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Two-loop helicity amplitudes for the production of two off-shell electroweak bosons in gluon fusion

  • Fabrizio CaolaEmail author
  • Johannes M. Henn
  • Kirill Melnikov
  • Alexander V. Smirnov
  • Vladimir A. Smirnov
Open Access
Regular Article - Theoretical Physics
First Online:

Abstract

We compute the part of the two-loop virtual amplitude for the process \( gg\to {V}_1{V}_2\to \left({l}_1{\overline{l}}_2^{\prime}\right)\left({l}_2{\overline{l}}_2^{\prime}\right) \), where V 1,2 are arbitrary electroweak gauge bosons, that receives contributions from loops of massless quarks. Invariant masses of electroweak bosons are allowed to be different from each other. Our result provides an important ingredient for improving the description of gluon fusion contribution to the production of four-lepton final states at the LHC.

Keywords

QCD Phenomenology NLO Computations 
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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]
    F. Cascioli et al., ZZ production at hadron colliders in NNLO QCD, Phys. Lett. B 735 (2014) 311 [arXiv:1405.2219] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    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
  3. [3]
    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
  4. [4]
    T. Binoth, M. Ciccolini, N. Kauer and M. Krämer, Gluon-induced W-boson pair production at the LHC, JHEP 12 (2006) 046 [hep-ph/0611170] [INSPIRE].
  5. [5]
    M. Spira, A. Djouadi, D. Graudenz and P.M. Zerwas, Higgs boson production at the LHC, Nucl. Phys. B 453 (1995) 17 [hep-ph/9504378] [INSPIRE].
  6. [6]
    S. Dawson, S. Dittmaier and M. Spira, Neutral Higgs boson pair production at hadron colliders: QCD corrections, Phys. Rev. D 58 (1998) 115012 [hep-ph/9805244] [INSPIRE].
  7. [7]
    L. Altenkamp, S. Dittmaier, R.V. Harlander, H. Rzehak and T.J.E. Zirke, Gluon-induced Higgs-strahlung at next-to-leading order QCD, JHEP 02 (2013) 078 [arXiv:1211.5015] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    Z. Bern, L.J. Dixon and C. Schmidt, Isolating a light Higgs boson from the diphoton background at the CERN LHC, Phys. Rev. D 66 (2002) 074018 [hep-ph/0206194] [INSPIRE].
  9. [9]
    J.M. Henn, K. Melnikov and V.A. Smirnov, Two-loop planar master integrals for the production of off-shell vector bosons in hadron collisions, JHEP 05 (2014) 090 [arXiv:1402.7078] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    F. Caola, J.M. Henn, K. Melnikov and V.A. Smirnov, Non-planar master integrals for the production of two off-shell vector bosons in collisions of massless partons, JHEP 09 (2014) 043 [arXiv:1404.5590] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    C.G. Papadopoulos, D. Tommasini and C. Wever, Two-loop master integrals with the simplified differential equations approach, JHEP 01 (2015) 072 [arXiv:1409.6114] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    T. Gehrmann, A. von Manteuffel and L. Tancredi, The two-loop helicity amplitudes for \( q{\overline{q}}^{\prime}\to {V}_1{V}_2\to 4 \) leptons, arXiv:1503.04812 [INSPIRE].
  13. [13]
    T. Gehrmann, A. von Manteuffel, L. Tancredi and E. Weihs, The two-loop master integrals for \( q\overline{q}\to VV \), JHEP 06 (2014) 032 [arXiv:1404.4853] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    T. Gehrmann, L. Tancredi and E. Weihs, Two-loop master integrals for \( q\overline{q}\to VV \) : the planar topologies, JHEP 08 (2013) 070 [arXiv:1306.6344] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    J.M. Campbell, R.K. Ellis and C. Williams, Gluon-gluon contributions to W + W − production and Higgs interference effects, JHEP 10 (2011) 005 [arXiv:1107.5569] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  16. [16]
    K. Melnikov and M. Dowling, Production of two Z-bosons in gluon fusion in the heavy top quark approximation, Phys. Lett. B 744 (2015) 43 [arXiv:1503.01274] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    F. Caola, J.M. Henn, K. Melnikov, A.V. Smirnov and V.A. Smirnov, Two-loop helicity amplitudes for the production of two off-shell electroweak bosons in quark-antiquark collisions, JHEP 11 (2014) 041 [arXiv:1408.6409] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    K. Nishijima, Generalized Furry’s theorem for closed loops, Prog. Theor. Phys. 6 (1951) 614.ADSCrossRefzbMATHGoogle Scholar
  19. [19]
    E.W.N. Glover and J.J. van der Bij, Vector boson pair production via gluon fusion, Phys. Lett. B 219 (1989) 488 [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    C. Kao and D.A. Dicus, Production of W + W − from gluon fusion, Phys. Rev. D 43 (1991) 1555 [INSPIRE].ADSGoogle Scholar
  21. [21]
    F.V. Tkachov, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett. B 100 (1981) 65 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    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 [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    J. Kuipers, T. Ueda, J.A.M. Vermaseren and J. Vollinga, FORM version 4.0, Comput. Phys. Commun. 184 (2013) 1453 [arXiv:1203.6543] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  25. [25]
    A.V. Smirnov, Algorithm FIRE — Feynman Integral REduction, JHEP 10 (2008) 107 [arXiv:0807.3243] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  26. [26]
    A.V. Smirnov and V.A. Smirnov, FIRE4, LiteRed and accompanying tools to solve integration by parts relations, Comput. Phys. Commun. 184 (2013) 2820 [arXiv:1302.5885] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  27. [27]
    A.V. Smirnov, FIRE5: a C++ implementation of Feynman Integral REduction, Comput. Phys. Commun. 189 (2014) 182 [arXiv:1408.2372] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  28. [28]
    J. Vollinga and S. Weinzierl, Numerical evaluation of multiple polylogarithms, Comput. Phys. Commun. 167 (2005) 177 [hep-ph/0410259] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    C. W. Bauer, A. Frink and R. Kreckel, Introduction to the GiNaC framework for symbolic computation within the C++ programming language, J. Symb. Comput. 33 (2002) 1 [cs/0004015].MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    E.W.N. Glover and J.J. van der Bij, Z boson pair production via gluon fusion, Nucl. Phys. B 321 (1989) 561 [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    T. Matsuura and J.J. van der Bij, Characteristics of leptonic signals for Z boson pairs at hadron colliders, Z. Phys. C 51 (1991) 259 [INSPIRE].Google Scholar
  33. [33]
    C. Zecher, T. Matsuura and J.J. van der Bij, Leptonic signals from off-shell Z boson pairs at hadron colliders, Z. Phys. C 64 (1994) 219 [hep-ph/9404295] [INSPIRE].ADSGoogle Scholar
  34. [34]
    T. Binoth, M. Ciccolini, N. Kauer and M. Krämer, Gluon-induced WW background to Higgs boson searches at the LHC, JHEP 03 (2005) 065 [hep-ph/0503094] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    J.M. Campbell, R.K. Ellis and C. Williams, http://mcfm.fnal.gov.
  36. [36]
    A. von Manteuffel and L. Tancredi, The two-loop helicity amplitudes for gg → V 1 V 2 → 4 leptons, arXiv:1503.08835 [INSPIRE].
  37. [37]
    J.M. Campbell, R.K. Ellis and C. Williams, Bounding the Higgs width at the LHC using full analytic results for gg → e − e + μ − μ +, JHEP 04 (2014) 060 [arXiv:1311.3589] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    F. Caola and K. Melnikov, Constraining the Higgs boson width with ZZ production at the LHC, Phys. Rev. D 88 (2013) 054024 [arXiv:1307.4935] [INSPIRE].ADSGoogle Scholar
  39. [39]
    CMS collaboration, Constraints on the Higgs boson width from off-shell production and decay to Z-boson pairs, Phys. Lett. B 736 (2014) 64 [arXiv:1405.3455] [INSPIRE].Google Scholar
  40. [40]
    ATLAS collaboration, Determination of the off-shell Higgs boson signal strength in the high-mass ZZ final state with the ATLAS detector, ATLAS-CONF-2014-042 (2014) [ATLAS-COM-CONF-2014-052].
  41. [41]
    N. Kauer and G. Passarino, Inadequacy of zero-width approximation for a light Higgs boson signal, JHEP 08 (2012) 116 [arXiv:1206.4803] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    J.M. Campbell, R.K. Ellis, E. Furlan and R. Röntsch, Interference effects for Higgs boson mediated Z-pair plus jet production, Phys. Rev. D 90 (2014) 093008 [arXiv:1409.1897] [INSPIRE].ADSGoogle Scholar
  43. [43]
    T. Melia, K. Melnikov, R. Rontsch, M. Schulze and G. Zanderighi, Gluon fusion contribution to W + W − + jet production, JHEP 08 (2012) 115 [arXiv:1205.6987] [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    P. Agrawal and A. Shivaji, Di-vector boson + jet production via gluon fusion at hadron colliders, Phys. Rev. D 86 (2012) 073013 [arXiv:1207.2927] [INSPIRE].ADSGoogle Scholar
  45. [45]
    F. Campanario, Q. Li, M. Rauch and M. Spira, ZZ + jet production via gluon fusion at the LHC, JHEP 06 (2013) 069 [arXiv:1211.5429] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Fabrizio Caola
    • 1
    Email author
  • Johannes M. Henn
    • 2
  • Kirill Melnikov
    • 3
  • Alexander V. Smirnov
    • 4
  • Vladimir A. Smirnov
    • 5
  1. 1.PH Department, TH Unit, CERNGeneva 23Switzerland
  2. 2.Institute for Advanced Study,PrincetonUSA
  3. 3.Institute for Theoretical Particle PhysicsKarlsruhe Institute of TechnologyKarlsruheGermany
  4. 4.Research Computing CenterMoscow State UniversityMoscowRussia
  5. 5.Skobeltsyn Institute of Nuclear PhysicsMoscow State UniversityMoscowRussia

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