Antenna subtraction at NNLO with hadronic initial states: Double real initial-initial configurations

Journal of High Energy Physics

Volumn 2012, Issue 10, 2012, Pages

  Gehrmann De Ridder, A ^a   Gehrmann, T ^b   Ritzmann, M ^c  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF ZURICH   (Switzerland)

^c CEA SACLAY   (France)

Author keywords

Hadronic colliders; Jets

Indexed keywords

EID: 84868141463     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP10(2012)047     Document Type: Article

References (126)

1. R.K. Ellis, W.J. Stirling and B.R. Webber, QCD and Collider Physics, Cambridge University Press, Cambridge, U.K. (1996).
2. G. Dissertori, I.G. Knowles and M. Schmelling, Quantum Chromodynamics: High Energy Experiments and Theory, Oxford University Press Oxford, U.K. (2003).
3. 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].
4. D.A. Kosower, All order collinear behavior in gauge theories, Nucl. Phys. B 552 (1999) 319 [hep-ph/9901201] [INSPIRE].
5. D.A. Kosower and P. Uwer, One loop splitting amplitudes in gauge theory, Nucl. Phys. B 563 (1999) 477 [hep-ph/9903515] [INSPIRE].
6. 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].
7. 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].
8. S. Catani and M. Grazzini, The soft gluon current at one loop order, Nucl. Phys. B 591 (2000) 435 [hep-ph/0007142] [INSPIRE].
9. D.A. Kosower, All orders singular emission in gauge theories, Phys. Rev. Lett. 91 (2003) 061602 [hep-ph/0301069] [INSPIRE].
10. S. Weinzierl, Subtraction terms for one loop amplitudes with one unresolved parton, JHEP 07 (2003) 052 [hep-ph/0306248] [INSPIRE].
11. C. Anastasiou, Z. Bern, L.J. Dixon and D. Kosower, Planar amplitudes in maximally supersymmetric Yang-Mills theory, Phys. Rev. Lett. 91 (2003) 251602 [hep-th/0309040] [INSPIRE].
12. Z. Bern, L.J. Dixon and D.A. Kosower, Two-loop g → gg splitting amplitudes in QCD, JHEP 08 (2004) 012 [hep-ph/0404293] [INSPIRE].
13. S. Badger and E.W.N. Glover, Two loop splitting functions in QCD, JHEP 07 (2004) 040 [hep-ph/0405236] [INSPIRE].
14. A. Gehrmann-De Ridder and E.W.N. Glover, A Complete O(ααs) calculation of the photon +1 jet rate in e+e- annihilation, Nucl. Phys. B 517 (1998) 269 [hep-ph/9707224] [INSPIRE].
15. J.M. Campbell and E.W.N. Glover, Double unresolved approximations to multiparton scattering amplitudes, Nucl. Phys. B 527 (1998) 264 [hep-ph/9710255] [INSPIRE].
16. S. Catani and M. Grazzini, Collinear factorization and splitting functions for next-to-next-to-leading order QCD calculations, Phys. Lett. B 446 (1999) 143 [hep-ph/9810389] [INSPIRE].
17. S. Catani and M. Grazzini, Infrared factorization of tree level QCD amplitudes at the next-to-next-to-leading order and beyond, Nucl. Phys. B 570 (2000) 287 [hep-ph/9908523] [INSPIRE].
18. F.A. Berends and W.T. Giele, Multiple Soft Gluon Radiation in Parton Processes, Nucl. Phys. B 313 (1989) 595 [INSPIRE].
19. V. Del Duca, A. Frizzo and F. Maltoni, Factorization of tree QCD amplitudes in the high-energy limit and in the collinear limit, Nucl. Phys. B 568 (2000) 211 [hep-ph/9909464] [INSPIRE].
20. T. Birthwright, E.W.N. Glover, V. Khoze and P. Marquard, Multi-gluon collinear limits from MHV diagrams, JHEP 05 (2005) 013 [hep-ph/0503063] [INSPIRE].
21. Z. Kunszt and D.E. Soper, Calculation of jet cross-sections in hadron collisions at order α S 3, Phys. Rev. D 46 (1992) 192 [INSPIRE].
22. 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].
23. 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] [hep-ph/9605323] [INSPIRE].
24. D.A. Kosower, Antenna factorization of gauge theory amplitudes, Phys. Rev. D 57 (1998) 5410 [hep-ph/9710213] [INSPIRE].
25. D.A. Kosower, Antenna factorization in strongly ordered limits, Phys. Rev. D 71 (2005) 045016 [hep-ph/0311272] [INSPIRE].
26. J.M. Campbell, M. Cullen and E.W.N. Glover, Four jet event shapes in electron-positron annihilation, Eur. Phys. J. C 9 (1999) 245 [hep-ph/9809429] [INSPIRE].
27. G. Somogyi, Subtraction with hadronic initial states at NLO: An NNLO-compatible scheme, JHEP 05 (2009) 016 [arXiv:0903.1218] [INSPIRE].
28. D.A. Kosower, Multiple singular emission in gauge theories, Phys. Rev. D 67 (2003) 116003 [hep-ph/0212097] [INSPIRE].
29. S. Weinzierl, Subtraction terms at NNLO, JHEP 03 (2003) 062 [hep-ph/0302180] [INSPIRE].
30. 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].
31. S. Frixione and M. Grazzini, Subtraction at NNLO, JHEP 06 (2005) 010 [hep-ph/0411399] [INSPIRE].
32. G. Somogyi, Z. Trócsányi and V. Del Duca, Matching of singly- and doubly-unresolved limits of tree-level QCD squared matrix elements, JHEP 06 (2005) 024 [hep-ph/0502226] [INSPIRE].
33. G. Somogyi, Z. Trócsányi and V. Del Duca, A Subtraction scheme for computing QCD jet cross sections at NNLO: Regularization of doubly-real emissions, JHEP 01 (2007) 070 [hep-ph/0609042] [INSPIRE].
34. G. Somogyi and Z. Trócsányi, A Subtraction scheme for computing QCD jet cross sections at NNLO: Regularization of real-virtual emission, JHEP 01 (2007) 052 [hep-ph/0609043] [INSPIRE].
35. G. Somogyi and Z. Trócsányi, A Subtraction scheme for computing QCD jet cross sections at NNLO: Integrating the subtraction terms. I, JHEP 08 (2008) 042 [arXiv:0807.0509] [INSPIRE].
36. U. Aglietti, V. Del Duca, C. Duhr, G. Somogyi and Z. Trócsá nyi, Analytic integration of real-virtual counterterms in NNLO jet cross sections. I, JHEP 09 (2008) 107 [arXiv:0807.0514] [INSPIRE].
37. P. Bolzoni, S.-O. Moch, G. Somogyi and Z. Trócsányi, Analytic integration of real-virtual counterterms in NNLO jet cross sections. II., JHEP 08 (2009) 079 [arXiv:0905.4390] [INSPIRE].
38. 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, JHEP 01 (2011) 059 [arXiv:1011.1909] [INSPIRE].
39. 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].
40. M. Czakon, A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett. B 693 (2010) 259 [arXiv:1005.0274] [INSPIRE].
41. 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].
42. 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].
43. C. Anastasiou, F. Herzog and A. Lazopoulos, On the factorization of overlapping singularities at NNLO, JHEP 03 (2011) 038 [arXiv:1011.4867] [INSPIRE].
44. C. Anastasiou, F. Herzog and A. Lazopoulos, The fully differential decay rate of a Higgs boson to bottom-quarks at NNLO in QCD, JHEP 03 (2012) 035 [arXiv:1110.2368] [INSPIRE].
45. S. Bühler, F. Herzog, A. Lazopoulos and R. Müller, The fully differential hadronic production of a Higgs boson via bottom quark fusion at NNLO, JHEP 07 (2012) 115 [arXiv:1204.4415] [INSPIRE].
46. A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna subtraction at NNLO, JHEP 09 (2005) 056 [hep-ph/0505111] [INSPIRE].
47. A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Infrared structure of e+e- → 2 jets at NNLO, Nucl. Phys. B 691 (2004) 195 [hep-ph/0403057] [INSPIRE].
48. A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Quark-gluon antenna functions from neutralino decay, Phys. Lett. B 612 (2005) 36 [hep-ph/0501291] [INSPIRE].
49. A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Gluon-gluon antenna functions from Higgs boson decay, Phys. Lett. B 612 (2005) 49 [hep-ph/0502110] [INSPIRE].
50. A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, Infrared structure of e+e- → 3 jets at NNLO, JHEP 11 (2007) 058 [arXiv:0710.0346] [INSPIRE].
51. A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, Jet rates in electron-positron annihilation at O(α s3) in QCD, Phys. Rev. Lett. 100 (2008) 172001 [arXiv:0802.0813] [INSPIRE].
52. S. Weinzierl, NNLO corrections to 3-jet observables in electron-positron annihilation, Phys. Rev. Lett. 101 (2008) 162001 [arXiv:0807.3241] [INSPIRE].
53. S. Weinzierl, The infrared structure of e+e- → 3 jets at NNLO reloaded, JHEP 07 (2009) 009 [arXiv:0904.1145] [INSPIRE].
54. 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].
55. A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, Second-order QCD corrections to the thrust distribution, Phys. Rev. Lett. 99 (2007) 132002 [arXiv:0707.1285] [INSPIRE].
56. A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, NNLO corrections to event shapes in e+e- annihilation, JHEP 12 (2007) 094 [arXiv:0711.4711] [INSPIRE].
57. A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, NNLO moments of event shapes in e+e- annihilation, JHEP 05 (2009) 106 [arXiv:0903.4658] [INSPIRE].
58. S. Weinzierl, Event shapes and jet rates in electron-positron annihilation at NNLO, JHEP 06 (2009) 041 [arXiv:0904.1077] [INSPIRE].
59. S. Weinzierl, Moments of event shapes in electron-positron annihilation at NNLO, Phys. Rev. D 80 (2009) 094018 [arXiv:0909.5056] [INSPIRE].
60. G. Dissertori et al., First determination of the strong coupling constant using NNLO predictions for hadronic event shapes in e+e- annihilations, JHEP 02 (2008) 040 [arXiv:0712.0327] [INSPIRE].
61. G. Dissertori et al., Determination of the strong coupling constant using matched NNLO+NLLA predictions for hadronic event shapes in e+e- annihilations, JHEP 08 (2009) 036 [arXiv:0906.3436] [INSPIRE].
62. G. Dissertori et al., Precise determination of the strong coupling constant at NNLO in QCD from the three-jet rate in electron-positron annihilation at LEP, Phys. Rev. Lett. 104 (2010) 072002 [arXiv:0910.4283] [INSPIRE].
63. T. Becher and M.D. Schwartz, A precise determination of αs from LEP thrust data using effective field theory, JHEP 07 (2008) 034 [arXiv:0803.0342] [INSPIRE].
64. Y.-T. Chien and M.D. Schwartz, Resummation of heavy jet mass and comparison to LEP data, JHEP 08 (2010) 058 [arXiv:1005.1644] [INSPIRE].
65. R. Abbate, M. Fickinger, A.H. Hoang, V. Mateu and I.W. Stewart, Thrust at N3LL with Power Corrections and a Precision Global Fit for αs(mZ), Phys. Rev. D 83 (2011) 074021 [arXiv:1006.3080] [INSPIRE].
66. R. Davison and B. Webber, Non-Perturbative Contribution to the Thrust Distribution in e+e- Annihilation, Eur. Phys. J. C 59 (2009) 13 [arXiv:0809.3326] [INSPIRE].
67. JADE collaboration, S. Bethke, S. Kluth, C. Pahl and J. Schieck, Determination of the Strong Coupling αs from hadronic Event Shapes with O(α s 3) and resummed QCD predictions using JADE Data, Eur. Phys. J. C 64 (2009) 351 [arXiv:0810.1389] [INSPIRE].
68. OPAL collaboration, G. Abbiendi et al., Determination of αs using OPAL hadronic event shapes at √s = 91 - 209 GeV and resummed NNLO calculations, Eur. Phys. J. C 71 (2011) 1733 [arXiv:1101.1470] [INSPIRE].
69. J. Schieck, S. Bethke, S. Kluth, C. Pahl and Z. Trócsányi, Measurement of the strong coupling αS from the three-jet rate in e+e-annihilation using JADE data, arXiv:1205.3714 [INSPIRE].
70. T. Gehrmann, M. Jaquier and G. Luisoni, Hadronization effects in event shape moments, Eur. Phys. J. C 67 (2010) 57 [arXiv:0911.2422] [INSPIRE].
71. A. Gehrmann-De Ridder and M. Ritzmann, NLO Antenna Subtraction with Massive Fermions, JHEP 07 (2009) 041 [arXiv:0904.3297] [INSPIRE].
72. G. Abelof and A. Gehrmann-De Ridder, Antenna subtraction for the production of heavy particles at hadron colliders, JHEP 04 (2011) 063 [arXiv:1102.2443] [INSPIRE].
73. G. Abelof and A. Gehrmann-De Ridder, Double real radiation corrections to tt̄ production at the LHC: the all-fermion processes, JHEP 04 (2012) 076 [arXiv:1112.4736] [INSPIRE].
74. W. Bernreuther, C. Bogner and O. Dekkers, The real radiation antenna function for S → Q̄Qqq̄ at NNLO QCD, JHEP 06 (2011) 032 [arXiv:1105.0530] [INSPIRE].
75. W.T. Giele, D.A. Kosower and P.Z. Skands, A simple shower and matching algorithm, Phys. Rev. D 78 (2008) 014026 [arXiv:0707.3652] [INSPIRE].
76. W.T. Giele, D. Kosower and P.Z. Skands, Higher-Order Corrections to Timelike Jets, Phys. Rev. D 84 (2011) 054003 [arXiv:1102.2126] [INSPIRE].
77. A. Gehrmann-De Ridder, M. Ritzmann and P.Z. Skands, Timelike Dipole-Antenna Showers with Massive Fermions, Phys. Rev. D 85 (2012) 014013 [arXiv:1108.6172] [INSPIRE].
78. J.J. Lopez-Villarejo and P.Z. Skands, Efficient Matrix-Element Matching with Sector Showers, JHEP 11 (2011) 150 [arXiv:1109.3608] [INSPIRE].
79. A. Daleo, T. Gehrmann and D. Maître, Antenna subtraction with hadronic initial states, JHEP 04 (2007) 016 [hep-ph/0612257] [INSPIRE].
80. E.W.N. Glover and J. Pires, Antenna subtraction for gluon scattering at NNLO, JHEP 06 (2010) 096 [arXiv:1003.2824] [INSPIRE].
81. A. Gehrmann-De Ridder, E.W.N. Glover and J. Pires, Real-Virtual corrections for gluon scattering at NNLO, JHEP 02 (2012) 141 [arXiv:1112.3613] [INSPIRE].
82. A. Daleo, A. Gehrmann-De Ridder, T. Gehrmann and G. Luisoni, Antenna subtraction at NNLO with hadronic initial states: initial-final configurations, JHEP 01 (2010) 118 [arXiv:0912.0374] [INSPIRE].
83. T. Gehrmann and P.F. Monni, Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations, JHEP 12 (2011) 049 [arXiv:1107.4037] [INSPIRE].
84. 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, JHEP 02 (2011) 098 [arXiv:1011.6631] [INSPIRE].
85. T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multiloop integrals, Nucl. Phys. B 585 (2000) 741 [hep-ph/0004013] [INSPIRE].
86. G. Heinrich, A numerical method for NNLO calculations, Nucl. Phys. Proc. Suppl. 116 (2003) 368 [hep-ph/0211144] [INSPIRE].
87. 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].
88. T. Binoth and G. Heinrich, Numerical evaluation of phase space integrals by sector decomposition, Nucl. Phys. B 693 (2004) 134 [hep-ph/0402265] [INSPIRE].
89. 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].
90. 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].
91. C. Anastasiou, G. Dissertori and F. Stoöckli, NNLO QCD predictions for the H → WW → ℓνℓν signal at the LHC, JHEP 09 (2007) 018 [arXiv:0707.2373] [INSPIRE].
92. K. Melnikov and F. Petriello, The W boson production cross section at the LHC through O(α s 2), Phys. Rev. Lett. 96 (2006) 231803 [hep-ph/0603182] [INSPIRE].
93. M. Grazzini, NNLO predictions for the Higgs boson signal in the H → WW → ℓνℓν and H → ZZ → 4ℓ decay channels, JHEP 02 (2008) 043 [arXiv:0801.3232] [INSPIRE].
94. 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].
95. S. Catani, G. Ferrera and M. Grazzini, W Boson Production at Hadron Colliders: The Lepton Charge Asymmetry in NNLO QCD, JHEP 05 (2010) 006 [arXiv:1002.3115] [INSPIRE].
96. 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].
97. S. Catani, L. Cieri, D. de Florian, G. Ferrera and M. Grazzini, Diphoton production at hadron colliders: a fully-differential QCD calculation at NNLO, Phys. Rev. Lett. 108 (2012) 072001 [arXiv:1110.2375] [INSPIRE].
98. P. Bärnreuther, M. Czakon and A. Mitov, Percent Level Precision Physics at the Tevatron: First Genuine NNLO QCD Corrections to qq̄ → tt̄ + X, arXiv:1204.5201 [INSPIRE].
99. M. Czakon and A. Mitov, NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels, arXiv:1207.0236 [INSPIRE].
100. J. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
101. J. Kuipers, T. Ueda, J. Vermaseren and J. Vollinga, FORM version 4.0, arXiv:1203.6543 [INSPIRE].
102. D. de Florian and M. Grazzini, The Structure of large logarithmic corrections at small transverse momentum in hadronic collisions, Nucl. Phys. B 616 (2001) 247 [hep-ph/0108273] [INSPIRE].
103. C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, High precision QCD at hadron colliders: Electroweak gauge boson rapidity distributions at NNLO, Phys. Rev. D 69 (2004) 094008 [hep-ph/0312266] [INSPIRE].
104. C. Anastasiou and K. Melnikov, Higgs boson production at hadron colliders in NNLO QCD, Nucl. Phys. B 646 (2002) 220 [hep-ph/0207004] [INSPIRE].
105. K. Chetyrkin and F. Tkachov, Integration by Parts: The Algorithm to Calculate β-functions in 4 Loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].
106. S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
107. A. Smirnov, Algorithm FIRE - Feynman Integral REduction, JHEP 10 (2008) 107 [arXiv:0807.3243] [INSPIRE].
108. P.F. Monni, T. Gehrmann and G. Luisoni, Two-Loop Soft Corrections and Resummation of the Thrust Distribution in the Dijet Region, JHEP 08 (2011) 010 [arXiv:1105.4560] [INSPIRE].
109. T. Huber and D. Maître, HypExp: A Mathematica package for expanding hypergeometric functions around integer-valued parameters, Comput. Phys. Commun. 175 (2006) 122 [hep-ph/0507094] [INSPIRE].
110. T. Huber and D. Maître, HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters, Comput. Phys. Commun. 178 (2008) 755 [arXiv:0708.2443] [INSPIRE].
111. E. Remiddi and J. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
112. C. Anastasiou, E.W.N. Glover, C. Oleari and M. Tejeda-Yeomans, Two-loop QCD corrections to the scattering of massless distinct quarks, Nucl. Phys. B 601 (2001) 318 [hep-ph/0010212] [INSPIRE].
113. E.W.N. Glover, C. Oleari and M. Tejeda-Yeomans, Two loop QCD corrections to gluon-gluon scattering, Nucl. Phys. B 605 (2001) 467 [hep-ph/0102201] [INSPIRE].
114. C. Anastasiou, E.W.N. Glover and M. Tejeda-Yeomans, Two loop QED and QCD corrections to massless fermion boson scattering, Nucl. Phys. B 629 (2002) 255 [hep-ph/0201274] [INSPIRE].
115. E.W.N. Glover and M. Tejeda-Yeomans, Two loop QCD helicity amplitudes for massless quark massless gauge boson scattering, JHEP 06 (2003) 033 [hep-ph/0304169] [INSPIRE].
116. E.W.N. Glover, Two loop QCD helicity amplitudes for massless quark quark scattering, JHEP 04 (2004) 021 [hep-ph/0401119] [INSPIRE].
117. Z. Bern, A. De Freitas and L.J. Dixon, Two loop amplitudes for gluon fusion into two photons, JHEP 09 (2001) 037 [hep-ph/0109078] [INSPIRE].
118. Z. Bern, A. De Freitas and L.J. Dixon, Two loop helicity amplitudes for gluon-gluon scattering in QCD and supersymmetric Yang-Mills theory, JHEP 03 (2002) 018 [hep-ph/0201161] [INSPIRE].
119. Z. Bern, A. De Freitas and L.J. Dixon, Two loop helicity amplitudes for quark gluon scattering in QCD and gluino gluon scattering in supersymmetric Yang-Mills theory, JHEP 06 (2003) 028 [hep-ph/0304168] [INSPIRE].
120. A. De Freitas and Z. Bern, Two-loop helicity amplitudes for quark-quark scattering in QCD and gluino-gluino scattering in supersymmetric Yang-Mills theory, JHEP 09 (2004) 039 [hep-ph/0409007] [INSPIRE].
121. L. Garland, T. Gehrmann, E.W.N. Glover, A. Koukoutsakis and E. Remiddi, The Two loop QCD matrix element for e+e- → 3 jets, Nucl. Phys. B 627 (2002) 107 [hep-ph/0112081] [INSPIRE].
122. L. Garland, T. Gehrmann, E.W.N. Glover, A. Koukoutsakis and E. Remiddi, Two loop QCD helicity amplitudes for e+e- → 3 jets, Nucl. Phys. B 642 (2002) 227 [hep-ph/0206067] [INSPIRE].
123. T. Gehrmann and L. Tancredi, Two-loop QCD helicity amplitudes for qq̄ → W±γ and qq̄ → Z0γ, JHEP 02 (2012) 004 [arXiv:1112.1531] [INSPIRE].
124. T. Gehrmann, M. Jaquier, E.W.N. Glover and A. Koukoutsakis, Two-Loop QCD Corrections to the Helicity Amplitudes for H → 3 partons, JHEP 02 (2012) 056 [arXiv:1112.3554] [INSPIRE].
125. J. Currie, Antenna Subtraction in pQCD at NNLO, arXiv:1111.4810 [INSPIRE].
126. A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and J. Pires, Double virtual corrections for gluon scattering at NNLO, in preparation.