Skip to main content

Higgs pair production: choosing benchmarks with cluster analysis

A preprint version of the article is available at arXiv.


New physics theories often depend on a large number of free parameters. The phenomenology they predict for fundamental physics processes is in some cases drastically affected by the precise value of those free parameters, while in other cases is left basically invariant at the level of detail experimentally accessible. When designing a strategy for the analysis of experimental data in the search for a signal predicted by a new physics model, it appears advantageous to categorize the parameter space describing the model according to the corresponding kinematical features of the final state. A multi-dimensional test statistic can be used to gauge the degree of similarity in the kinematics predicted by different models; a clustering algorithm using that metric may allow the division of the space into homogeneous regions, each of which can be successfully represented by a benchmark point. Searches targeting those benchmarks are then guaranteed to be sensitive to a large area of the parameter space.

In this document we show a practical implementation of the above strategy for the study of non-resonant production of Higgs boson pairs in the context of extensions of the standard model with anomalous couplings of the Higgs bosons. A non-standard value of those couplings may significantly enhance the Higgs boson pair-production cross section, such that the process could be detectable with the data that the LHC will collect in Run 2.


  1. [1]

    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].

  2. [2]

    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].

  3. [3]

    F. Goertz, Electroweak Symmetry Breaking without the μ 2 Term, arXiv:1504.00355 [INSPIRE].

  4. [4]

    E.W.N. Glover and J.J. van der Bij, Higgs boson pair production via gluon fusion, Nucl. Phys. B 309 (1988) 282 [INSPIRE].

    ADS  Article  Google Scholar 

  5. [5]

    S. Dawson, A. Ismail and I. Low, What’s in the loop? The anatomy of double Higgs production, Phys. Rev. D 91 (2015) 115008 [arXiv:1504.05596] [INSPIRE].

    ADS  Google Scholar 

  6. [6]

    A. Azatov, R. Contino, G. Panico and M. Son, Effective field theory analysis of double Higgs boson production via gluon fusion, Phys. Rev. D 92 (2015) 035001 [arXiv:1502.00539] [INSPIRE].

    ADS  Google Scholar 

  7. [7]

    M. Slawinska, W. van den Wollenberg, B. van Eijk and S. Bentvelsen, Phenomenology of the trilinear Higgs coupling at proton-proton colliders, arXiv:1408.5010 [INSPIRE].

  8. [8]

    V. Barger, L.L. Everett, C.B. Jackson and G. Shaughnessy, Higgs-Pair Production and Measurement of the Triscalar Coupling at LHC(8,14), Phys. Lett. B 728 (2014) 433 [arXiv:1311.2931] [INSPIRE].

    ADS  Article  Google Scholar 

  9. [9]

    A.J. Barr, M.J. Dolan, C. Englert, D.E. Ferreira de Lima and M. Spannowsky, Higgs Self-Coupling Measurements at a 100 TeV Hadron Collider, JHEP 02 (2015) 016 [arXiv:1412.7154] [INSPIRE].

    ADS  Article  Google Scholar 

  10. [10]

    N. Liu, S. Hu, B. Yang and J. Han, Impact of top-Higgs couplings on Di-Higgs production at future colliders, JHEP 01 (2015) 008 [arXiv:1408.4191] [INSPIRE].

    ADS  Google Scholar 

  11. [11]

    F. Goertz, A. Papaefstathiou, L.L. Yang and J. Zurita, Higgs boson pair production in the D = 6 extension of the SM,JHEP 04 (2015) 167 [arXiv:1410.3471] [INSPIRE].

    ADS  Article  Google Scholar 

  12. [12]

    C.-R. Chen and I. Low, Double take on new physics in double Higgs boson production, Phys. Rev. D 90 (2014) 013018 [arXiv:1405.7040] [INSPIRE].

    ADS  Google Scholar 

  13. [13]

    M.J. Dolan, C. Englert and M. Spannowsky, New Physics in LHC Higgs boson pair production, Phys. Rev. D 87 (2013) 055002 [arXiv:1210.8166] [INSPIRE].

    ADS  Google Scholar 

  14. [14]

    F. Goertz, A. Papaefstathiou, L.L. Yang and J. Zurita, Higgs Boson self-coupling measurements using ratios of cross sections, JHEP 06 (2013) 016 [arXiv:1301.3492] [INSPIRE].

    ADS  Article  Google Scholar 

  15. [15]

    K. Nishiwaki, S. Niyogi and A. Shivaji, ttH Anomalous Coupling in Double Higgs Production, JHEP 04 (2014) 011 [arXiv:1309.6907] [INSPIRE].

  16. [16]

    W. Yao, Studies of measuring Higgs self-coupling with \( HH\to b\overline{b}\gamma \gamma \) at the future hadron colliders, arXiv:1308.6302 [INSPIRE].

  17. [17]

    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].

    ADS  Article  Google Scholar 

  18. [18]

    D. Wardrope, E. Jansen, N. Konstantinidis, B. Cooper, R. Falla and N. Norjoharuddeen, Non-resonant Higgs-pair production in the \( b\overline{b}\ b\overline{b} \) final state at the LHC, Eur. Phys. J. C 75 (2015) 219 [arXiv:1410.2794] [INSPIRE].

    ADS  Article  Google Scholar 

  19. [19]

    M.J. Dolan, C. Englert, N. Greiner, K. Nordstrom and M. Spannowsky, hhjj production at the LHC, Eur. Phys. J. C 75 (2015) 387 [arXiv:1506.08008] [INSPIRE].

  20. [20]

    H.-J. He, J. Ren and W. Yao, Probing new physics of cubic Higgs boson interaction via Higgs pair production at hadron colliders, Phys. Rev. D 93 (2016) 015003 [arXiv:1506.03302] [INSPIRE].

    ADS  Google Scholar 

  21. [21]

    C.-T. Lu, J. Chang, K. Cheung and J.S. Lee, An exploratory study of Higgs-boson pair production, JHEP 08 (2015) 133 [arXiv:1505.00957] [INSPIRE].

    ADS  Article  Google Scholar 

  22. [22]

    J. Cao, Z. Heng, L. Shang, P. Wan and J.M. Yang, Pair Production of a 125 GeV Higgs Boson in MSSM and NMSSM at the LHC, JHEP 04 (2013) 134 [arXiv:1301.6437] [INSPIRE].

    ADS  Article  Google Scholar 

  23. [23]

    J. Cao, D. Li, L. Shang, P. Wu and Y. Zhang, Exploring the Higgs Sector of a Most Natural NMSSM and its Prediction on Higgs Pair Production at the LHC, JHEP 12 (2014) 026 [arXiv:1409.8431] [INSPIRE].

    ADS  Article  Google Scholar 

  24. [24]

    A. Papaefstathiou, Discovering Higgs boson pair production through rare final states at a 100 TeV collider, Phys. Rev. D 91 (2015) 113016 [arXiv:1504.04621] [INSPIRE].

    ADS  Google Scholar 

  25. [25]

    D.E. Ferreira de Lima, A. Papaefstathiou and M. Spannowsky, Standard model Higgs boson pair production in the \( \left(b\overline{b}\right)\;\left(b\overline{b}\right) \) final state, JHEP 08 (2014) 030 [arXiv:1404.7139] [INSPIRE].

    Article  Google Scholar 

  26. [26]

    P. Maierhöfer and A. Papaefstathiou, Higgs Boson pair production merged to one jet, JHEP 03 (2014) 126 [arXiv:1401.0007] [INSPIRE].

    ADS  Article  Google Scholar 

  27. [27]

    A. Papaefstathiou, L.L. Yang and J. Zurita, Higgs boson pair production at the LHC in the \( b\ \overline{b}\ {W}^{+}{W}^{-} \) channel, Phys. Rev. D 87 (2013) 011301 [arXiv:1209.1489] [INSPIRE].

    ADS  Google Scholar 

  28. [28]

    V. Hankele, G. Klamke, D. Zeppenfeld and T. Figy, Anomalous Higgs boson couplings in vector boson fusion at the CERN LHC, Phys. Rev. D 74 (2006) 095001 [hep-ph/0609075] [INSPIRE].

  29. [29]

    O. Bondu, R. Rosenfeld, V. Sanz, A. Belyaev, A. Massironi and A. Oliveira, Resonant Higgs Pair Production in Vector Boson Fusion at the LHC with di-higgs final states, Les Houches 2013 proceedings, to be published.

  30. [30]

    C. Englert, F. Krauss, M. Spannowsky and J. Thompson, Di-Higgs phenomenology in tthh: The forgotten channel, Phys. Lett. B 743 (2015) 93 [arXiv:1409.8074] [INSPIRE].

    ADS  Article  Google Scholar 

  31. [31]

    T. Liu and H. Zhang, Measuring Di-Higgs Physics via the \( t\overline{t}hh\to t\overline{t}b\overline{b}b\overline{b} \) Channel, arXiv:1410.1855 [INSPIRE].

  32. [32]

    CMS collaboration, Precise determination of the mass of the Higgs boson and tests of compatibility of its couplings with the standard model predictions using proton collisions at 7 and 8 TeV, Eur. Phys. J. C 75 (2015) 212 [arXiv:1412.8662] [INSPIRE].

  33. [33]

    ATLAS collaboration, Measurements of the Higgs boson production and decay rates and coupling strengths using pp collision data at \( \sqrt{s}=7 \) and 8 TeV in the ATLAS experiment, ATLAS-CONF-2015-007 (2015).

  34. [34]

    F. Goertz, Indirect Handle on the Down-Quark Yukawa Coupling, Phys. Rev. Lett. 113 (2014) 261803 [arXiv:1406.0102] [INSPIRE].

    ADS  Article  Google Scholar 

  35. [35]

    G.F. Giudice, C. Grojean, A. Pomarol and R. Rattazzi, The Strongly-Interacting Light Higgs, JHEP 06 (2007) 045 [hep-ph/0703164] [INSPIRE].

  36. [36]

    W. Buchmüller and D. Wyler, Effective Lagrangian Analysis of New Interactions and Flavor Conservation, Nucl. Phys. B 268 (1986) 621 [INSPIRE].

    ADS  Article  Google Scholar 

  37. [37]

    R. Contino, M. Ghezzi, C. Grojean, M. Muhlleitner and M. Spira, Effective Lagrangian for a light Higgs-like scalar, JHEP 07 (2013) 035 [arXiv:1303.3876] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  38. [38]

    M. Gillioz, R. Grober, C. Grojean, M. Muhlleitner and E. Salvioni, Higgs Low-Energy Theorem (and its corrections) in Composite Models, JHEP 10 (2012) 004 [arXiv:1206.7120] [INSPIRE].

    ADS  Article  Google Scholar 

  39. [39]

    T. Plehn, M. Spira and P.M. Zerwas, Pair production of neutral Higgs particles in gluon-gluon collisions, Nucl. Phys. B 479 (1996) 46 [Erratum ibid. B 531 (1998) 655] [hep-ph/9603205] [INSPIRE].

  40. [40]

    A. Belyaev, M. Drees, O.J.P. Eboli, J.K. Mizukoshi and S.F. Novaes, Supersymmetric Higgs pair discovery prospects at hadron colliders, hep-ph/9910400 [INSPIRE].

  41. [41]

    M. Spira and J.D. Wells, Higgs bosons strongly coupled to the top quark, Nucl. Phys. B 523 (1998) 3 [hep-ph/9711410] [INSPIRE].

  42. [42]

    C. Han, X. Ji, L. Wu, P. Wu and J.M. Yang, Higgs pair production with SUSY QCD correction: revisited under current experimental constraints, JHEP 04 (2014) 003 [arXiv:1307.3790] [INSPIRE].

    ADS  Article  Google Scholar 

  43. [43]

    T. Corbett, O.J.P. Eboli, D. Goncalves, J. Gonzalez-Fraile, T. Plehn and M. Rauch, The Higgs Legacy of the LHC Run I, JHEP 08 (2015) 156 [arXiv:1505.05516] [INSPIRE].

    ADS  Article  Google Scholar 

  44. [44]

    M.J. Dugan, H. Georgi and D.B. Kaplan, Anatomy of a Composite Higgs Model, Nucl. Phys. B 254 (1985) 299 [INSPIRE].

    ADS  Article  Google Scholar 

  45. [45]

    A. Falkowski and F. Riva, Model-independent precision constraints on dimension-6 operators, JHEP 02 (2015) 039 [arXiv:1411.0669] [INSPIRE].

    ADS  Article  Google Scholar 

  46. [46]

    A. Falkowski, Effective field theory approach to LHC Higgs data, arXiv:1505.00046 [INSPIRE].

  47. [47]

    M. Duehrssen-Debling, A.T. Mendes, A. Falkowski and G. Isidori., Higgs Basis: Proposal for an EFT basis choice for LHC HXSWG, LHCHXSWG-INT-2015-001 (2015).

  48. [48]

    B. Fuks, F. Maltoni, K. Mawatari, K. Mimasu and V. Sanz, Higgs EFT Rosetta,

  49. [49]

    S. Dawnson et al., LHC Higgs Cross section Working Group HH Cross-group (Higgs Pair Production), Tech. Rep.

  50. [50]

    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].

    Article  Google Scholar 

  51. [51]

    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] [INSPIRE].

    ADS  Article  Google Scholar 

  52. [52]

    D. de Florian and J. Mazzitelli, Next-to-Next-to-Leading Order QCD Corrections to Higgs Boson Pair Production, PoS (LL2014) 029 [arXiv:1405.4704] [INSPIRE].

  53. [53]

    J. Grigo, K. Melnikov and M. Steinhauser, Virtual corrections to Higgs boson pair production in the large top quark mass limit, Nucl. Phys. B 888 (2014) 17 [arXiv:1408.2422] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  54. [54]

    J. Gao et al., CT10 next-to-next-to-leading order global analysis of QCD, Phys. Rev. D 89 (2014) 033009 [arXiv:1302.6246] [INSPIRE].

    ADS  Google Scholar 

  55. [55]

    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].

    ADS  Article  Google Scholar 

  56. [56]

    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].

    ADS  Article  Google Scholar 

  57. [57]

    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].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  58. [58]

    R. Grober, M. Muhlleitner, M. Spira and J. Streicher, NLO QCD Corrections to Higgs Pair Production including Dimension-6 Operators, JHEP 09 (2015) 092 [arXiv:1504.06577] [INSPIRE].

    ADS  Article  Google Scholar 

  59. [59]

    B. Hespel, D. Lopez-Val and E. Vryonidou, Higgs pair production via gluon fusion in the Two-Higgs-Doublet Model, JHEP 09 (2014) 124 [arXiv:1407.0281] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  60. [60]

    S. Frixione, F. Stoeckli, P. Torrielli and B.R. Webber, NLO QCD corrections in HERWIG++ with MC@NLO, JHEP 01 (2011) 053 [arXiv:1010.0568] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  61. [61]

    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].

    ADS  Article  Google Scholar 

  62. [62]

    NNPDF collaboration, R.D. Ball et al., Precision determination of electroweak parameters and the strange content of the proton from neutrino deep-inelastic scattering, Nucl. Phys. B 823 (2009) 195 [arXiv:0906.1958] [INSPIRE].

  63. [63]

    A. Carvalho et al., Analytical Parametrisation and shape classification of anomalous HH production in EFT approach, LHCHXSWG-INT-2016-001 (2016).

  64. [64]

    P. Artoisenet et al., A framework for Higgs characterisation, JHEP 11 (2013) 043 [arXiv:1306.6464] [INSPIRE].

    ADS  Article  Google Scholar 

  65. [65]

    B. Dumont, S. Fichet and G. von Gersdorff, A Bayesian view of the Higgs sector with higher dimensional operators, JHEP 07 (2013) 065 [arXiv:1304.3369] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  66. [66]

    J. Elias-Miro, J.R. Espinosa, E. Masso and A. Pomarol, Higgs windows to new physics through D = 6 operators: constraints and one-loop anomalous dimensions, JHEP 11 (2013) 066 [arXiv:1308.1879] [INSPIRE].

    ADS  Article  Google Scholar 

  67. [67]

    A. Pomarol and F. Riva, Towards the Ultimate SM Fit to Close in on Higgs Physics, JHEP 01 (2014) 151 [arXiv:1308.2803] [INSPIRE].

    ADS  Article  Google Scholar 

  68. [68]

    R.S. Gupta, A. Pomarol and F. Riva, BSM Primary Effects, Phys. Rev. D 91 (2015) 035001 [arXiv:1405.0181] [INSPIRE].

    ADS  Google Scholar 

  69. [69]

    ATLAS collaboration, Search For Higgs Boson Pair Production in the γγbb Final State using pp Collision Data at \( \sqrt{s}=8 \) TeV from the ATLAS Detector, Phys. Rev. Lett. 114 (2015) 081802 [arXiv:1406.5053] [INSPIRE].

  70. [70]

    ATLAS collaboration, Search for Higgs boson pair production in the bbbb final state from pp collisions at \( \sqrt{s}=8 \) TeVwith the ATLAS detector, Eur. Phys. J. C 75 (2015) 412 [arXiv:1506.00285] [INSPIRE].

  71. [71]

    J.C. Collins and D.E. Soper, Angular Distribution of Dileptons in High-Energy Hadron Collisions, Phys. Rev. D 16 (1977) 2219 [INSPIRE].

    ADS  Google Scholar 

  72. [72]

    A.N. Pettitt, A two sample Anderson-Darling rank statistic, Biometrika 63 (1976) 161.

    MathSciNet  MATH  Google Scholar 

  73. [73]

    B. Aslan and G. Zech, A new class of binning free, multivariate goodness of fit tests: The energy tests, hep-ex/0203010 [INSPIRE].

  74. [74]

    S. Baker and R.D. Cousins, Clarification of the Use of Chi Square and Likelihood Functions in Fits to Histograms, Nucl. Instrum. Meth. 221 (1984) 437 [INSPIRE].

    Article  Google Scholar 

  75. [75]

    S. Wilks, The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses, Annals Math. Statist. 9 (1938) 60.

    Article  MATH  Google Scholar 

  76. [76]

    Twiki with the full set of results,

Download references

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.

Author information



Corresponding author

Correspondence to Alexandra Carvalho.

Additional information

ArXiv ePrint: 1507.02245

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Carvalho, A., Dall’Osso, M., Dorigo, T. et al. Higgs pair production: choosing benchmarks with cluster analysis. J. High Energ. Phys. 2016, 126 (2016).

Download citation


  • Beyond Standard Model
  • Higgs Physics