Petriello, The W boson production cross section at the LHC through \(O\left( {\alpha_s^2} \right) \), Phys. Rev. Lett.96 (2006) 231803 [hep-ph/0603182] [INSPIRE]. · doi:10.1103/PhysRevLett.96.231803
[56] A. Gehrmann-De Ridder, T. Gehrmann and E. Glover, Quark-gluon antenna functions from neutralino decay, Phys. Lett.B 612 (2005) 36 [hep-ph/0501291] [INSPIRE].
[57] A. Gehrmann-De Ridder, T. Gehrmann and E. Glover, Gluon-gluon antenna functions from Higgs boson decay, Phys. Lett.B 612 (2005) 49 [hep-ph/0502110] [INSPIRE].
[58] A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, Infrared structure of e+e− → 3 jets at NNLO, JHEP11 (2007) 058 [arXiv:0710.0346] [INSPIRE]. · doi:10.1088/1126-6708/2007/11/058
[59] S. Weinzierl, The Infrared structure of e+e− → 3 jets at NNLO reloaded, JHEP07 (2009) 009 [arXiv:0904.1145] [INSPIRE]. · doi:10.1088/1126-6708/2009/07/009
[60] A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, Second-order QCD corrections to the thrust distribution, Phys. Rev. Lett.99 (2007) 132002 [arXiv:0707.1285] [INSPIRE]. · doi:10.1103/PhysRevLett.99.132002
[61] A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, NNLO corrections to event shapes in e+e−annihilation, JHEP12 (2007) 094 [arXiv:0711.4711] [INSPIRE]. · doi:10.1088/1126-6708/2007/12/094
[62] S. Weinzierl, NNLO corrections to 3-jet observables in electron-positron annihilation, Phys. Rev. Lett.101 (2008) 162001 [arXiv:0807.3241] [INSPIRE]. · doi:10.1103/PhysRevLett.101.162001
[63] S. Weinzierl, Event shapes and jet rates in electron-positron annihilation at NNLO, JHEP06 (2009) 041 [arXiv:0904.1077] [INSPIRE]. · doi:10.1088/1126-6708/2009/06/041
[64] A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, NNLO moments of event shapes in e+e−annihilation, JHEP05 (2009) 106 [arXiv:0903.4658] [INSPIRE]. · doi:10.1088/1126-6708/2009/05/106
[65] S. Weinzierl, Moments of event shapes in electron-positron annihilation at NNLO, Phys. Rev.D 80 (2009) 094018 [arXiv:0909.5056] [INSPIRE].
[66] A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, Jet rates in electron-positron annihilation at \(O\left( {\alpha_s^3} \right)\) in QCD, Phys. Rev. Lett.100 (2008) 172001 [arXiv:0802.0813] [INSPIRE]. · doi:10.1103/PhysRevLett.100.172001
[67] S. Weinzierl, Jet algorithms in electron-positron annihilation: Perturbative higher order predictions, Eur. Phys. J.C 71 (2011) 1565 [Erratum ibid.C 71 (2011) 1717] [arXiv:1011.6247] [INSPIRE].
[68] A. Gehrmann-De Ridder and M. Ritzmann, NLO antenna subtraction with massive fermions, JHEP07 (2009) 041 [arXiv:0904.3297] [INSPIRE]. · doi:10.1088/1126-6708/2009/07/041
[69] G. Abelof and A. Gehrmann-De Ridder, Antenna subtraction for the production of heavy particles at hadron colliders, JHEP04 (2011) 063 [arXiv:1102.2443] [INSPIRE]. · doi:10.1007/JHEP04(2011)063
[70] W. Bernreuther, C. Bogner and O. Dekkers, The real radiation antenna function for \(S \to Q\overline Q q\overline q\) at NNLO QCD,JHEP06(2011) 032 [arXiv:1105.0530] [INSPIRE]. · Zbl 1298.81368 · doi:10.1007/JHEP06(2011)032
[71] A. Daleo, T. Gehrmann and D. Maître, Antenna subtraction with hadronic initial states, JHEP04 (2007) 016 [hep-ph/0612257] [INSPIRE]. · doi:10.1088/1126-6708/2007/04/016
[72] A. Daleo, A. Gehrmann-De Ridder, T. Gehrmann and G. Luisoni, Antenna subtraction at NNLO with hadronic initial states: initial-final configurations, JHEP01 (2010) 118 [arXiv:0912.0374] [INSPIRE]. · Zbl 1269.81194 · doi:10.1007/JHEP01(2010)118
[73] R. Boughezal, A. Gehrmann-De Ridder and M. Ritzmann, Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours, JHEP02 (2011) 098 [arXiv:1011.6631] [INSPIRE]. · Zbl 1294.81270 · doi:10.1007/JHEP02(2011)098
[74] T. Gehrmann and P.F. Monni, Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations, JHEP12 (2011) 049 [arXiv:1107.4037] [INSPIRE]. · Zbl 1306.81339 · doi:10.1007/JHEP12(2011)049
[75] E. Nigel Glover and J. Pires, Antenna subtraction for gluon scattering at NNLO, JHEP06 (2010) 096 [arXiv:1003.2824] [INSPIRE]. · Zbl 1288.81147 · doi:10.1007/JHEP06(2010)096
[76] S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett.B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
[77] G.F. Sterman and M.E. Tejeda-Yeomans, Multiloop amplitudes and resummation, Phys. Lett.B 552 (2003) 48 [hep-ph/0210130] [INSPIRE]. · Zbl 1005.81519
[78] 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]. · Zbl 1049.81644 · doi:10.1016/0550-3213(94)90179-1
[79] Z. Bern, V. Del Duca and C.R. Schmidt, The infrared behavior of one loop gluon amplitudes at next-to-next-to-leading order, Phys. Lett.B 445 (1998) 168 [hep-ph/9810409] [INSPIRE].
[80] D.A. Kosower, All order collinear behavior in gauge theories, Nucl. Phys.B 552 (1999) 319 [hep-ph/9901201] [INSPIRE]. · doi:10.1016/S0550-3213(99)00251-5
[81] D.A. Kosower and P. Uwer, One loop splitting amplitudes in gauge theory, Nucl. Phys.B 563 (1999) 477 [hep-ph/9903515] [INSPIRE]. · doi:10.1016/S0550-3213(99)00583-0
[82] Z. Bern, V. Del Duca, W.B. Kilgore and C.R. Schmidt, The infrared behavior of one loop QCD amplitudes at next-to-next-to leading order, Phys. Rev.D 60 (1999) 116001 [hep-ph/9903516] [INSPIRE].
[83] S. Catani and M. Grazzini, The soft gluon current at one loop order, Nucl. Phys.B 591 (2000) 435 [hep-ph/0007142] [INSPIRE]. · doi:10.1016/S0550-3213(00)00572-1
[84] I. Bierenbaum, M. Czakon and A. Mitov, The singular behavior of one-loop massive QCD amplitudes with one external soft gluon, Nucl. Phys.B 856 (2012) 228 [arXiv:1107.4384] [INSPIRE]. · Zbl 1246.81420 · doi:10.1016/j.nuclphysb.2011.11.002
[85] S. Catani, D. de Florian and G. Rodrigo, The triple collinear limit of one loop QCD amplitudes, Phys. Lett.B 586 (2004) 323 [hep-ph/0312067] [INSPIRE].
[86] D.A. Kosower, Multiple singular emission in gauge theories, Phys. Rev.D 67 (2003) 116003 [hep-ph/0212097] [INSPIRE].
[87] D.A. Kosower, All orders singular emission in gauge theories, Phys. Rev. Lett.91 (2003) 061602 [hep-ph/0301069] [INSPIRE]. · doi:10.1103/PhysRevLett.91.061602
[88] S. Weinzierl, Subtraction terms for one loop amplitudes with one unresolved parton, JHEP07 (2003) 052 [hep-ph/0306248] [INSPIRE]. · doi:10.1088/1126-6708/2003/07/052
[89] Z. Bern, L.J. Dixon and D.A. Kosower, Two-loop g → gg splitting amplitudes in QCD, JHEP08 (2004) 012 [hep-ph/0404293] [INSPIRE]. · doi:10.1088/1126-6708/2004/08/012
[90] S. Badger and E. Glover, Two loop splitting functions in QCD, JHEP07 (2004) 040 [hep-ph/0405236] [INSPIRE]. · doi:10.1088/1126-6708/2004/07/040
[91] A. Gehrmann-De Ridder, T. Gehrmann and G. Heinrich, Four particle phase space integrals in massless QCD, Nucl. Phys.B 682 (2004) 265 [hep-ph/0311276] [INSPIRE]. · Zbl 1045.81558 · doi:10.1016/j.nuclphysb.2004.01.023
[92] W.A. Bardeen, A. Buras, D. Duke and T. Muta, Deep inelastic scattering beyond the leading order in asymptotically free gauge theories, Phys. Rev.D 18 (1978) 3998 [INSPIRE].
[93] D. Gross and F. Wilczek, Ultraviolet behavior of nonabelian gauge theories, Phys. Rev. Lett.30 (1973) 1343 [INSPIRE]. · doi:10.1103/PhysRevLett.30.1343
[94] H. Politzer, Reliable perturbative results for strong interactions?, Phys. Rev. Lett.30 (1973) 1346 [INSPIRE]. · doi:10.1103/PhysRevLett.30.1346
[95] W.E. Caswell, Asymptotic behavior of nonabelian gauge theories to two loop order, Phys. Rev. Lett.33 (1974) 244 [INSPIRE]. · doi:10.1103/PhysRevLett.33.244
[96] D. Jones, Two loop diagrams in Yang-Mills theory, Nucl. Phys.B 75 (1974) 531 [INSPIRE]. · doi:10.1016/0550-3213(74)90093-5
[97] G. Altarelli and G. Parisi, Asymptotic freedom in parton language, Nucl. Phys.B 126 (1977) 298 [INSPIRE]. · doi:10.1016/0550-3213(77)90384-4
[98] G. Curci, W. Furmanski and R. Petronzio, Evolution of parton densities beyond leading order: the nonsinglet case, Nucl. Phys.B 175 (1980) 27 [INSPIRE]. · doi:10.1016/0550-3213(80)90003-6
[99] W. Furmanski and R. Petronzio, Singlet parton densities beyond leading order, Phys. Lett.B 97 (1980) 437 [INSPIRE].
[100] E. Floratos, D. Ross and C.T. Sachrajda, Higher order effects in asymptotically free gauge theories: the anomalous dimensions of Wilson operators, Nucl. Phys.B 129 (1977) 66 [Erratum ibid.B 139 (1978) 545-546] [INSPIRE].
[101] E. Floratos, D. Ross and C.T. Sachrajda, Higher order effects in asymptotically free gauge theories. 2. Flavor singlet Wilson operators and coefficient functions, Nucl. Phys.B 152 (1979) 493 [INSPIRE]. · doi:10.1016/0550-3213(79)90094-4
[102] F.A. Berends and W. Giele, The six gluon process as an example of Weyl-Van Der Waerden spinor calculus, Nucl. Phys.B 294 (1987) 700 [INSPIRE]. · doi:10.1016/0550-3213(87)90604-3
[103] D. Kosower, B.-H. Lee and V. Nair, Multi gluon scattering: a string based calculation, Phys. Lett.B 201 (1988) 85 [INSPIRE].
[104] M.L. Mangano, S.J. Parke and Z. Xu, Duality and multi-gluon scattering, Nucl. Phys.B 298 (1988) 653 [INSPIRE]. · doi:10.1016/0550-3213(88)90001-6
[105] M.L. Mangano and S.J. Parke, Multiparton amplitudes in gauge theories, Phys. Rept.200 (1991) 301 [hep-th/0509223] [INSPIRE]. · doi:10.1016/0370-1573(91)90091-Y
[106] Z. Bern, L.J. Dixon and D.A. Kosower, One loop corrections to five gluon amplitudes, Phys. Rev. Lett.70 (1993) 2677 [hep-ph/9302280] [INSPIRE]. · doi:10.1103/PhysRevLett.70.2677
[107] S. Badger, B. Biedermann and P. Uwer, NGluon: a package to calculate one-loop multi-gluon amplitudes, Comput. Phys. Commun.182 (2011) 1674 [arXiv:1011.2900] [INSPIRE]. · Zbl 1262.81102 · doi:10.1016/j.cpc.2011.04.008
[108] R. Kleiss, W. Stirling and S. Ellis, A new Monte Carlo treatment of multiparticle phase space at high-energies, Comput. Phys. Commun.40 (1986) 359 [INSPIRE]. · doi:10.1016/0010-4655(86)90119-0
[109] M. Cacciari and G.P. Salam, Dispelling the N3myth for the ktjet-finder, Phys. Lett.B 641 (2006) 57 [hep-ph/0512210] [INSPIRE].
[110] M. Cacciari, G.P. Salam and G. Soyez, The anti-ktjet clustering algorithm, JHEP04 (2008) 063 [arXiv:0802.1189] [INSPIRE]. · doi:10.1088/1126-6708/2008/04/063
[111] J. Pires and E. Glover, Double real radiation corrections to gluon scattering at NNLO, Nucl. Phys. Proc. Suppl.205-206 (2010) 176 [arXiv:1006.1849] [INSPIRE]. · doi:10.1016/j.nuclphysbps.2010.08.039
[112] S. Weinzierl, Status of jet cross sections to NNLO, Nucl. Phys. Proc. Suppl.160 (2006) 126 [hep-ph/0606301] [INSPIRE]. · doi:10.1016/j.nuclphysbps.2006.09.038
[113] D.A. Kosower, Antenna factorization of gauge theory amplitudes, Phys. Rev.D 57 (1998) 5410 [hep-ph/9710213] [INSPIRE].
[114] D.A. Kosower, Antenna factorization in strongly ordered limits, Phys. Rev.D 71 (2005) 045016 [hep-ph/0311272] [INSPIRE].
[115] A. Vogt, S. Moch and J. Vermaseren, The three-loop splitting functions in QCD: the singlet case, Nucl. Phys.B 691 (2004) 129 [hep-ph/0404111] [INSPIRE]. · Zbl 1109.81374 · doi:10.1016/j.nuclphysb.2004.04.024
[116] S. Buehler and C. Duhr, CHAPLIN — Complex harmonic polylogarithms in Fortran, arXiv:1106.5739 [INSPIRE]. · Zbl 1360.33002
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