Advertisement

NLO electroweak automation and precise predictions for W + multijet production at the LHC

  • S. Kallweit
  • J. M. Lindert
  • P. Maierhöfer
  • S. Pozzorini
  • M. Schönherr
Open Access
Regular Article - Theoretical Physics

Abstract

We present a fully automated implementation of next-to-leading order electroweak (NLO EW) corrections in the OpenLoops matrix-element generator combined with the Sherpa and Munich Monte Carlo frameworks. The process-independent character of the implemented algorithms opens the door to NLO QCD + EW simulations for a vast range of Standard Model processes, up to high particle multiplicity, at current and future colliders. As a first application, we present NLO QCD + EW predictions for the production of positively charged on-shell W bosons in association with up to three jets at the Large Hadron Collider. At the TeV energy scale, due to the presence of large Sudakov logarithms, EW corrections reach the 20-40% level and play an important role for searches of physics beyond the Standard Model. The dependence of NLO EW effects on the jet multiplicity is investigated in detail, and we find that W + multijet final states feature genuinely different EW effects as compared to the case of W + 1 jet.

Keywords

NLO Computations Hadronic Colliders 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    ATLAS collaboration, Measurement of the production cross section for W bosons in association with jets in pp collisions at \( \sqrt{s} \) = 7 TeV with the ATLAS detector, Phys. Lett. B 698 (2011) 325 [arXiv:1012.5382] [INSPIRE].ADSGoogle Scholar
  2. [2]
    ATLAS collaboration, Study of jets produced in association with a W boson in pp collisions at \( \sqrt{s} \) = 7 TeV with the ATLAS detector, Phys. Rev. D 85 (2012) 092002 [arXiv:1201.1276] [INSPIRE].ADSGoogle Scholar
  3. [3]
    ATLAS collaboration, Measurements of the W production cross sections in association with jets with the ATLAS detector, Eur. Phys. J. C 75 (2015) 82 [arXiv:1409.8639] [INSPIRE].ADSGoogle Scholar
  4. [4]
    CMS collaboration, Jet production rates in association with W and Z bosons in pp collisions at \( \sqrt{s} \) = 7 TeV, JHEP 01 (2012) 010 [arXiv:1110.3226] [INSPIRE].ADSGoogle Scholar
  5. [5]
    CMS collaboration, Study of the dijet mass spectrum in ppW + jets events at \( \sqrt{s} \) = 7 TeV, Phys. Rev. Lett. 109 (2012) 251801 [arXiv:1208.3477] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    CMS collaboration, Differential cross section measurements for the production of a W boson in association with jets in proton-proton collisions at \( \sqrt{s} \) = 7 TeV, Phys. Lett. B 741 (2015) 12 [arXiv:1406.7533] [INSPIRE].Google Scholar
  7. [7]
    P.B. Arnold and M.H. Reno, The complete computation of high p T W and Z production in 2nd order QCD, Nucl. Phys. B 319 (1989) 37 [Erratum ibid. B 330 (1990) 284] [INSPIRE].
  8. [8]
    P.B. Arnold, R.K. Ellis and M.H. Reno, High p T W and Z production at the Tevatron, Phys. Rev. D 40 (1989) 912 [INSPIRE].ADSGoogle Scholar
  9. [9]
    R.K. Ellis and S. Veseli, Strong radiative corrections to \( Wb\overline{b} \) production in \( p\overline{p} \) collisions, Phys. Rev. D 60 (1999) 011501 [hep-ph/9810489] [INSPIRE].ADSGoogle Scholar
  10. [10]
    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
  11. [11]
    F. Febres Cordero, L. Reina and D. Wackeroth, NLO QCD corrections to W boson production with a massive b-quark jet pair at the Tevatron \( p\overline{p} \) collider, Phys. Rev. D 74 (2006) 034007 [hep-ph/0606102] [INSPIRE].ADSGoogle Scholar
  12. [12]
    J.M. Campbell, R.K. Ellis, F. Maltoni and S. Willenbrock, Production of a W boson and two jets with one b quark tag, Phys. Rev. D 75 (2007) 054015 [hep-ph/0611348] [INSPIRE].ADSGoogle Scholar
  13. [13]
    J.M. Campbell et al., Associated production of a W boson and one b jet, Phys. Rev. D 79 (2009) 034023 [arXiv:0809.3003] [INSPIRE].ADSGoogle Scholar
  14. [14]
    F. Febres Cordero, L. Reina and D. Wackeroth, W - and Z-boson production with a massive bottom-quark pair at the Large Hadron Collider, Phys. Rev. D 80 (2009) 034015 [arXiv:0906.1923] [INSPIRE].ADSGoogle Scholar
  15. [15]
    S. Badger, J.M. Campbell and R.K. Ellis, QCD corrections to the hadronic production of a heavy quark pair and a W -boson including decay correlations, JHEP 03 (2011) 027 [arXiv:1011.6647] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  16. [16]
    R. Frederix 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
  17. [17]
    J.M. Campbell, F. Caola, F. Febres Cordero, L. Reina and D. Wackeroth, NLO QCD predictions for W + 1 jet and W + 2 jet production with at least one b jet at the 7 TeV LHC, Phys. Rev. D 86 (2012) 034021 [arXiv:1107.3714] [INSPIRE].ADSGoogle Scholar
  18. [18]
    R.K. Ellis, Z. Kunszt, K. Melnikov and G. Zanderighi, One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts, Phys. Rept. 518 (2012) 141 [arXiv:1105.4319] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    H. Ita, SUSY theories and QCD: numerical approaches, J. Phys. A 44 (2011) 454005 [arXiv:1109.6527] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  20. [20]
    C.F. Berger et al., Precise predictions for W + 3 jet production at hadron colliders, Phys. Rev. Lett. 102 (2009) 222001 [arXiv:0902.2760] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    R.K. Ellis, K. Melnikov and G. Zanderighi, Generalized unitarity at work: first NLO QCD results for hadronic W + 3 jet production, JHEP 04 (2009) 077 [arXiv:0901.4101] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    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
  23. [23]
    C.F. Berger 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
  24. [24]
    C.F. Berger 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
  25. [25]
    Z. Bern et al., Next-to-leading order W + 5-jet production at the LHC, Phys. Rev. D 88 (2013) 014025 [arXiv:1304.1253] [INSPIRE].ADSGoogle Scholar
  26. [26]
    V.S. Fadin, L.N. 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
  27. [27]
    J.H. Kühn, A.A. Penin and V.A. Smirnov, Summing up subleading Sudakov logarithms, Eur. Phys. J. C 17 (2000) 97 [hep-ph/9912503] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    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
  29. [29]
    A. Denner and S. Pozzorini, One loop leading logarithms in electroweak radiative corrections. 2. Factorization of collinear singularities, Eur. Phys. J. C 21 (2001) 63 [hep-ph/0104127] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    M. Ciafaloni, P. Ciafaloni and D. Comelli, Bloch-Nordsieck violating electroweak corrections to inclusive TeV scale hard processes, Phys. Rev. Lett. 84 (2000) 4810 [hep-ph/0001142] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    U. Baur, Weak boson emission in hadron collider processes, Phys. Rev. D 75 (2007) 013005 [hep-ph/0611241] [INSPIRE].ADSGoogle Scholar
  32. [32]
    K. Mishra et al., Electroweak corrections at high energies, arXiv:1308.1430 [INSPIRE].
  33. [33]
    J.H. Kühn, A. Kulesza, S. Pozzorini and M. Schulze, Electroweak corrections to large transverse momentum production of W bosons at the LHC, Phys. Lett. B 651 (2007) 160 [hep-ph/0703283] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    J.H. Kühn, A. Kulesza, S. Pozzorini and M. Schulze, Electroweak corrections to hadronic production of W bosons at large transverse momenta, Nucl. Phys. B 797 (2008) 27 [arXiv:0708.0476] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    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
  36. [36]
    M. Chiesa et al., Electroweak Sudakov corrections to new physics searches at the LHC, Phys. Rev. Lett. 111 (2013) 121801 [arXiv:1305.6837] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    S. Actis, A. Denner, L. Hofer, A. Scharf and S. Uccirati, Recursive generation of one-loop amplitudes in the standard model, JHEP 04 (2013) 037 [arXiv:1211.6316] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    S. Actis, A. Denner, L. Hofer, A. Scharf and S. Uccirati, EW and QCD one-loop amplitudes with RECOLA, PoS(RADCOR 2013)034 [arXiv:1311.6662] [INSPIRE].
  39. [39]
    A. Denner, L. Hofer, A. Scharf and S. Uccirati, Electroweak corrections to Z + 2 jets production at the LHC, PoS(RADCOR 2013)019 [arXiv:1311.5336] [INSPIRE].
  40. [40]
    A. Denner, L. Hofer, A. Scharf and S. Uccirati, Electroweak corrections to lepton pair production in association with two hard jets at the LHC, JHEP 01 (2015) 094 [arXiv:1411.0916] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    S. Frixione, V. Hirschi, D. Pagani, H.S. Shao and M. Zaro, Weak corrections to Higgs hadroproduction in association with a top-quark pair, JHEP 09 (2014) 065 [arXiv:1407.0823] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    J. Alwall et al., The automated computation of tree-level and next-to-leading order differential cross sections and their matching to parton shower simulations, JHEP 07 (2014) 079 [arXiv:1405.0301] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    G. Cullen et al., GoSam-2.0: a tool for automated one-loop calculations within the standard model and beyond, Eur. Phys. J. C 74 (2014) 3001 [arXiv:1404.7096] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    F. Cascioli, P. Maierhöfer and S. Pozzorini, Scattering amplitudes with open loops, Phys. Rev. Lett. 108 (2012) 111601 [arXiv:1111.5206] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    S. Höche and M. Schönherr, in preparation.Google Scholar
  46. [46]
    T. Gleisberg and F. Krauss, Automating dipole subtraction for QCD NLO calculations, Eur. Phys. J. C 53 (2008) 501 [arXiv:0709.2881] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    T. Gleisberg et al., Event generation with SHERPA 1.1, JHEP 02 (2009) 007 [arXiv:0811.4622] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    F. Cascioli et al., Precise Higgs-background predictions: merging NLO QCD and squared quark-loop corrections to four-lepton +0, 1 jet production, JHEP 01 (2014) 046 [arXiv:1309.0500] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    F. Cascioli, P. Maierhöfer, N. Moretti, S. Pozzorini and F. Siegert, NLO matching for \( t\overline{t}b\overline{b} \) production with massive b-quarks, Phys. Lett. B 734 (2014) 210 [arXiv:1309.5912] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    F. Cascioli, S. Kallweit, P. Maierhöfer and S. Pozzorini, A unified NLO description of top-pair and associated Wt production, Eur. Phys. J. C 74 (2014) 2783 [arXiv:1312.0546] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    P. Maierhöfer and A. Papaefstathiou, Higgs boson pair production merged to one jet, JHEP 03 (2014) 126 [arXiv:1401.0007] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    S. Höche et al., Next-to-leading order QCD predictions for top-quark pair production with up to two jets merged with a parton shower, arXiv:1402.6293 [INSPIRE].
  53. [53]
    S. Höche et al., Triple vector boson production through Higgs-Strahlung with NLO multijet merging, Phys. Rev. D 89 (2014) 093015 [arXiv:1403.7516] [INSPIRE].ADSGoogle Scholar
  54. [54]
    G. Abelof, A. Gehrmann-De Ridder, P. Maierhöfer and S. Pozzorini, NNLO QCD subtraction for top-antitop production in the \( q\overline{q} \) channel, JHEP 08 (2014) 035 [arXiv:1404.6493] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    M. Grazzini, S. Kallweit, D. Rathlev and A. Torre, Zγ production at hadron colliders in NNLO QCD, Phys. Lett. B 731 (2014) 204 [arXiv:1309.7000] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    F. Cascioli et al., ZZ production at hadron colliders in NNLO QCD, Phys. Lett. B 735 (2014) 311 [arXiv:1405.2219] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    T. Gehrmann et al., W + W production at hadron colliders in next to next to leading order QCD, Phys. Rev. Lett. 113 (2014) 212001 [arXiv:1408.5243] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    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
  59. [59]
    A. Denner, S. Dittmaier, S. Kallweit and S. Pozzorini, NLO QCD corrections to off-shell top-antitop production with leptonic decays at hadron colliders, JHEP 10 (2012) 110 [arXiv:1207.5018] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    A. Denner, L. Hosekova and S. Kallweit, NLO QCD corrections to W + W + jj production in vector-boson fusion at the LHC, Phys. Rev. D 86 (2012) 114014 [arXiv:1209.2389] [INSPIRE].ADSGoogle Scholar
  61. [61]
    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].ADSCrossRefGoogle Scholar
  62. [62]
    S. Höche, F. Krauss, M. Schönherr and F. Siegert, W + n-jet predictions at the Large Hadron Collider at next-to-leading order matched with a parton shower, Phys. Rev. Lett. 110 (2013) 052001 [arXiv:1201.5882] [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    S. Höche, F. Krauss, M. Schönherr and F. Siegert, QCD matrix elements + parton showers: the NLO case, JHEP 04 (2013) 027 [arXiv:1207.5030] [INSPIRE].CrossRefGoogle Scholar
  64. [64]
    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] [INSPIRE].
  65. [65]
    S. Catani, S. Dittmaier, M.H. Seymour and Z. Trócsányi, The dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys. B 627 (2002) 189 [hep-ph/0201036] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  66. [66]
    J. Butterworth et al., Les Houches 2013: physics at TeV colliders: standard model working group report, arXiv:1405.1067 [INSPIRE].
  67. [67]
    A.D. Martin, R.G. Roberts, W.J. Stirling and R.S. Thorne, Parton distributions incorporating QED contributions, Eur. Phys. J. C 39 (2005) 155 [hep-ph/0411040] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    NNPDF collaboration, R.D. Ball et al., Parton distributions with QED corrections, Nucl. Phys. B 877 (2013) 290 [arXiv:1308.0598] [INSPIRE].zbMATHGoogle Scholar
  69. [69]
    E.W.N. Glover and A.G. Morgan, Measuring the photon fragmentation function at LEP, Z. Phys. C 62 (1994) 311 [INSPIRE].ADSGoogle Scholar
  70. [70]
    A. Gehrmann-De Ridder, T. Gehrmann and E.W.N. Glover, Radiative corrections to the photon +1 jet rate at LEP, Phys. Lett. B 414 (1997) 354 [hep-ph/9705305] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    A. Gehrmann-De Ridder and E.W.N. Glover, Final state photon production at LEP, Eur. Phys. J. C 7 (1999) 29 [hep-ph/9806316] [INSPIRE].ADSCrossRefGoogle Scholar
  72. [72]
    ALEPH collaboration, D. Buskulic et al., First measurement of the quark to photon fragmentation function, Z. Phys. C 69 (1996) 365 [INSPIRE].Google Scholar
  73. [73]
    L. Bourhis, M. Fontannaz and J.P. Guillet, Quarks and gluon fragmentation functions into photons, Eur. Phys. J. C 2 (1998) 529 [hep-ph/9704447] [INSPIRE].ADSCrossRefGoogle Scholar
  74. [74]
    M. Fontannaz, J.P. Guillet and G. Heinrich, Isolated prompt photon photoproduction at NLO, Eur. Phys. J. C 21 (2001) 303 [hep-ph/0105121] [INSPIRE].ADSGoogle Scholar
  75. [75]
    M. Klasen, Theory of hard photoproduction, Rev. Mod. Phys. 74 (2002) 1221 [hep-ph/0206169] [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    A. Gehrmann-De Ridder, T. Gehrmann and E. Poulsen, Measuring the photon fragmentation function at HERA, Eur. Phys. J. C 47 (2006) 395 [hep-ph/0604030] [INSPIRE].ADSCrossRefGoogle Scholar
  77. [77]
    F. Krauss, R. Kuhn and G. Soff, AMEGIC++ 1.0: a matrix element generator in C++, JHEP 02 (2002) 044 [hep-ph/0109036] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    T. Gleisberg and S. Höche, Comix, a new matrix element generator, JHEP 12 (2008) 039 [arXiv:0808.3674] [INSPIRE].ADSCrossRefGoogle Scholar
  79. [79]
    S. Alioli et al., Update of the Binoth Les Houches accord for a standard interface between Monte Carlo tools and one-loop programs, Comput. Phys. Commun. 185 (2014) 560 [arXiv:1308.3462] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  80. [80]
    J. Bellm et al., HERWIG++ 2.7 release note, arXiv:1310.6877 [INSPIRE].
  81. [81]
    A. van Hameren, Multi-gluon one-loop amplitudes using tensor integrals, JHEP 07 (2009) 088 [arXiv:0905.1005] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  82. [82]
    A. Denner, S. Dittmaier and L. Hofer, COLLIERa fortran-library for one-loop integrals, PoS(LL2014)071 [arXiv:1407.0087] [INSPIRE].
  83. [83]
    A. Denner and S. Dittmaier, Reduction of one loop tensor five point integrals, Nucl. Phys. B 658 (2003) 175 [hep-ph/0212259] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  84. [84]
    A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys. B 734 (2006) 62 [hep-ph/0509141] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  85. [85]
    A. Denner and S. Dittmaier, Scalar one-loop 4-point integrals, Nucl. Phys. B 844 (2011) 199 [arXiv:1005.2076] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  86. [86]
    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].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  87. [87]
    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
  88. [88]
    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].ADSCrossRefzbMATHGoogle Scholar
  89. [89]
    A. van Hameren, OneLOop: for the evaluation of one-loop scalar functions, Comput. Phys. Commun. 182 (2011) 2427 [arXiv:1007.4716] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  90. [90]
    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].ADSMathSciNetCrossRefGoogle Scholar
  91. [91]
    T. Binoth, J.P. Guillet and G. Heinrich, Algebraic evaluation of rational polynomials in one-loop amplitudes, JHEP 02 (2007) 013 [hep-ph/0609054] [INSPIRE].ADSCrossRefGoogle Scholar
  92. [92]
    A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD corrections to ttbb production at the LHC: 1. Quark-antiquark annihilation, JHEP 08 (2008) 108 [arXiv:0807.1248] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  93. [93]
    P. Draggiotis, M.V. Garzelli, C.G. Papadopoulos and R. Pittau, Feynman rules for the rational part of the QCD 1-loop amplitudes, JHEP 04 (2009) 072 [arXiv:0903.0356] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  94. [94]
    M.V. Garzelli, I. Malamos and R. Pittau, Feynman rules for the rational part of the electroweak 1-loop amplitudes, JHEP 01 (2010) 040 [Erratum ibid. 10 (2010) 097] [arXiv:0910.3130] [INSPIRE].
  95. [95]
    M.V. Garzelli, I. Malamos and R. Pittau, Feynman rules for the rational part of the electroweak 1-loop amplitudes in the R ξ gauge and in the Unitary gauge, JHEP 01 (2011) 029 [arXiv:1009.4302] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  96. [96]
    M.V. Garzelli and I. Malamos, R2SM: a package for the analytic computation of the R 2 rational terms in the standard model of the electroweak interactions, Eur. Phys. J. C 71 (2011) 1605 [arXiv:1010.1248] [INSPIRE].ADSCrossRefGoogle Scholar
  97. [97]
    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 γ 5 scheme, JHEP 09 (2011) 048 [arXiv:1106.5030] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  98. [98]
    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
  99. [99]
    A. Denner, S. Dittmaier, M. Roth and L.H. 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] [hep-ph/0505042] [INSPIRE].
  100. [100]
    S. Dittmaier, A general approach to photon radiation off fermions, Nucl. Phys. B 565 (2000) 69 [hep-ph/9904440] [INSPIRE].ADSCrossRefGoogle Scholar
  101. [101]
    S. Dittmaier, A. Kabelschacht and T. Kasprzik, Polarized QED splittings of massive fermions and dipole subtraction for non-collinear-safe observables, Nucl. Phys. B 800 (2008) 146 [arXiv:0802.1405] [INSPIRE].ADSCrossRefGoogle Scholar
  102. [102]
    T. Gehrmann and N. Greiner, Photon radiation with MadDipole, JHEP 12 (2010) 050 [arXiv:1011.0321] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  103. [103]
    A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 2. Full hadronic results, JHEP 03 (2010) 021 [arXiv:1001.4006] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  104. [104]
    Z. Nagy and Z. Trócsányi, Next-to-leading order calculation of four jet observables in electron positron annihilation, Phys. Rev. D 59 (1999) 014020 [Erratum ibid. D 62 (2000) 099902] [hep-ph/9806317] [INSPIRE].
  105. [105]
    Z. Nagy, Next-to-leading order calculation of three jet observables in hadron hadron collision, Phys. Rev. D 68 (2003) 094002 [hep-ph/0307268] [INSPIRE].ADSGoogle Scholar
  106. [106]
    J.M. Campbell, R.K. Ellis and F. Tramontano, Single top production and decay at next-to-leading order, Phys. Rev. D 70 (2004) 094012 [hep-ph/0408158] [INSPIRE].ADSGoogle Scholar
  107. [107]
    G. Bevilacqua, M. Czakon, C.G. Papadopoulos, R. Pittau and M. Worek, Assault on the NLO wishlist: \( pp\ \to\ t\overline{t}b\overline{b} \), JHEP 09 (2009) 109 [arXiv:0907.4723] [INSPIRE].ADSCrossRefGoogle Scholar
  108. [108]
    J.M. Campbell and F. Tramontano, Next-to-leading order corrections to Wt production and decay, Nucl. Phys. B 726 (2005) 109 [hep-ph/0506289] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  109. [109]
    R. Frederix, T. Gehrmann and N. Greiner, Integrated dipoles with MadDipole in the MadGraph framework, JHEP 06 (2010) 086 [arXiv:1004.2905] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  110. [110]
    M. Cacciari, G.P. Salam and G. Soyez, The anti-k t jet clustering algorithm, JHEP 04 (2008) 063 [arXiv:0802.1189] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • S. Kallweit
    • 1
    • 3
  • J. M. Lindert
    • 1
  • P. Maierhöfer
    • 1
    • 2
  • S. Pozzorini
    • 1
  • M. Schönherr
    • 1
    • 2
  1. 1.Physik-InstitutUniversität ZürichZürichSwitzerland
  2. 2.Institute for Particle Physics PhenomenologyDurham UniversityDurhamUnited Kingdom
  3. 3.Institut für Physik & PRISMA Cluster of ExcellenceJohannes Gutenberg UniversitätMainzGermany

Personalised recommendations