Advertisement

Higgs pair production from bottom quark annihilation to NNLO in QCD

  • A. H. Ajjath
  • Pulak Banerjee
  • Amlan Chakraborty
  • Prasanna K. Dhani
  • Pooja MukherjeeEmail author
  • Narayan Rana
  • V. Ravindran
Open Access
Regular Article - Theoretical Physics
  • 24 Downloads

Abstract

We present the first results on the two-loop massless QCD corrections to the four-point amplitude \( b+\overline{b}\to H+H \) in the five flavor scheme, treating bottom quarks as massless. This amplitude is sensitive to the trilinear Higgs boson coupling. Our two-loop result for this amplitude constitutes of purely virtual contributions to the next-to-next-to-leading order QCD predictions for the production of a pair of Higgs bosons at the Large Hadron Collider. Using these two loop amplitudes and exploiting the universality of the soft contributions in perturbative QCD, we obtain the NNLO QCD effects in the soft plus virtual approximation. We find that the inclusion of higher order terms reduce the uncertainties resulting from the unphysical renormalisation and factorisation scales.

Keywords

NLO Computations QCD Phenomenology 

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.

Supplementary material

References

  1. [1]
    CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
  2. [2]
    ATLAS collaboration, Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
  3. [3]
    C. Englert et al., Precision measurements of Higgs couplings: implications for new physics scales, J. Phys. G 41 (2014) 113001 [arXiv:1403.7191].
  4. [4]
    T. Binoth, S. Karg, N. Kauer and R. Ruckl, Multi-Higgs boson production in the Standard Model and beyond, Phys. Rev. D 74 (2006) 113008 [hep-ph/0608057] [INSPIRE].
  5. [5]
    ATLAS collaboration, Prospects for measuring Higgs pair production in the channel \( H\left(\to\ \gamma \gamma \right)H\left(\to b\overline{b}\right) \) using the ATLAS detector at the HL-LHC, ATL-PHYS-PUB-2014-019 (2014).
  6. [6]
    ATLAS collaboration, Higgs pair production in the \( H\left(\to \tau \tau \right)H\left(\to b\overline{b}\right) \) channel at the High-Luminosity LHC, ATL-PHYS-PUB-2015-046 (2015).
  7. [7]
    CMS collaboration, Higgs pair production at the High Luminosity LHC, CMS-PAS-FTR-15-002 (Higgs pair production at the High Luminosity LHC).
  8. [8]
    CMS collaboration, Updates on projections of physics reach with the upgraded CMS detector for high luminosity LHC, CMS-DP-2016-064 (2016).
  9. [9]
    H.P. Nilles, Supersymmetry, supergravity and particle physics, Phys. Rept. 110 (1984) 1.ADSCrossRefGoogle Scholar
  10. [10]
    E.W.N. Glover and J.J. van der Bij, Higgs boson pair production via gluon fusion, Nucl. Phys. B 309 (1988) 282 [INSPIRE].
  11. [11]
    O.J.P. Eboli, G.C. Marques, S.F. Novaes and A.A. Natale, Twin Higgs boson production, Phys. Lett. B 197 (1987) 269 [INSPIRE].
  12. [12]
    T. Plehn, M. Spira and P.M. Zerwas, Pair production of neutral Higgs particles in gluon-gluon collisions, Nucl. Phys. B 479 (1996) 46 [hep-ph/9603205] [INSPIRE].
  13. [13]
    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].
  14. [14]
    A. Djouadi, W. Kilian, M. Muhlleitner and P.M. Zerwas, Testing Higgs selfcouplings at e + e linear colliders, Eur. Phys. J. C 10 (1999) 27 [hep-ph/9903229] [INSPIRE].
  15. [15]
    A. Djouadi, W. Kilian, M. Muhlleitner and P.M. Zerwas, Production of neutral Higgs boson pairs at LHC, Eur. Phys. J. C 10 (1999) 45 [hep-ph/9904287] [INSPIRE].
  16. [16]
    M.M. Mühlleitner, Higgs particles in the standard model and supersymmetric theories, Ph.D. thesis, Hamburg University, Hamburg, Germany (2000), hep-ph/0008127.
  17. [17]
    J. Grigo, J. Hoff, K. Melnikov and M. Steinhauser, On the Higgs boson pair production at the LHC, Nucl. Phys. B 875 (2013) 1 [arXiv:1305.7340] [INSPIRE].
  18. [18]
    R. Frederix et al., Higgs pair production at the LHC with NLO and parton-shower effects, Phys. Lett. B 732 (2014) 142 [arXiv:1401.7340] [INSPIRE].
  19. [19]
    F. Maltoni, E. Vryonidou and M. Zaro, Top-quark mass effects in double and triple Higgs production in gluon-gluon fusion at NLO, JHEP 11 (2014) 079 [arXiv:1408.6542] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    G. Degrassi, P.P. Giardino and R. Gröber, On the two-loop virtual QCD corrections to Higgs boson pair production in the Standard Model, Eur. Phys. J. C 76 (2016) 411 [arXiv:1603.00385] [INSPIRE].
  21. [21]
    R. Gröber, A. Maier and T. Rauh, Reconstruction of top-quark mass effects in Higgs pair production and other gluon-fusion processes, JHEP 03 (2018) 020 [arXiv:1709.07799] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    R. Bonciani, G. Degrassi, P.P. Giardino and R. Gröber, Analytical method for next-to-leading-order QCD corrections to double-Higgs production, Phys. Rev. Lett. 121 (2018)162003 [arXiv:1806.11564] [INSPIRE].
  23. [23]
    S. Borowka et al., Higgs boson pair production in gluon fusion at next-to-leading order with full top-quark mass dependence, Phys. Rev. Lett. 117 (2016) 012001 [arXiv:1604.06447] [INSPIRE].
  24. [24]
    S. Borowka et al., Full top quark mass dependence in Higgs boson pair production at NLO, JHEP 10 (2016) 107 [arXiv:1608.04798].ADSCrossRefGoogle Scholar
  25. [25]
    D. de Florian and J. Mazzitelli, Higgs boson pair production at next-to-next-to-leading order in QCD, Phys. Rev. Lett. 111 (2013) 201801 [arXiv:1309.6594].ADSCrossRefGoogle Scholar
  26. [26]
    D. de Florian and J. Mazzitelli, Two-loop virtual corrections to Higgs pair production, Phys. Lett. B 724 (2013) 306 [arXiv:1305.5206] [INSPIRE].
  27. [27]
    J. Grigo, J. Hoff and M. Steinhauser, Higgs boson pair production: top quark mass effects at NLO and NNLO, Nucl. Phys. B 900 (2015) 412 [arXiv:1508.00909] [INSPIRE].
  28. [28]
    Q. Li, Q.-S. Yan and X. Zhao, Higgs pair production: improved description by matrix element matching, Phys. Rev. D 89 (2014) 033015 [arXiv:1312.3830] [INSPIRE].
  29. [29]
    P. Maierhöfer and A. Papaefstathiou, Higgs Boson pair production merged to one jet, JHEP 03 (2014) 126 [arXiv:1401.0007] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    D.Y. Shao, C.S. Li, H.T. Li and J. Wang, Threshold resummation effects in Higgs boson pair production at the LHC, JHEP 07 (2013) 169 [arXiv:1301.1245] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    D. de Florian and J. Mazzitelli, Higgs pair production at next-to-next-to-leading logarithmic accuracy at the LHC, JHEP 09 (2015) 053 [arXiv:1505.07122] [INSPIRE].CrossRefGoogle Scholar
  32. [32]
    M. Grazzini et al., Higgs boson pair production at NNLO with top quark mass effects, JHEP 05 (2018) 059 [arXiv:1803.02463] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    P. Banerjee et al., Two-loop massless QCD corrections to the g + gH + H four-point amplitude, JHEP 11 (2018) 130 [arXiv:1809.05388] [INSPIRE].
  34. [34]
    M.A.G. Aivazis, J.C. Collins, F.I. Olness and W.K. Tung, Leptoproduction of heavy quarks. 2. A unified QCD formulation of charged and neutral current processes from fixed target to collider energies, Phys. Rev. D 50 (1994) 3102 [hep-ph/9312319].
  35. [35]
    J.C. Collins, Hard scattering factorization with heavy quarks: a general treatment, Phys. Rev. D 58 (1998) 094002 [hep-ph/9806259] [INSPIRE].
  36. [36]
    M. Krämer, F.I. Olness and D.E. Soper, Treatment of heavy quarks in deeply inelastic scattering, Phys. Rev. D 62 (2000) 096007 [hep-ph/0003035] [INSPIRE].
  37. [37]
    D.A. Dicus and S. Willenbrock, Higgs boson production from heavy quark fusion, Phys. Rev. D 39 (1989) 751 [INSPIRE].
  38. [38]
    D. Dicus, T. Stelzer, Z. Sullivan and S. Willenbrock, Higgs boson production in association with bottom quarks at next-to-leading order, Phys. Rev. D 59 (1999) 094016 [hep-ph/9811492] [INSPIRE].
  39. [39]
    F. Maltoni, Z. Sullivan and S. Willenbrock, Higgs-boson production via bottom-quark fusion, Phys. Rev. D 67 (2003) 093005 [hep-ph/0301033] [INSPIRE].
  40. [40]
    F.I. Olness and W.-K. Tung, When is a heavy quark not a parton? Charged Higgs production and heavy quark mass effects in the QCD based parton model, Nucl. Phys. B 308 (1988) 813 [INSPIRE].
  41. [41]
    J.F. Gunion et al., Neutral and charged Higgs detection: heavy quark fusion, top quark mass dependence and rare decays, Nucl. Phys. B 294 (1987) 621 [INSPIRE].
  42. [42]
    R.V. Harlander and W.B. Kilgore, Higgs boson production in bottom quark fusion at next-to-next-to leading order, Phys. Rev. D 68 (2003) 013001 [hep-ph/0304035] [INSPIRE].
  43. [43]
    T. Ahmed, M. Mahakhud, P. Mathews, N. Rana and V. Ravindran, Two-loop QCD corrections to \( Higgs\to b+\overline{b}+g \) amplitude, JHEP 08 (2014) 075 [arXiv:1405.2324] [INSPIRE].
  44. [44]
    T. Gehrmann and D. Kara, The \( Hb\overline{b} \) form factor to three loops in QCD, JHEP 09 (2014) 174 [arXiv:1407.8114] [INSPIRE].
  45. [45]
    T. Ahmed, N. Rana and V. Ravindran, Higgs boson production through \( b\overline{b} \) annihilation at threshold in N 3 LO QCD, JHEP 10 (2014) 139 [arXiv:1408.0787].
  46. [46]
    T. Ahmed, M.K. Mandal, N. Rana and V. Ravindran, Higgs rapidity distribution in \( b\overline{b} \) annihilation at threshold in N 3 LO QCD, JHEP 02 (2015) 131 [arXiv:1411.5301] [INSPIRE].
  47. [47]
    M. Buza, Y. Matiounine, J. Smith and W.L. van Neerven, Charm electroproduction viewed in the variable flavor number scheme versus fixed order perturbation theory, Eur. Phys. J. C 1 (1998)301 [hep-ph/9612398] [INSPIRE].
  48. [48]
    I. Bierenbaum, J. Blumlein and S. Klein, Mellin moments of the O(α s3) heavy flavor contributions to unpolarized deep-inelastic scattering at Q 2m 2 and anomalous dimensions, Nucl. Phys. B 820 (2009) 417 [arXiv:0904.3563].
  49. [49]
    J. Ablinger et al., Three loop massive operator matrix elements and asymptotic Wilson coefficients with two different masses, Nucl. Phys. B 921 (2017) 585 [arXiv:1705.07030] [INSPIRE].
  50. [50]
    J. Blümlein, A. De Freitas, C. Schneider and K. Schönwald, The variable flavor number scheme at next-to-leading order, Phys. Lett. B 782 (2018) 362 [arXiv:1804.03129] [INSPIRE].
  51. [51]
    S. Dawson, C. Kao, Y. Wang and P. Williams, QCD corrections to Higgs pair production in bottom quark fusion, Phys. Rev. D 75 (2007) 013007 [hep-ph/0610284] [INSPIRE].
  52. [52]
    S. Dawson, C. Kao and Y. Wang, SUSY QCD corrections to Higgs pair production from bottom quark fusion, Phys. Rev. D 77 (2008) 113005 [arXiv:0710.4331] [INSPIRE].
  53. [53]
    H.-S. Hou et al., Pair production of charged Higgs bosons from bottom-quark fusion, Phys. Rev. D 71 (2005) 075014 [hep-ph/0502214] [INSPIRE].
  54. [54]
    J.-J. Liu et al., Higgs boson pair production in the little Higgs model at hadron collider, Phys. Rev. D 70 (2004) 015001 [hep-ph/0404171] [INSPIRE].
  55. [55]
    S. Catani, The singular behavior of QCD amplitudes at two loop order, Phys. Lett. B 427 (1998)161 [hep-ph/9802439] [INSPIRE].
  56. [56]
    V. Ravindran, Higher-order threshold effects to inclusive processes in QCD, Nucl. Phys. B 752 (2006)173 [hep-ph/0603041] [INSPIRE].
  57. [57]
    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].
  58. [58]
    P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279.ADSMathSciNetCrossRefzbMATHGoogle Scholar
  59. [59]
    J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
  60. [60]
    A. von Manteuffel and C. Studerus, Reduze 2Distributed Feynman integral reduction, arXiv:1201.4330 [INSPIRE].
  61. [61]
    F.V. Tkachov, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett. B 100 (1981) 65.Google Scholar
  62. [62]
    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].
  63. [63]
    T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B 580 (2000) 485 [hep-ph/9912329] [INSPIRE].
  64. [64]
    R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser. 523 (2014) 012059 [arXiv:1310.1145] [INSPIRE].
  65. [65]
    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].
  66. [66]
    D.J. Gross and F. Wilczek, Ultraviolet behavior of nonabelian gauge theories, Phys. Rev. Lett. 30 (1973) 1343 [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    H.D. Politzer, Reliable perturbative results for strong interactions?, Phys. Rev. Lett. 30 (1973)1346 [INSPIRE].
  68. [68]
    W.E. Caswell, Asymptotic behavior of nonabelian gauge theories to two loop order, Phys. Rev. Lett. 33 (1974) 244 [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    D.R.T. Jones, Two loop diagrams in Yang-Mills theory, Nucl. Phys. B 75 (1974) 531 [INSPIRE].
  70. [70]
    E. Egorian and O.V. Tarasov, Two loop renormalization of the QCD in an arbitrary gauge, Teor. Mat. Fiz. 41 (1979) 26 [INSPIRE].Google Scholar
  71. [71]
    T. Kinoshita, Mass singularities of Feynman amplitudes, J. Math. Phys. 3 (1962) 650 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  72. [72]
    T.D. Lee and M. Nauenberg, Degenerate systems and mass singularities, Phys. Rev. 133 (1964) B1549 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  73. [73]
    J.C. Collins, D.E. Soper and G.F. Sterman, Factorization for short distance hadron-hadron scattering, Nucl. Phys. B 261 (1985) 104 [INSPIRE].
  74. [74]
    N. Kidonakis, G. Oderda and G.F. Sterman, Evolution of color exchange in QCD hard scattering, Nucl. Phys. B 531 (1998) 365 [hep-ph/9803241] [INSPIRE].
  75. [75]
    A. Sen, Asymptotic behavior of the wide angle on-shell quark scattering amplitudes in nonabelian gauge theories, Phys. Rev. D 28 (1983) 860 [INSPIRE].
  76. [76]
    L.W. Garland et al., The two loop QCD matrix element for e + e → 3 jets, Nucl. Phys. B 627 (2002)107 [hep-ph/0112081] [INSPIRE].
  77. [77]
    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] [INSPIRE].
  78. [78]
    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] [INSPIRE].
  79. [79]
    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] [INSPIRE].
  80. [80]
    Z. Bern, L.J. Dixon and D.A. Kosower, Two-loop ggg splitting amplitudes in QCD, JHEP 08 (2004) 012 [hep-ph/0404293] [INSPIRE].
  81. [81]
    G.F. Sterman and M.E. Tejeda-Yeomans, Multiloop amplitudes and resummation, Phys. Lett. B 552 (2003) 48 [hep-ph/0210130] [INSPIRE].
  82. [82]
    S.M. Aybat, L.J. Dixon and G.F. Sterman, The two-loop anomalous dimension matrix for soft gluon exchange, Phys. Rev. Lett. 97 (2006) 072001 [hep-ph/0606254] [INSPIRE].
  83. [83]
    S.M. Aybat, L.J. Dixon and G.F. Sterman, The two-loop soft anomalous dimension matrix and resummation at next-to-next-to leading pole, Phys. Rev. D 74 (2006) 074004 [hep-ph/0607309] [INSPIRE].
  84. [84]
    T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett. 102 (2009) 162001 [Erratum ibid. 111 (2013) 199905] [arXiv:0901.0722] [INSPIRE].
  85. [85]
    E. Gardi and L. Magnea, Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes, JHEP 03 (2009) 079 [arXiv:0901.1091] [INSPIRE].ADSCrossRefGoogle Scholar
  86. [86]
    B.W. Harris and J.F. Owens, The two cutoff phase space slicing method, Phys. Rev. D 65 (2002)094032 [hep-ph/0102128] [INSPIRE].
  87. [87]
    L.A. Harland-Lang, A.D. Martin, P. Motylinski and R.S. Thorne, Parton distributions in the LHC era: MMHT 2014 PDFs, Eur. Phys. J. C 75 (2015) 204 [arXiv:1412.3989] [INSPIRE].
  88. [88]
    A. Buckley et al., LHAPDF6: parton density access in the LHC precision era, Eur. Phys. J. C 75 (2015) 132 [arXiv:1412.7420] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • A. H. Ajjath
    • 1
  • Pulak Banerjee
    • 1
  • Amlan Chakraborty
    • 1
  • Prasanna K. Dhani
    • 1
    • 2
  • Pooja Mukherjee
    • 1
    Email author
  • Narayan Rana
    • 3
    • 4
  • V. Ravindran
    • 1
  1. 1.The Institute of Mathematical Sciences, HBNIChennaiIndia
  2. 2.INFN — Sezione di FirenzeFlorenceItaly
  3. 3.Deutsches Elektronen-Synchrotron, DESYZeuthenGermany
  4. 4.INFN — Sezione di MilanoMilanoItaly

Personalised recommendations