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Recursive generation of one-loop amplitudes in the Standard Model

  • S. Actis
  • A. Denner
  • L. Hofer
  • A. Scharf
  • S. Uccirati
Article

Abstract

We introduce the computer code Recola for the recursive generation of tree-level and one-loop amplitudes in the Standard Model. Tree-level amplitudes are constructed using off-shell currents instead of Feynman diagrams as basic building blocks. One-loop amplitudes are represented as linear combinations of tensor integrals whose coefficients are calculated similarly to the tree-level amplitudes by recursive construction of loop off-shell currents. We introduce a novel algorithm for the treatment of colour, assigning a colour structure to each off-shell current which enables us to recursively construct the colour structure of the amplitude efficiently. Recola is interfaced with a tensor-integral library and provides complete one-loop Standard Model amplitudes including rational terms and counterterms. As a first application we consider Z + 2 jets production at the LHC and calculate with Recola the next-to-leading-order electroweak corrections to the dominant partonic channels.

Keywords

NLO Computations Hadronic Colliders 

References

  1. [1]
    M. Ciccolini, A. Denner and S. Dittmaier, Electroweak and QCD corrections to Higgs production via vector-boson fusion at the LHC, Phys. Rev. D 77 (2008) 013002 [arXiv:0710.4749] [INSPIRE].ADSGoogle Scholar
  2. [2]
    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].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    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] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    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] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    G. Ossola, C.G. Papadopoulos and R. Pittau, Numerical evaluation of six-photon amplitudes, JHEP 07 (2007) 085 [arXiv:0704.1271] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    R.K. Ellis, W. Giele and Z. Kunszt, A numerical unitarity formalism for evaluating one-loop amplitudes, JHEP 03 (2008) 003 [arXiv:0708.2398] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    W.T. Giele, Z. Kunszt and K. Melnikov, Full one-loop amplitudes from tree amplitudes, JHEP 04 (2008) 049 [arXiv:0801.2237] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    G. Passarino and M. Veltman, One loop corrections for e + e annihilation into μ + μ in the Weinberg model, Nucl. Phys. B 160 (1979) 151 [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    C. Berger, Z. Bern, L. Dixon, F. Febres Cordero, D. Forde et al., An automated implementation of on-shell methods for one-loop amplitudes, Phys. Rev. D 78 (2008) 036003 [arXiv:0803.4180] [INSPIRE].ADSGoogle Scholar
  12. [12]
    W. Giele and G. Zanderighi, On the numerical evaluation of one-loop amplitudes: the gluonic case, JHEP 06 (2008) 038 [arXiv:0805.2152] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    A. Lazopoulos, Multi-gluon one-loop amplitudes numerically, arXiv:0812.2998 [INSPIRE].
  14. [14]
    W. Giele, Z. Kunszt and J. Winter, Efficient color-dressed calculation of virtual corrections, Nucl. Phys. B 840 (2010) 214 [arXiv:0911.1962] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    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].ADSCrossRefzbMATHGoogle Scholar
  16. [16]
    V. Hirschi, R. Frederix, S. Frixione, M.V. Garzelli, F. Maltoni et al., Automation of one-loop QCD corrections, JHEP 05 (2011) 044 [arXiv:1103.0621] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    G. Bevilacqua, M. Czakon, M. Garzelli, A. van Hameren, A. Kardos et al., HELAC-NLO, Comput. Phys. Commun. 184 (2013) 986 [arXiv:1110.1499] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    G. Cullen, N. Greiner, G. Heinrich, G. Luisoni, P. Mastrolia et al., Automated one-loop calculations with GoSam, Eur. Phys. J. C 72 (2012) 1889 [arXiv:1111.2034] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    C. Berger, Z. Bern, L.J. Dixon, F. Febres Cordero, D. Forde et al., Next-to-leading order QCD predictions for W + 3-jet distributions at hadron colliders, Phys. Rev. D 80 (2009) 074036 [arXiv:0907.1984] [INSPIRE].ADSGoogle Scholar
  20. [20]
    R.K. Ellis, K. Melnikov and G. Zanderighi, W + 3 jet production at the Tevatron, Phys. Rev. D 80 (2009) 094002 [arXiv:0906.1445] [INSPIRE].ADSGoogle Scholar
  21. [21]
    C. Berger, Z. Bern, L.J. Dixon, F. Febres Cordero, D. Forde et al., Precise predictions for W +3 jet production at hadron colliders, Phys. Rev. Lett. 102 (2009) 222001 [arXiv:0902.2760] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    G. Bevilacqua, M. Czakon, C. Papadopoulos, R. Pittau and M. Worek, Assault on the NLO wishlist: pp\( t\overline{t}b\overline{b} \), JHEP 09 (2009) 109 [arXiv:0907.4723] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    K. Melnikov and G. Zanderighi, W + 3 jet production at the LHC as a signal or background, Phys. Rev. D 81 (2010) 074025 [arXiv:0910.3671] [INSPIRE].ADSGoogle Scholar
  24. [24]
    G. Bevilacqua, M. Czakon, C. Papadopoulos and M. Worek, Dominant QCD backgrounds in Higgs boson analyses at the LHC: a study of pp\( t\overline{t} \) + 2 jets at next-to-leading order, Phys. Rev. Lett. 104 (2010) 162002 [arXiv:1002.4009] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    C. Berger, Z. Bern, L.J. Dixon, F. Febres Cordero, D. Forde et al., Next-to-leading order QCD predictions for Z, γ + 3-jet distributions at the Tevatron, Phys. Rev. D 82 (2010) 074002 [arXiv:1004.1659] [INSPIRE].ADSGoogle Scholar
  26. [26]
    T. Melia, K. Melnikov, R. Rontsch and G. Zanderighi, Next-to-leading order QCD predictions for W + W + jj production at the LHC, JHEP 12 (2010) 053 [arXiv:1007.5313] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    C. Berger, Z. Bern, L.J. Dixon, F. Febres Cordero, D. Forde et al., Precise predictions for W +4 jet production at the large hadron collider, Phys. Rev. Lett. 106(2011) 092001 [arXiv:1009.2338] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    G. Bevilacqua, M. Czakon, A. van Hameren, C.G. Papadopoulos and M. Worek, Complete off-shell effects in top quark pair hadroproduction with leptonic decay at next-to-leading order, JHEP 02 (2011) 083 [arXiv:1012.4230] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    T. Melia, K. Melnikov, R. Rontsch and G. Zanderighi, NLO QCD corrections for W + W pair production in association with two jets at hadron colliders, Phys. Rev. D 83 (2011) 114043 [arXiv:1104.2327] [INSPIRE].ADSGoogle Scholar
  30. [30]
    R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, R. Pittau et al., W and Z/γ∗ boson production in association with a bottom-antibottom pair, JHEP 09 (2011) 061 [arXiv:1106.6019] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    H. Ita, Z. Bern, L. Dixon, F. Febres Cordero, D. Kosower et al., Precise predictions for Z + 4 jets at hadron colliders, Phys. Rev. D 85 (2012) 031501 [arXiv:1108.2229] [INSPIRE].ADSGoogle Scholar
  32. [32]
    G. Bevilacqua, M. Czakon, C. Papadopoulos and M. Worek, Hadronic top-quark pair production in association with two jets at next-to-leading order QCD, Phys. Rev. D 84 (2011) 114017 [arXiv:1108.2851] [INSPIRE].ADSGoogle Scholar
  33. [33]
    Z. Bern, G. Diana, L. Dixon, F. Febres Cordero, S. Höche et al., Four-jet production at the large hadron collider at next-to-leading order in QCD, Phys. Rev. Lett. 109 (2012) 042001 [arXiv:1112.3940] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    N. Greiner, G. Heinrich, P. Mastrolia, G. Ossola, T. Reiter et al., NLO QCD corrections to the production of W + W plus two jets at the LHC, Phys. Lett. B 713 (2012) 277 [arXiv:1202.6004] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    G. Bevilacqua and M. Worek, Constraining BSM physics at the LHC: four top final states with NLO accuracy in perturbative QCD, JHEP 07 (2012) 111 [arXiv:1206.3064] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    S. Badger, B. Biedermann, P. Uwer and V. Yundin, NLO QCD corrections to multi-jet production at the LHC with a centre-of-mass energy of \( \sqrt{s}=8 \) TeV, Phys. Lett. B 718 (2013) 965 [arXiv:1209.0098] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    SM AND NLO MULTILEG and SM MC Working Groups collaboration, J. Alcaraz Maestre et al., The SM and NLO multileg and SM MC working groups: summary report, arXiv:1203.6803 [INSPIRE].
  38. [38]
    D.E. Soper, Techniques for QCD calculations by numerical integration, Phys. Rev. D 62 (2000) 014009 [hep-ph/9910292] [INSPIRE].ADSGoogle Scholar
  39. [39]
    S. Becker, C. Reuschle and S. Weinzierl, Numerical NLO QCD calculations, JHEP 12 (2010) 013 [arXiv:1010.4187] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    S. Becker, D. Goetz, C. Reuschle, C. Schwan and S. Weinzierl, NLO results for five, six and seven jets in electron-positron annihilation, Phys. Rev. Lett. 108 (2012) 032005 [arXiv:1111.1733] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    G. Heinrich, G. Ossola, T. Reiter and F. Tramontano, Tensorial reconstruction at the integrand level, JHEP 10 (2010) 105 [arXiv:1008.2441] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    R. Pittau, Testing and improving the numerical accuracy of the NLO predictions, Comput. Phys. Commun. 181 (2010) 1941 [arXiv:1006.3773] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  45. [45]
    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] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  46. [46]
    A. Denner and S. Dittmaier, Reduction of one loop tensor five point integrals, Nucl. Phys. B 658 (2003) 175 [hep-ph/0212259] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  47. [47]
    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] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  48. [48]
    A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys. B 734 (2006) 62 [hep-ph/0509141] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    A. Bredenstein, A. Denner, S. Dittmaier and M. Weber, Radiative corrections to the semileptonic and hadronic Higgs-boson decays HW W/ZZ → 4 fermions, JHEP 02 (2007) 080 [hep-ph/0611234] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    A. Denner, S. Dittmaier, T. Kasprzik and A. Mück, Electroweak corrections to W + jet hadroproduction including leptonic W-boson decays, JHEP 08 (2009) 075 [arXiv:0906.1656] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    A. Denner, S. Dittmaier, T. Kasprzik and A. Mück, Electroweak corrections to dilepton + jet production at hadron colliders, JHEP 06 (2011) 069 [arXiv:1103.0914] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    A. Denner, S. Dittmaier, S. Kallweit and A. Mück, Electroweak corrections to Higgs-strahlung off W/Z bosons at the Tevatron and the LHC with HAWK, JHEP 03 (2012) 075 [arXiv:1112.5142] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD corrections to pp\( t\overline{t}b\overline{b} \) + × at the LHC, Phys. Rev. Lett. 103 (2009) 012002 [arXiv:0905.0110] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    A. Denner, S. Dittmaier, S. Kallweit and S. Pozzorini, NLO QCD corrections to WWbb production at hadron colliders, Phys. Rev. Lett. 106 (2011) 052001 [arXiv:1012.3975] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    F. Campanario, C. Englert, M. Rauch and D. Zeppenfeld, Precise predictions for Wγγ +jet production at hadron colliders, Phys. Lett. B 704 (2011) 515 [arXiv:1106.4009] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    L. Reina and T. Schutzmeier, Towards \( Wb\overline{b} \) + j at NLO with an automatized approach to one-loop computations, JHEP 09 (2012) 119 [arXiv:1110.4438] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  57. [57]
    F. Cascioli, P. Maierhofer and S. Pozzorini, Scattering amplitudes with open loops, Phys. Rev. Lett. 108 (2012) 111601 [arXiv:1111.5206] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    A. van Hameren, Multi-gluon one-loop amplitudes using tensor integrals, JHEP 07 (2009) 088 [arXiv:0905.1005] [INSPIRE].CrossRefGoogle Scholar
  59. [59]
    F.A. Berends and W. Giele, Recursive calculations for processes with N gluons, Nucl. Phys. B 306 (1988) 759 [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    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] [INSPIRE].ADSGoogle Scholar
  61. [61]
    J.M. Campbell, R.K. Ellis and D.L. Rainwater, Next-to-leading order QCD predictions for W +2 jet and Z+2 jet production at the CERN LHC, Phys. Rev. D 68(2003) 094021 [hep-ph/0308195] [INSPIRE].ADSGoogle Scholar
  62. [62]
    C. Oleari and D. Zeppenfeld, QCD corrections to electroweak ν l jj and+ jj production, Phys. Rev. D 69 (2004) 093004 [hep-ph/0310156] [INSPIRE].ADSGoogle Scholar
  63. [63]
    F. Dyson, The S matrix in quantum electrodynamics, Phys. Rev. 75 (1949) 1736 [INSPIRE].MathSciNetADSCrossRefzbMATHGoogle Scholar
  64. [64]
    J.S. Schwinger, On the Greens functions of quantized fields. 1., Proc. Nat. Acad. Sci. 37 (1951)452 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  65. [65]
    J.S. Schwinger, On the Greens functions of quantized fields. 2., Proc. Nat. Acad. Sci. 37 (1951)455 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  66. [66]
    A. Kanaki and C.G. Papadopoulos, HELAC: a package to compute electroweak helicity amplitudes, Comput. Phys. Commun. 132 (2000) 306 [hep-ph/0002082] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  67. [67]
    C.G. Papadopoulos and M. Worek, Multi-parton cross sections at hadron colliders, Eur. Phys. J. C 50 (2007) 843 [hep-ph/0512150] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    A. Cafarella, C.G. Papadopoulos and M. Worek, Helac-Phegas: a generator for all parton level processes, Comput. Phys. Commun. 180 (2009) 1941 [arXiv:0710.2427] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    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 [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    F. Caravaglios and M. Moretti, An algorithm to compute Born scattering amplitudes without Feynman graphs, Phys. Lett. B 358 (1995) 332 [hep-ph/9507237] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    G. Ossola, C.G. Papadopoulos and R. Pittau, On the rational terms of the one-loop amplitudes, JHEP 05 (2008) 004 [arXiv:0802.1876] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  72. [72]
    P. Draggiotis, M. Garzelli, C. Papadopoulos and R. Pittau, Feynman rules for the rational part of the QCD 1-loop amplitudes, JHEP 04 (2009) 072 [arXiv:0903.0356] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  73. [73]
    M. Garzelli, I. Malamos and R. Pittau, Feynman rules for the rational part of the electroweak 1-loop amplitudes, JHEP 01 (2010) 040 [Erratum ibid. 1010 (2010) 097] [arXiv:0910.3130] [INSPIRE].ADSCrossRefGoogle Scholar
  74. [74]
    H.-S. Shao, Y.-J. Zhang and K.-T. Chao, Feynman rules for the rational part of the standard model one-loop amplitudes in thet Hooft-Veltman γ5 scheme, JHEP 09 (2011) 048 [arXiv:1106.5030] [INSPIRE].ADSCrossRefGoogle Scholar
  75. [75]
    A. Denner, Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200, Fortsch. Phys. 41 (1993) 307 [arXiv:0709.1075] [INSPIRE].ADSGoogle Scholar
  76. [76]
    A. Denner, S. Dittmaier, M. Roth and D. Wackeroth, Predictions for all processes e + e → 4 fermions +γ, Nucl. Phys. B 560 (1999) 33 [hep-ph/9904472] [INSPIRE].ADSCrossRefGoogle Scholar
  77. [77]
    A. Denner, S. Dittmaier, M. Roth and L. Wieders, Electroweak corrections to charged-current e + e → 4 fermion processes: technical details and further results, Nucl. Phys. B 724 (2005) 247 [Erratum ibid. B 854 (2012) 504–507] [hep-ph/0505042] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    Z. Bern and D.A. Kosower, Color decomposition of one loop amplitudes in gauge theories, Nucl. Phys. B 362 (1991) 389 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  79. [79]
    G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].MathSciNetADSGoogle Scholar
  80. [80]
    A. Kanaki and C.G. Papadopoulos, HELAC-PHEGAS: automatic computation of helicity amplitudes and cross-sections, hep-ph/0012004 [INSPIRE].
  81. [81]
    F. Maltoni, K. Paul, T. Stelzer and S. Willenbrock, Color flow decomposition of QCD amplitudes, Phys. Rev. D 67 (2003) 014026 [hep-ph/0209271] [INSPIRE].ADSGoogle Scholar
  82. [82]
    A. Denner and S. Dittmaier, The complex-mass scheme for perturbative calculations with unstable particles, Nucl. Phys. Proc. Suppl. 160 (2006) 22 [hep-ph/0605312] [INSPIRE].ADSCrossRefGoogle Scholar
  83. [83]
    D.Y. Bardin, A. Leike, T. Riemann and M. Sachwitz, Energy dependent width effects in e + e annihilation near the Z boson pole, Phys. Lett. B 206 (1988) 539 [INSPIRE].ADSGoogle Scholar
  84. [84]
    W. Beenakker and A. Denner, Infrared divergent scalar box integrals with applications in the electroweak standard model, Nucl. Phys. B 338 (1990) 349 [INSPIRE].ADSCrossRefGoogle Scholar
  85. [85]
    A. Denner, U. Nierste and R. Scharf, A compact expression for the scalar one loop four point function, Nucl. Phys. B 367 (1991) 637 [INSPIRE].ADSCrossRefGoogle Scholar
  86. [86]
    A. Denner and S. Dittmaier, Scalar one-loop 4-point integrals, Nucl. Phys. B 844 (2011) 199 [arXiv:1005.2076] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  87. [87]
    S. Dittmaier and M. Krämer, Electroweak radiative corrections to W boson production at hadron colliders, Phys. Rev. D 65 (2002) 073007 [hep-ph/0109062] [INSPIRE].ADSGoogle Scholar
  88. [88]
    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].ADSCrossRefGoogle Scholar
  89. [89]
    A. Denner, S. Dittmaier, T. Gehrmann and C. Kurz, Electroweak corrections to hadronic event shapes and jet production in e + e annihilation, Nucl. Phys. B 836 (2010) 37 [arXiv:1003.0986] [INSPIRE].ADSCrossRefGoogle Scholar
  90. [90]
    E.N. Glover and A. Morgan, Measuring the photon fragmentation function at LEP, Z. Phys. C 62 (1994) 311 [INSPIRE].ADSGoogle Scholar
  91. [91]
    ALEPH collaboration, D. Buskulic et al., First measurement of the quark to photon fragmentation function, Z. Phys. C 69 (1996) 365 [INSPIRE].Google Scholar
  92. [92]
    A. Denner, S. Dittmaier and L. Hofer, COLLIER, a Complex One-Loop Library In Extended Regularizations, in preparation.Google Scholar
  93. [93]
    T. Motz, Generic Monte Carlo event generator for LHC processes, PhD Thesis, ETH, Zürich (2011).Google Scholar
  94. [94]
    T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  95. [95]
    T. Hahn and C. Schappacher, The implementation of the minimal supersymmetric standard model in FeynArts and FormCalc, Comput. Phys. Commun. 143 (2002) 54 [hep-ph/0105349] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  96. [96]
    T. Hahn and M. Pérez-Victoria, Automatized one loop calculations in four-dimensions and d-dimensions, Comput. Phys. Commun. 118 (1999) 153 [hep-ph/9807565] [INSPIRE].ADSCrossRefGoogle Scholar
  97. [97]
    S. Dittmaier, Weyl-van der Waerden formalism for helicity amplitudes of massive particles, Phys. Rev. D 59 (1998) 016007 [hep-ph/9805445] [INSPIRE].ADSGoogle Scholar
  98. [98]
    E. Accomando, A. Denner and C. Meier, Electroweak corrections to W γ and Zγ production at the LHC, Eur. Phys. J. C 47 (2006) 125 [hep-ph/0509234] [INSPIRE].ADSCrossRefGoogle Scholar
  99. [99]
    S. Dittmaier and M. Roth, LUSIFER: a LUcid approach to SIx FERmion production, Nucl. Phys. B 642 (2002) 307 [hep-ph/0206070] [INSPIRE].ADSCrossRefGoogle Scholar
  100. [100]
    Particle Data Group collaboration, J. Beringer et al., Review of particle physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].ADSGoogle Scholar
  101. [101]
    Tevatron Electroweak Working Group, CDF Collaboration, D0 collaboration, Combination of CDF and D0 results on the mass of the top quark using up to 5.8 fb −1 of data, arXiv:1107.5255 [INSPIRE].
  102. [102]
    A. Martin, W. Stirling, R. Thorne and G. Watt, Parton distributions for the LHC, Eur. Phys. J. C 63 (2009) 189 [arXiv:0901.0002] [INSPIRE].ADSCrossRefGoogle Scholar
  103. [103]
    M. Cacciari, G.P. Salam and G. Soyez, The k t jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].ADSCrossRefGoogle Scholar
  104. [104]
    P. Ciafaloni and D. Comelli, Sudakov enhancement of electroweak corrections, Phys. Lett. B 446 (1999) 278 [hep-ph/9809321] [INSPIRE].ADSCrossRefGoogle Scholar
  105. [105]
    J.H. Kühn and A. Penin, Sudakov logarithms in electroweak processes, hep-ph/9906545 [INSPIRE].
  106. [106]
    V.S. Fadin, L. Lipatov, A.D. Martin and M. Melles, Resummation of double logarithms in electroweak high-energy processes, Phys. Rev. D 61 (2000) 094002 [hep-ph/9910338] [INSPIRE].ADSGoogle Scholar
  107. [107]
    A. Denner and S. Pozzorini, One loop leading logarithms in electroweak radiative corrections. 1. Results, Eur. Phys. J. C 18 (2001) 461 [hep-ph/0010201] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • S. Actis
    • 1
  • A. Denner
    • 2
  • L. Hofer
    • 2
  • A. Scharf
    • 2
  • S. Uccirati
    • 3
  1. 1.Paul Scherrer Institut, Würenlingen und VilligenVilligen PSISwitzerland
  2. 2.Universität Würzburg, Institut für Theoretische Physik und AstrophysikWürzburgGermany
  3. 3.Università di Torino, Dipartimento di Fisica, and INFN, Sezione di TorinoTorinoItaly

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