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Antenna subtraction at NNLO with hadronic initial states: initial-final configurations

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Abstract

We extend the antenna subtraction method to include initial states containing one hadron at NNLO. We present results for all the necessary subtraction terms, antenna functions, for the master integrals required to integrate them over the relevant phase space and finally for the integrated antennae themselves. Where applicable, our results are cross-checked against the known NNLO coefficient functions for deep inelastic scattering processes.

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References

  1. R.K. Ellis, W.J. Stirling and B.R. Webber, QCD and collider physics, Cambridge University Press, Cambridge U.K. (1996).

    Google Scholar 

  2. G. Dissertori, I.G. Knowles and M. Schmelling, Quantum chromodynamics: high energy experiments and theory, Oxford University Press, Oxford U.K. (2003).

    Google Scholar 

  3. Z. Bern, L.J. Dixon and A. Ghinculov, Two-loop correction to Bhabha scattering, Phys. Rev. D 63 (2001) 053007 [hep-ph/0010075] [SPIRES].

    ADS  Google Scholar 

  4. C. Anastasiou, E.W.N. Glover, C. Oleari and M.E. Tejeda-Yeomans, Two-loop QCD corrections to the scattering of massless distinct quarks, Nucl. Phys. B 601 (2001) 318 [hep-ph/0010212] [SPIRES].

    Article  ADS  Google Scholar 

  5. C. Anastasiou, E.W.N. Glover, C. Oleari and M.E. Tejeda-Yeomans, Two-loop QCD corrections to massless identical quark scattering, Nucl. Phys. B 601 (2001) 341 [hep-ph/0011094] [SPIRES].

    Article  ADS  Google Scholar 

  6. C. Anastasiou, E.W.N. Glover, C. Oleari and M.E. Tejeda-Yeomans, Two-loop QCD corrections to massless quark-gluon scattering, Nucl. Phys. B 605 (2001) 486 [hep-ph/0101304] [SPIRES].

    Article  ADS  Google Scholar 

  7. E.W.N. Glover, C. Oleari and M.E. Tejeda-Yeomans, Two-loop QCD corrections to gluon-gluon scattering, Nucl. Phys. B 605 (2001) 467 [hep-ph/0102201] [SPIRES].

    Article  ADS  Google Scholar 

  8. C. Anastasiou, E.W.N. Glover and M.E. Tejeda-Yeomans, Two-loop QED and QCD corrections to massless fermion-boson scattering, Nucl. Phys. B 629 (2002) 255 [hep-ph/0201274] [SPIRES].

    Article  ADS  Google Scholar 

  9. E.W.N. Glover and M.E. Tejeda-Yeomans, Two-loop QCD helicity amplitudes for massless quark-massless gauge boson scattering, JHEP 06 (2003) 033 [hep-ph/0304169] [SPIRES].

    Article  ADS  Google Scholar 

  10. E.W.N. Glover, Two-loop QCD helicity amplitudes for massless quark-quark scattering, JHEP 04 (2004) 021 [hep-ph/0401119] [SPIRES].

    Article  ADS  Google Scholar 

  11. 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] [SPIRES].

    Article  ADS  Google Scholar 

  12. 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] [SPIRES].

    Article  ADS  Google Scholar 

  13. 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] [SPIRES].

    Article  ADS  Google Scholar 

  14. 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] [SPIRES].

    Article  Google Scholar 

  15. Z. Bern, A. De Freitas, L.J. Dixon, A. Ghinculov and H.L. Wong, QCD and QED corrections to light-by-light scattering, JHEP 11 (2001) 031 [hep-ph/0109079] [SPIRES].

    Article  ADS  Google Scholar 

  16. T. Binoth, E.W.N. Glover, P. Marquard and J.J. van der Bij, Two-loop corrections to light-by-light scattering in supersymmetric QED, JHEP 05 (2002) 060 [hep-ph/0202266] [SPIRES].

    Article  ADS  Google Scholar 

  17. L.W. 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] [SPIRES].

    Article  ADS  Google Scholar 

  18. L.W. 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] [SPIRES].

    Article  ADS  Google Scholar 

  19. J.M. Campbell and R.K. Ellis, Next-to-leading order corrections to W + 2 jet and Z + 2 jet production at hadron colliders, Phys. Rev. D 65 (2002) 113007 [hep-ph/0202176] [SPIRES].

    ADS  Google Scholar 

  20. A. Signer and L.J. Dixon, Electron positron annihilation into four jets at next-to-leading order in αs, Phys. Rev. Lett. 78 (1997) 811 [hep-ph/9609460] [SPIRES].

    Article  ADS  Google Scholar 

  21. L.J. Dixon and A. Signer, Complete O(α 3s ) results for e + e − → (γ, Z) → four jets, Phys. Rev. D 56 (1997) 4031 [hep-ph/9706285] [SPIRES].

    ADS  Google Scholar 

  22. Z. Nagy and Z. Trócsányi, Next-to-leading order calculation of four-jet shape variables, Phys. Rev. Lett. 79 (1997) 3604 [hep-ph/9707309] [SPIRES].

    Article  ADS  Google Scholar 

  23. J.M. Campbell, M.A. Cullen and E.W.N. Glover, Four jet event shapes in electron positron annihilation, Eur. Phys. J. C 9 (1999) 245 [hep-ph/9809429] [SPIRES].

    Article  ADS  Google Scholar 

  24. S. Weinzierl and D.A. Kosower, QCD corrections to four-jet production and three-jet structure in e + e − annihilation, Phys. Rev. D 60 (1999) 054028 [hep-ph/9901277] [SPIRES].

    ADS  Google Scholar 

  25. W.B. Kilgore and W.T. Giele, Next-to-leading order gluonic three jet production at hadron colliders, Phys. Rev. D 55 (1997) 7183 [hep-ph/9610433] [SPIRES].

    ADS  Google Scholar 

  26. Z. Nagy and Z. Trócsányi, Multi-jet cross sections in deep inelastic scattering at next-to-leading order, Phys. Rev. Lett. 87 (2001) 082001 [hep-ph/0104315] [SPIRES].

    Article  ADS  Google Scholar 

  27. Z. Nagy, Three-jet cross sections in hadron hadron collisions at next-to-leading order, Phys. Rev. Lett. 88 (2002) 122003 [hep-ph/0110315] [SPIRES].

    Article  ADS  Google Scholar 

  28. Z. Nagy, Next-to-leading order calculation of three jet observables in hadron hadron collision, Phys. Rev. D 68 (2003) 094002 [hep-ph/0307268] [SPIRES].

    ADS  Google Scholar 

  29. 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] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  30. D.A. Kosower, All-order collinear behavior in gauge theories, Nucl. Phys. B 552 (1999) 319 [hep-ph/9901201] [SPIRES].

    Article  ADS  Google Scholar 

  31. D.A. Kosower and P. Uwer, One-loop splitting amplitudes in gauge theory, Nucl. Phys. B 563 (1999) 477 [hep-ph/9903515] [SPIRES].

    Article  ADS  Google Scholar 

  32. 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] [SPIRES].

    ADS  Google Scholar 

  33. 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] [SPIRES].

    ADS  Google Scholar 

  34. S. Catani and M. Grazzini, The soft-gluon current at one-loop order, Nucl. Phys. B 591 (2000) 435 [hep-ph/0007142] [SPIRES].

    Article  ADS  Google Scholar 

  35. D.A. Kosower, All-orders singular emission in gauge theories, Phys. Rev. Lett. 91 (2003) 061602 [hep-ph/0301069] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  36. S. Weinzierl, Subtraction terms for one-loop amplitudes with one unresolved parton, JHEP 07 (2003) 052 [hep-ph/0306248] [SPIRES].

    Article  ADS  Google Scholar 

  37. C. Anastasiou, Z. Bern, L.J. Dixon and D.A. Kosower, Planar amplitudes in maximally supersymmetric Yang-Mills theory, Phys. Rev. Lett. 91 (2003) 251602 [hep-th/0309040] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  38. Z. Bern, L.J. Dixon and D.A. Kosower, Two-loop g → gg splitting amplitudes in QCD, JHEP 08 (2004) 012 [hep-ph/0404293] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  39. S.D. Badger and E.W.N. Glover, Two-loop splitting functions in QCD, JHEP 07 (2004) 040 [hep-ph/0405236] [SPIRES].

    Article  ADS  Google Scholar 

  40. A. Gehrmann-De Ridder and E.W.N. Glover, A complete \( \mathcal{O}\left( {\alpha {\alpha_s}} \right) \) calculation of the photon + 1 jet rate in e + e − annihilation, Nucl. Phys. B 517 (1998) 269 [hep-ph/9707224] [SPIRES].

    Article  ADS  Google Scholar 

  41. J.M. Campbell and E.W.N. Glover, Double unresolved approximations to multiparton scattering amplitudes, Nucl. Phys. B 527 (1998) 264 [hep-ph/9710255] [SPIRES].

    Article  ADS  Google Scholar 

  42. 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] [SPIRES].

    ADS  Google Scholar 

  43. 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] [SPIRES].

    Article  Google Scholar 

  44. F.A. Berends and W.T. Giele, Multiple soft gluon radiation in parton processes, Nucl. Phys. B 313 (1989) 595 [SPIRES].

    Article  ADS  Google Scholar 

  45. 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] [SPIRES].

    Article  ADS  Google Scholar 

  46. T.G. Birthwright, E.W.N. Glover, V.V. Khoze and P. Marquard, Multi-gluon collinear limits from MHV diagrams, JHEP 05 (2005) 013 [hep-ph/0503063] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  47. 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 [SPIRES].

    ADS  Google Scholar 

  48. 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] [SPIRES].

    Article  ADS  Google Scholar 

  49. S. Catani and M.H. 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] [SPIRES].

    Article  ADS  Google Scholar 

  50. D.A. Kosower, Antenna factorization of gauge-theory amplitudes, Phys. Rev. D 57 (1998) 5410 [hep-ph/9710213] [SPIRES].

    ADS  Google Scholar 

  51. D.A. Kosower, Antenna factorization in strongly-ordered limits, Phys. Rev. D 71 (2005) 045016 [hep-ph/0311272] [SPIRES].

    ADS  Google Scholar 

  52. Z. Nagy, G. Somogyi and Z. Trócsányi, Separation of soft and collinear infrared limits of QCD squared matrix elements, hep-ph/0702273 [SPIRES].

  53. G. Somogyi, Subtraction with hadronic initial states: an NNLO-compatible scheme, JHEP 05 (2009) 016 [arXiv:0903.1218] [SPIRES].

    Article  ADS  Google Scholar 

  54. D.A. Kosower, Multiple singular emission in gauge theories, Phys. Rev. D 67 (2003) 116003 [hep-ph/0212097] [SPIRES].

    ADS  Google Scholar 

  55. S. Weinzierl, Subtraction terms at NNLO, JHEP 03 (2003) 062 [hep-ph/0302180] [SPIRES].

    Article  ADS  Google Scholar 

  56. 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] [SPIRES].

    ADS  Google Scholar 

  57. S. Frixione and M. Grazzini, Subtraction at NNLO, JHEP 06 (2005) 010 [hep-ph/0411399] [SPIRES].

    Article  ADS  Google Scholar 

  58. 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] [SPIRES].

    Article  ADS  Google Scholar 

  59. 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] [SPIRES].

    Article  ADS  Google Scholar 

  60. 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] [SPIRES].

    Article  ADS  Google Scholar 

  61. 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] [SPIRES].

    Article  ADS  Google Scholar 

  62. U. Aglietti, V. Del Duca, C. Duhr, G. Somogyi and Z. Trócsányi, Analytic integration of real-virtual counterterms in NNLO jet cross sections I, JHEP 09 (2008) 107 [arXiv:0807.0514] [SPIRES].

    Article  ADS  Google Scholar 

  63. 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] [SPIRES].

    Article  ADS  Google Scholar 

  64. 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] [SPIRES].

    Article  ADS  Google Scholar 

  65. A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Antenna subtraction at NNLO, JHEP 09 (2005) 056 [hep-ph/0505111] [SPIRES].

    Article  ADS  Google Scholar 

  66. 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] [SPIRES].

    Article  ADS  Google Scholar 

  67. 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] [SPIRES].

    ADS  Google Scholar 

  68. 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] [SPIRES].

    ADS  Google Scholar 

  69. 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] [SPIRES].

    Article  ADS  Google Scholar 

  70. A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover and G. Heinrich, Jet rates in electron-positron annihilation at O(α s 3) in QCD, Phys. Rev. Lett. 100 (2008) 172001 [arXiv:0802.0813] [SPIRES].

    Article  ADS  Google Scholar 

  71. S. Weinzierl, NNLO corrections to 3-jet observables in electron-positron annihilation, Phys. Rev. Lett. 101 (2008) 162001 [arXiv:0807.3241] [SPIRES].

    Article  ADS  Google Scholar 

  72. S. Weinzierl, The infrared structure of e + e − → 3 jets at NNLO reloaded, JHEP 07 (2009) 009 [arXiv:0904.1145] [SPIRES].

    Article  ADS  Google Scholar 

  73. 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] [SPIRES].

    Article  ADS  Google Scholar 

  74. 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] [SPIRES].

    Article  ADS  Google Scholar 

  75. 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] [SPIRES].

    Article  ADS  Google Scholar 

  76. S. Weinzierl, Event shapes and jet rates in electron-positron annihilation at NNLO, JHEP 06 (2009) 041 [arXiv:0904.1077] [SPIRES].

    Article  ADS  Google Scholar 

  77. S. Weinzierl, Moments of event shapes in electron-positron annihilation at NNLO, Phys. Rev. D 80 (2009) 094018 [arXiv:0909.5056] [SPIRES].

    Google Scholar 

  78. 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] [SPIRES].

    Article  ADS  Google Scholar 

  79. 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] [SPIRES].

    Article  ADS  Google Scholar 

  80. 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, arXiv:0910.4283 [SPIRES].

  81. T. Becher and M.D. Schwartz, A precise determination of α s from LEP thrust data using effective field theory, JHEP 07 (2008) 034 [arXiv:0803.0342] [SPIRES].

    Article  ADS  Google Scholar 

  82. R.A. Davison and B.R. Webber, Non-perturbative contribution to the thrust distribution in e + e − annihilation, Eur. Phys. J. C 59 (2009) 13 [arXiv:0809.3326] [SPIRES].

    Article  ADS  Google Scholar 

  83. JADE collaboration, S. Bethke, S. Kluth, C. Pahl and J. Schieck, Determination of the strong coupling α S from hadronic event shapes and NNLO QCD predictions using JADE data, Eur. Phys. J. C 64 (2009) 351 [arXiv:0810.1389] [SPIRES].

    Article  Google Scholar 

  84. T. Gehrmann, M. Jaquier and G. Luisoni, Hadronization effects in event shape moments, arXiv:0911.2422 [SPIRES].

  85. 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] [SPIRES].

    ADS  Google Scholar 

  86. S. Catani, L. Trentadue, G. Turnock and B.R. Webber, Resummation of large logarithms in e + e − event shape distributions, Nucl. Phys. B 407 (1993) 3 [SPIRES].

    Article  ADS  Google Scholar 

  87. T. Gehrmann, G. Luisoni and H. Stenzel, Matching NLLA+NNLO for event shape distributions, Phys. Lett. B 664 (2008) 265 [arXiv:0803.0695] [SPIRES].

    ADS  Google Scholar 

  88. A. Gehrmann-De Ridder and M. Ritzmann, NLO antenna subtraction with massive fermions, JHEP 07 (2009) 041 [arXiv:0904.3297] [SPIRES].

    Article  ADS  Google Scholar 

  89. A. Daleo, T. Gehrmann and D. Maître, Antenna subtraction with hadronic initial states, JHEP 04 (2007) 016 [hep-ph/0612257] [SPIRES].

    Article  ADS  Google Scholar 

  90. T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multi-loop integrals, Nucl. Phys. B 585 (2000) 741 [hep-ph/0004013] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  91. G. Heinrich, A numerical method for NNLO calculations, Nucl. Phys. (Proc. Suppl.) 116 (2003) 368 [hep-ph/0211144] [SPIRES].

    Article  MATH  ADS  Google Scholar 

  92. C. Anastasiou, K. Melnikov and F. Petriello, A new method for real radiation at NNLO, Phys. Rev. D 69 (2004) 076010 [hep-ph/0311311] [SPIRES].

    ADS  Google Scholar 

  93. T. Binoth and G. Heinrich, Numerical evaluation of phase space integrals by sector decomposition, Nucl. Phys. B 693 (2004) 134 [hep-ph/0402265] [SPIRES].

    Article  ADS  Google Scholar 

  94. 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] [SPIRES].

    Article  ADS  Google Scholar 

  95. 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] [SPIRES].

    Article  ADS  Google Scholar 

  96. C. Anastasiou, G. Dissertori and F. Stockli, NNLO QCD predictions for the H → WW → ℓℓνν signal at the LHC, JHEP 09 (2007) 018 [arXiv:0707.2373] [SPIRES].

    Article  ADS  Google Scholar 

  97. 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] [SPIRES].

    Article  ADS  Google Scholar 

  98. 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] [SPIRES].

    Article  ADS  Google Scholar 

  99. 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] [SPIRES].

    Article  ADS  Google Scholar 

  100. C. Anastasiou and K. Melnikov, Higgs boson production at hadron colliders in NNLO QCD, Nucl. Phys. B 646 (2002) 220 [hep-ph/0207004] [SPIRES].

    Article  ADS  Google Scholar 

  101. F.V. Tkachov, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett. B 100 (1981) 65 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  102. 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 [SPIRES].

    Article  ADS  Google Scholar 

  103. T. Gehrmann and E. Remiddi, Differential equations for two-loop four-point functions, Nucl. Phys. B 580 (2000) 485 [hep-ph/9912329] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  104. S. Laporta, High-precision calculation of multi-loop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  105. A.V. Kotikov, Differential equations method: new technique for massive Feynman diagrams calculation, Phys. Lett. B 254 (1991) 158 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  106. A.V. Kotikov, Differential equations method: the calculation of vertex type Feynman diagrams, Phys. Lett. B 259 (1991) 314 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  107. A.V. Kotikov, Differential equation method: the calculation of N point Feynman diagrams, Phys. Lett. B 267 (1991) 123 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  108. E. Remiddi, Differential equations for Feynman graph amplitudes, Nuovo Cim. A 110 (1997) 1435 [hep-th/9711188] [SPIRES].

    ADS  Google Scholar 

  109. M. Caffo, H. Czyz, S. Laporta and E. Remiddi, Master equations for master amplitudes, Acta Phys. Polon. B 29 (1998) 2627 [hep-th/9807119] [SPIRES].

    Google Scholar 

  110. M. Caffo, H. Czyz, S. Laporta and E. Remiddi, Master equations for master amplitudes, Acta Phys. Polon. B 29 (1998) 2627 [hep-th/9807119] [SPIRES].

    Google Scholar 

  111. M. Caffo, H. Czyz, S. Laporta and E. Remiddi, The master differential equations for the 2-loop sunrise selfmass amplitudes, Nuovo Cim. A 111 (1998) 365 [hep-th/9805118] [SPIRES].

    ADS  Google Scholar 

  112. 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] [SPIRES].

    Article  ADS  Google Scholar 

  113. E.B. Zijlstra and W.L. van Neerven, Order α s 2 QCD corrections to the deep inelastic proton structure functions F 2 and F L , Nucl. Phys. B 383 (1992) 525 [SPIRES].

    Article  ADS  Google Scholar 

  114. E.B. Zijlstra and W.L. van Neerven, Order α s 2 correction to the structure function F 3(x, Q 2) in deep inelastic neutrino-hadron scattering, Phys. Lett. B 297 (1992) 377 [SPIRES].

    ADS  Google Scholar 

  115. E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  116. T. Gehrmann and E. Remiddi, Numerical evaluation of harmonic polylogarithms, Comput. Phys. Commun. 141 (2001) 296 [hep-ph/0107173] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  117. D. Maître, HPL, a Mathematica implementation of the harmonic polylogarithms, Comput. Phys. Commun. 174 (2006) 222 [hep-ph/0507152] [SPIRES].

    Article  ADS  Google Scholar 

  118. D. Maître, Extension of HPL to complex arguments, hep-ph/0703052 [SPIRES].

  119. D. Graudenz, Three jet production in deep inelastic electron-proton scattering to order α s 2, Phys. Lett. B 256 (1991) 518 [SPIRES].

    ADS  Google Scholar 

  120. D. Graudenz, Next-to-leading order QCD corrections to jet cross-sections and jet rates in deeply inelastic electron proton scattering, Phys. Rev. D 49 (1994) 3291 [hep-ph/9307311] [SPIRES].

    ADS  Google Scholar 

  121. D. Graudenz, DISASTER++ version 1.0, hep-ph/9710244 [SPIRES].

  122. E. Mirkes and D. Zeppenfeld, Dijet production at HERA in next-to-leading order, Phys. Lett. B 380 (1996) 205 [hep-ph/9511448] [SPIRES].

    ADS  Google Scholar 

  123. S. Catani and M.H. Seymour, The dipole formalism for the calculation of QCD jet cross sections at next-to-leading order, Phys. Lett. B 378 (1996) 287 [hep-ph/9602277] [SPIRES].

    ADS  Google Scholar 

  124. B. Pötter, JetViP 1.1: calculating one jet and two jet cross-sections with virtual photons in NLO QCD, Comput. Phys. Commun. 119 (1999) 45 [hep-ph/9806437] [SPIRES].

    Article  ADS  Google Scholar 

  125. T. Gehrmann and E. Remiddi, Analytic continuation of massless two-loop four-point functions, Nucl. Phys. B 640 (2002) 379 [hep-ph/0207020] [SPIRES].

    Article  ADS  Google Scholar 

  126. T. Gehrmann and E.W.N. Glover, Two-loop QCD helicity amplitudes for (2 + 1)-jet production in deep inelastic scattering, Phys. Lett. B 676 (2009) 146 [arXiv:0904.2665] [SPIRES].

    ADS  Google Scholar 

  127. S. Moch and J.A.M. Vermaseren, Deep inelastic structure functions at two loops, Nucl. Phys. B 573 (2000) 853 [hep-ph/9912355] [SPIRES].

    Article  ADS  Google Scholar 

  128. G. Soar, A. Vogt, S. Moch and J. Vermaseren, On Higgs-exchange DIS, physical evolution kernels and fourth-order splitting functions at large x, arXiv:0912.0369 [SPIRES].

  129. T. Gehrmann, T. Huber and D. Maître, Two-loop quark and gluon form factors in dimensional regularisation, Phys. Lett. B 622 (2005) 295 [hep-ph/0507061] [SPIRES].

    ADS  Google Scholar 

  130. H1 collaboration, A. Aktas et al., Measurement of inclusive jet production in deep-inelastic scattering at high Q 2 and determination of the strong coupling, Phys. Lett. B 653 (2007) 134 [arXiv:0706.3722] [SPIRES].

    ADS  Google Scholar 

  131. H1 collaboration, C. Adloff et al., Measurement of inclusive jet cross-sections in deep-inelastic e p scattering at HERA, Phys. Lett. B 542 (2002) 193 [hep-ex/0206029] [SPIRES].

    ADS  Google Scholar 

  132. H1 collaboration, C. Adloff et al., Dijet production in charged and neutral current e + p interactions at high Q 2, Eur. Phys. J. C 19 (2001) 429 [hep-ex/0010016] [SPIRES].

    ADS  Google Scholar 

  133. ZEUS collaboration, S. Chekanov et al., Inclusive-jet and dijet cross sections in deep inelastic scattering at HERA, Nucl. Phys. B 765 (2007) 1 [hep-ex/0608048] [SPIRES].

    ADS  Google Scholar 

  134. ZEUS collaboration, S. Chekanov et al., Jet-radius dependence of inclusive-jet cross sections in deep inelastic scattering at HERA, Phys. Lett. B 649 (2007) 12 [hep-ex/0701039] [SPIRES].

    ADS  Google Scholar 

  135. ZEUS collaboration, S. Chekanov et al., Dijet production in neutral current deep inelastic scattering at HERA, Eur. Phys. J. C 23 (2002) 13 [hep-ex/0109029] [SPIRES].

    ADS  Google Scholar 

  136. H1 collaboration, M. Gouzevitch, Jet cross sections and α S in DIS, in Proceedings of the 16th International Workshop on “Deep Inelastic Scattering and QCD (DIS 08)”, London U.K. 2008, R. Devenish, M. Wing and R. Thorne eds., pg. 171 [SPIRES].

  137. H1 and ZEUS collaborations, T. Kluge, Combined H1-ZEUS α S fit to jets in DIS, in Proceedings of the 16th International Workshop on “Deep Inelastic Scattering and QCD (DIS 08)”, London U.K. 2008, R. Devenish, M. Wing and R. Thorne eds., pg. 172 [SPIRES].

  138. A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, Update of parton distributions at NNLO, Phys. Lett. B 652 (2007) 292 [arXiv:0706.0459] [SPIRES].

    ADS  Google Scholar 

  139. S. Alekhin, K. Melnikov and F. Petriello, Fixed target Drell-Yan data and NNLO QCD fits of parton distribution functions, Phys. Rev. D 74 (2006) 054033 [hep-ph/0606237] [SPIRES].

    ADS  Google Scholar 

  140. P. Jimenez-Delgado and E. Reya, Dynamical NNLO parton distributions, Phys. Rev. D 79 (2009) 074023 [arXiv:0810.4274] [SPIRES].

    ADS  Google Scholar 

  141. A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, Parton distributions for the LHC, Eur. Phys. J. C 63 (2009) 189 [arXiv:0901.0002] [SPIRES].

    Article  Google Scholar 

  142. S. Moch, J.A.M. Vermaseren and A. Vogt, The three-loop splitting functions in QCD: the non-singlet case, Nucl. Phys. B 688 (2004) 101 [hep-ph/0403192] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  143. A. Vogt, S. Moch and J.A.M. Vermaseren, The three-loop splitting functions in QCD: the singlet case, Nucl. Phys. B 691 (2004) 129 [hep-ph/0404111] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  144. R. Hamberg, W.L. van Neerven and T. Matsuura, A complete calculation of the order α s 2 correction to the Drell-Yan K factor, Nucl. Phys. B 359 (1991) 343 [Erratum ibid. B 644 (2002) 403] [SPIRES].

    Article  ADS  Google Scholar 

  145. 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] [SPIRES].

    ADS  Google Scholar 

  146. K. Melnikov and F. Petriello, Electroweak gauge boson production at hadron colliders through O(α s 2 ), Phys. Rev. D 74 (2006) 114017 [hep-ph/0609070] [SPIRES].

    ADS  Google Scholar 

  147. S. Alekhin and S. Moch, Higher order QCD corrections to charged-lepton deep-inelastic scattering and global fits of parton distributions, Phys. Lett. B 672 (2009) 166 [arXiv:0811.1412] [SPIRES].

    ADS  Google Scholar 

  148. K. Hagiwara and D. Zeppenfeld, Amplitudes for multiparton processes involving a current at e + e − , e ± p and hadron colliders, Nucl. Phys. B 313 (1989) 560 [SPIRES].

    Article  ADS  Google Scholar 

  149. F.A. Berends, W.T. Giele and H. Kuijf, Exact expressions for processes involving a vector boson and up to five partons, Nucl. Phys. B 321 (1989) 39 [SPIRES].

    Article  ADS  Google Scholar 

  150. N.K. Falck, D. Graudenz and G. Kramer, Cross-section for five jet production in e + e − annihilation, Nucl. Phys. B 328 (1989) 317 [SPIRES].

    Article  ADS  Google Scholar 

  151. Z. Bern, L.J. Dixon, D.A. Kosower and S. Weinzierl, One-loop amplitudes for \( {e^{+} }{e^{-} } \to \bar qq\bar QQ \), Nucl. Phys. B 489 (1997) 3 [hep-ph/9610370] [SPIRES].

    Article  ADS  Google Scholar 

  152. Z. Bern, L.J. Dixon and D.A. Kosower, One-loop amplitudes for e + e − to four partons, Nucl. Phys. B 513 (1998) 3 [hep-ph/9708239] [SPIRES].

    Article  ADS  Google Scholar 

  153. E.W.N. Glover and D.J. Miller, The one-loop QCD corrections for \( \gamma ^{*} \to Q\bar Qq\bar q \), Phys. Lett. B 396 (1997) 257 [hep-ph/9609474] [SPIRES].

    ADS  Google Scholar 

  154. J.M. Campbell, E.W.N. Glover and D.J. Miller, The one-loop QCD corrections for \( \gamma ^{*} \to q\bar qgg \), Phys. Lett. B 409 (1997) 503 [hep-ph/9706297] [SPIRES].

    ADS  Google Scholar 

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Authors and Affiliations

  1. Institute for Theoretical Physics, ETH, CH-8093, Zürich, Switzerland

    Alejandro Daleo & Aude Gehrmann-De Ridder

  2. Institut für Theoretische Physik, Universität Zürich, Winterthurerstrasse 190, CH-8057, Zürich, Switzerland

    Thomas Gehrmann & Gionata Luisoni

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Daleo, A., Gehrmann-De Ridder, A., Gehrmann, T. et al. Antenna subtraction at NNLO with hadronic initial states: initial-final configurations. J. High Energ. Phys. 2010, 118 (2010). https://doi.org/10.1007/JHEP01(2010)118

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