NLO QCD and electroweak corrections to W + γ production with leptonic W-boson decays

  • Ansgar Denner
  • Stefan Dittmaier
  • Markus Hecht
  • Christian Pasold
Open Access
Regular Article - Theoretical Physics

Abstract

We present a calculation of the next-to-leading-order electroweak corrections to W+γ production, including the leptonic decay of the W boson and taking into account all off-shell effects of the W boson, where the finite width of the W boson is implemented using the complex-mass scheme. Corrections induced by incoming photons are fully included and find particular emphasis in the discussion of phenomenological predictions for the LHC. The corresponding next-to-leading-order QCD corrections are reproduced as well. In order to separate hard photons from jets, a quark-to-photon fragmentation function á la Glover and Morgan is employed. Our results are implemented into Monte Carlo programs allowing for the evaluation of arbitrary differential cross sections. We present integrated cross sections for the LHC at 7 TeV, 8 TeV, and 14 TeV as well as differential distributions at 14 TeV for bare muons and dressed leptons. Finally, we discuss the impact of anomalous W W γ couplings.

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]
    M.S. Neubauer, Diboson production at colliders, Ann. Rev. Nucl. Part. Sci. 61 (2011) 223 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    D0 collaboration, V.M. Abazov et al., W γ production and limits on anomalous W W γ couplings in \( p\overline{p} \) collisions, Phys. Rev. Lett. 107 (2011) 241803 [arXiv:1109.4432] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    CMS collaboration, Measurement of the W γ and Zγ inclusive cross sections in pp collisions at \( \sqrt{s}=7 \) TeV and limits on anomalous triple gauge boson couplings, Phys. Rev. D 89 (2014) 092005 [arXiv:1308.6832] [INSPIRE].ADSGoogle Scholar
  4. [4]
    ATLAS collaboration, Measurements of W γ and Zγ production in pp collisions at \( \sqrt{s}=7 \) TeV with the ATLAS detector at the LHC, Phys. Rev. D 87 (2013) 112003 [arXiv:1302.1283] [INSPIRE].ADSGoogle Scholar
  5. [5]
    ATLAS collaboration, Search for new resonances in W γ and Zγ final states in pp collisions at \( \sqrt{s}=8 \) TeV with the ATLAS detector, Phys. Lett. B 738 (2014) 428 [arXiv:1407.8150] [INSPIRE].ADSGoogle Scholar
  6. [6]
    M. Schott and J. Zhu, Diboson production in proton-proton collisions at \( \sqrt{s}=7 \) TeV, Int. J. Mod. Phys. A 29 (2014) 1430053 [arXiv:1406.7731] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    R.W. Brown, D. Sahdev and K.O. Mikaelian, W ± Z 0 and W ±γ Pair Production in νe, pp and \( \overline{p}p \) Collisions, Phys. Rev. D 20 (1979) 1164 [INSPIRE].ADSGoogle Scholar
  8. [8]
    J. Smith, D. Thomas and W.L. van Neerven, QCD Corrections to the Reaction \( p\overline{p} \)WγX, Z. Phys. C 44 (1989) 267 [INSPIRE].Google Scholar
  9. [9]
    J. Ohnemus, Order α s calculations of hadronic W ±γ and Zγ production, Phys. Rev. D 47 (1993) 940 [INSPIRE].ADSGoogle Scholar
  10. [10]
    U. Baur, T. Han and J. Ohnemus, QCD corrections to hadronic W γ production with nonstandard W W γ couplings, Phys. Rev. D 48 (1993) 5140 [hep-ph/9305314] [INSPIRE].ADSGoogle Scholar
  11. [11]
    L.J. Dixon, Z. Kunszt and A. Signer, Helicity amplitudes for O(α s ) production of W + W , W ± Z, ZZ, W ±γ, or Zγ pairs at hadron colliders, Nucl. Phys. B 531 (1998) 3 [hep-ph/9803250] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    D. De Florian and A. Signer, Wγ and Zγ production at hadron colliders, Eur. Phys. J. C 16 (2000) 105 [hep-ph/0002138] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    J.M. Campbell, R.K. Ellis and C. Williams, Vector boson pair production at the LHC, JHEP 07 (2011) 018 [arXiv:1105.0020] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    K.L. Adamson, D. de Florian and A. Signer, Gluon induced contributions to W Z and W γ production at NNLO, Phys. Rev. D 65 (2002) 094041 [hep-ph/0202132] [INSPIRE].ADSGoogle Scholar
  15. [15]
    M. Grazzini, Vector-boson pair production at NNLO, PoS(LL2014)027 [arXiv:1407.1618] [INSPIRE].
  16. [16]
    L. Barze et al., Wγ production in hadronic collisions using the POWHEG+MiNLO method, JHEP 12 (2014) 039 [arXiv:1408.5766] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    W. Beenakker, A. Denner, S. Dittmaier, R. Mertig and T. Sack, High-energy approximation for on-shell W pair production, Nucl. Phys. B 410 (1993) 245 [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    M. Beccaria, G. Montagna, F. Piccinini, F.M. Renard and C. Verzegnassi, Rising bosonic electroweak virtual effects at high-energy e + e colliders, Phys. Rev. D 58 (1998) 093014 [hep-ph/9805250] [INSPIRE].ADSGoogle Scholar
  19. [19]
    P. Ciafaloni and D. Comelli, Sudakov enhancement of electroweak corrections, Phys. Lett. B 446 (1999) 278 [hep-ph/9809321] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    J.H. Kühn and A.A. Penin, Sudakov logarithms in electroweak processes, hep-ph/9906545 [INSPIRE].
  21. [21]
    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
  22. [22]
    E. Accomando, A. Denner and S. Pozzorini, Electroweak correction effects in gauge boson pair production at the CERN LHC, Phys. Rev. D 65 (2002) 073003 [hep-ph/0110114] [INSPIRE].ADSGoogle Scholar
  23. [23]
    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
  24. [24]
    E.W.N. Glover and A.G. Morgan, Measuring the photon fragmentation function at LEP, Z. Phys. C 62 (1994) 311 [INSPIRE].ADSGoogle Scholar
  25. [25]
    E.W.N. Glover and A.G. Morgan, The Photon + 1 jet event rate with the cone algorithm in hadronic events at LEP, Phys. Lett. B 334 (1994) 208 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    S. Frixione, Isolated photons in perturbative QCD, Phys. Lett. B 429 (1998) 369 [hep-ph/9801442] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    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
  28. [28]
    A. Denner, S. Dittmaier and L. Hofer, COLLIERA fortran-library for one-loop integrals, PoS(LL2014)071 [arXiv:1407.0087] [INSPIRE].
  29. [29]
    A. Denner and S. Dittmaier, Reduction of one loop tensor five point integrals, Nucl. Phys. B 658 (2003) 175 [hep-ph/0212259] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  30. [30]
    A. Denner and S. Dittmaier, Reduction schemes for one-loop tensor integrals, Nucl. Phys. B 734 (2006) 62 [hep-ph/0509141] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  31. [31]
    A. Denner and S. Dittmaier, Scalar one-loop 4-point integrals, Nucl. Phys. B 844 (2011) 199 [arXiv:1005.2076] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  33. [33]
    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].ADSCrossRefMATHGoogle Scholar
  34. [34]
    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
  35. [35]
    S. Dittmaier and M. Roth, LUSIFER: A LUcid approach to six FERmion production, Nucl. Phys. B 642 (2002) 307 [hep-ph/0206070] [INSPIRE].
  36. [36]
    G.P. Lepage, A New Algorithm for Adaptive Multidimensional Integration, J. Comput. Phys. 27 (1978) 192 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  37. [37]
    G.P. Lepage, VEGASan adaptive multi-dimensional integration programm, CLNS-80/447 (1980).Google Scholar
  38. [38]
    J. Küblbeck, M. Böhm and A. Denner, Feyn Arts: Computer Algebraic Generation of Feynman Graphs and Amplitudes, Comput. Phys. Commun. 60 (1990) 165 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    A. Denner, S. Dittmaier, M. Roth and D. Wackeroth, Predictions for all processes e + e → 4 fermions + gamma, Nucl. Phys. B 560 (1999) 33 [hep-ph/9904472] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    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].
  41. [41]
    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
  42. [42]
    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
  43. [43]
    D.B. Melrose, Reduction of Feynman diagrams, Nuovo Cim. 40 (1965) 181 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  44. [44]
    G. Passarino and M.J.G. Veltman, One Loop Corrections for e + e Annihilation into μ + μ in the Weinberg Model, Nucl. Phys. B 160 (1979) 151 [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    G. ’t Hooft and M.J.G. Veltman, Scalar One Loop Integrals, Nucl. Phys. B 153 (1979) 365 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  46. [46]
    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
  47. [47]
    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
  48. [48]
    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].
  49. [49]
    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].
  50. [50]
    S. Dittmaier, A General approach to photon radiation off fermions, Nucl. Phys. B 565 (2000) 69 [hep-ph/9904440] [INSPIRE].
  51. [51]
    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
  52. [52]
    U. Baur, S. Keller and D. Wackeroth, Electroweak radiative corrections to W boson production in hadronic collisions, Phys. Rev. D 59 (1999) 013002 [hep-ph/9807417] [INSPIRE].ADSGoogle Scholar
  53. [53]
    S. Dittmaier and M. Huber, Radiative corrections to the neutral-current Drell-Yan process in the Standard Model and its minimal supersymmetric extension, JHEP 01 (2010) 060 [arXiv:0911.2329] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  54. [54]
    NNPDF collaboration, R.D. Ball et al., Parton distributions with QED corrections, Nucl. Phys. B 877 (2013) 290 [arXiv:1308.0598] [INSPIRE].MATHGoogle Scholar
  55. [55]
    K.-P.O. Diener, S. Dittmaier and W. Hollik, Electroweak higher-order effects and theoretical uncertainties in deep-inelastic neutrino scattering, Phys. Rev. D 72 (2005) 093002 [hep-ph/0509084] [INSPIRE].ADSGoogle Scholar
  56. [56]
    T. Kinoshita, Mass singularities of Feynman amplitudes, J. Math. Phys. 3 (1962) 650 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  57. [57]
    T. Lee and M. Nauenberg, Degenerate Systems and Mass Singularities, Phys. Rev. 133 (1964) B1549.ADSMathSciNetCrossRefGoogle Scholar
  58. [58]
    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
  59. [59]
    ALEPH collaboration, D. Buskulic et al., First measurement of the quark to photon fragmentation function, Z. Phys. C 69 (1996) 365 [INSPIRE].
  60. [60]
    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].ADSCrossRefMATHGoogle Scholar
  61. [61]
    Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].Google Scholar
  62. [62]
    J. Butterworth et al., Les Houches 2013: Physics at TeV Colliders: Standard Model Working Group Report, arXiv:1405.1067 [INSPIRE].
  63. [63]
    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].ADSCrossRefGoogle Scholar
  64. [64]
    L.J. Dixon, Z. Kunszt and A. Signer, Vector boson pair production in hadronic collisions at order α s : Lepton correlations and anomalous couplings, Phys. Rev. D 60 (1999) 114037 [hep-ph/9907305] [INSPIRE].ADSGoogle Scholar
  65. [65]
    S. Haywood et al., Electroweak physics, hep-ph/0003275 [INSPIRE].
  66. [66]
    U. Baur, S. Errede and G.L. Landsberg, Rapidity correlations in W γ production at hadron colliders, Phys. Rev. D 50 (1994) 1917 [hep-ph/9402282] [INSPIRE].
  67. [67]
    Z. Bern et al., Left-Handed W Bosons at the LHC, Phys. Rev. D 84 (2011) 034008 [arXiv:1103.5445] [INSPIRE].ADSGoogle Scholar
  68. [68]
    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
  69. [69]
    K. Hagiwara, R.D. Peccei, D. Zeppenfeld and K. Hikasa, Probing the Weak Boson Sector in e + e W + W , Nucl. Phys. B 282 (1987) 253 [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    ATLAS collaboration, Measurement of W γ and Zγ production cross sections in pp collisions at \( \sqrt{s}=7 \) TeV and limits on anomalous triple gauge couplings with the ATLAS detector, Phys. Lett. B 717 (2012) 49 [arXiv:1205.2531] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Ansgar Denner
    • 1
  • Stefan Dittmaier
    • 2
  • Markus Hecht
    • 2
  • Christian Pasold
    • 1
  1. 1.Julius-Maximilians-Universität Würzburg, Institut für Theoretische Physik und AstrophysikWürzburgGermany
  2. 2.Albert-Ludwigs-Universität Freiburg, Physikalisches InstitutFreiburgGermany

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