General composite Higgs models

  • David Marzocca
  • Marco SeroneEmail author
  • Jing Shu


We construct a general class of pseudo-Goldstone composite Higgs models, within the minimal SO(5)/SO(4) coset structure, that are not necessarily of moose-type. We characterize the main properties these models should have in order to give rise to a Higgs mass around 125 GeV. We assume the existence of relatively light and weakly coupled spin 1 and 1/2 resonances. In absence of a symmetry principle, we introduce the Minimal Higgs Potential (MHP) hypothesis: the Higgs potential is assumed to be one-loop dominated by the SM fields and the above resonances, with a contribution that is made calculable by imposing suitable generalizations of the first and second Weinberg sum rules. We show that a 125 GeV Higgs requires light, often sub-TeV, fermion resonances. Their presence can also be important for the models to successfully pass the electroweak precision tests. Interestingly enough, the latter can also be passed by models with a heavy Higgs around 320 GeV. The composite Higgs models of the moose-type considered in the literature can be seen as particular limits of our class of models.


Beyond Standard Model Technicolor and Composite Models Higgs Physics 


  1. [1]
    D.B. Kaplan and H. Georgi, SU(2) × U(1) Breaking by Vacuum Misalignment, Phys. Lett. B 136 (1984) 183 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    M.J. Dugan, H. Georgi and D.B. Kaplan, Anatomy of a Composite Higgs Model, Nucl. Phys. B 254 (1985) 299 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 1., Phys. Rev. 177 (1969) 2239 [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    C.G. Callan Jr., S.R. Coleman, J. Wess and B. Zumino, Structure of phenomenological Lagrangians. 2., Phys. Rev. 177 (1969) 2247 [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    G. Giudice, C. Grojean, A. Pomarol and R. Rattazzi, The Strongly-Interacting Light Higgs, JHEP 06 (2007) 045 [hep-ph/0703164] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    H. Hatanaka, T. Inami and C. Lim, The Gauge hierarchy problem and higher dimensional gauge theories, Mod. Phys. Lett. A 13 (1998) 2601 [hep-th/9805067] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    L.J. Hall, Y. Nomura and D. Tucker-Smith, Gauge Higgs unification in higher dimensions, Nucl. Phys. B 639 (2002) 307 [hep-ph/0107331] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    M. Kubo, C. Lim and H. Yamashita, The Hosotani mechanism in bulk gauge theories with an orbifold extra space S 1/Z 2, Mod. Phys. Lett. A 17 (2002) 2249 [hep-ph/0111327] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    G. Burdman and Y. Nomura, Unification of Higgs and gauge fields in five-dimensions, Nucl. Phys. B 656 (2003) 3 [hep-ph/0210257] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    C.A. Scrucca, M. Serone and L. Silvestrini, Electroweak symmetry breaking and fermion masses from extra dimensions, Nucl. Phys. B 669 (2003) 128 [hep-ph/0304220] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    R. Contino, Y. Nomura and A. Pomarol, Higgs as a holographic pseudo-Goldstone boson, Nucl. Phys. B 671 (2003) 148 [hep-ph/0306259] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    Y. Hosotani and M. Mabe, Higgs boson mass and electroweak-gravity hierarchy from dynamical gauge-Higgs unification in the warped spacetime, Phys. Lett. B 615 (2005) 257 [hep-ph/0503020] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    G. Panico, M. Serone and A. Wulzer, A Model of electroweak symmetry breaking from a fifth dimension, Nucl. Phys. B 739 (2006) 186 [hep-ph/0510373] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    G. Panico, M. Serone and A. Wulzer, Electroweak Symmetry Breaking and Precision Tests with a Fifth Dimension, Nucl. Phys. B 762 (2007) 189 [hep-ph/0605292] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    G. Cacciapaglia, C. Csáki and S.C. Park, Fully radiative electroweak symmetry breaking, JHEP 03 (2006) 099 [hep-ph/0510366] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    R. Contino, L. Da Rold and A. Pomarol, Light custodians in natural composite Higgs models, Phys. Rev. D 75 (2007) 055014 [hep-ph/0612048] [INSPIRE].ADSGoogle Scholar
  17. [17]
    A.D. Medina, N.R. Shah and C.E. Wagner, Gauge-Higgs Unification and Radiative Electroweak Symmetry Breaking in Warped Extra Dimensions, Phys. Rev. D 76 (2007) 095010 [arXiv:0706.1281] [INSPIRE].ADSGoogle Scholar
  18. [18]
    G. Panico, E. Ponton, J. Santiago and M. Serone, Dark Matter and Electroweak Symmetry Breaking in Models with Warped Extra Dimensions, Phys. Rev. D 77 (2008) 115012 [arXiv:0801.1645] [INSPIRE].ADSGoogle Scholar
  19. [19]
    K. Agashe, R. Contino and A. Pomarol, The Minimal composite Higgs model, Nucl. Phys. B 719 (2005) 165 [hep-ph/0412089] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    G. Panico and A. Wulzer, The Discrete Composite Higgs Model, JHEP 09 (2011) 135 [arXiv:1106.2719] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    S. De Curtis, M. Redi and A. Tesi, The 4D Composite Higgs, JHEP 04 (2012) 042 [arXiv:1110.1613] [INSPIRE].CrossRefGoogle Scholar
  22. [22]
    N. Arkani-Hamed, A.G. Cohen and H. Georgi, (De)constructing dimensions, Phys. Rev. Lett. 86 (2001) 4757 [hep-th/0104005] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    N. Arkani-Hamed, A.G. Cohen and H. Georgi, Electroweak symmetry breaking from dimensional deconstruction, Phys. Lett. B 513 (2001) 232 [hep-ph/0105239] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    D.B. Kaplan, Flavor at SSC energies: A New mechanism for dynamically generated fermion masses, Nucl. Phys. B 365 (1991) 259 [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    Y. Grossman and M. Neubert, Neutrino masses and mixings in nonfactorizable geometry, Phys. Lett. B 474 (2000) 361 [hep-ph/9912408] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    T. Gherghetta and A. Pomarol, Bulk fields and supersymmetry in a slice of AdS, Nucl. Phys. B 586 (2000) 141 [hep-ph/0003129] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    S.J. Huber and Q. Shafi, Fermion masses, mixings and proton decay in a Randall-Sundrum model, Phys. Lett. B 498 (2001) 256 [hep-ph/0010195] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    ATLAS collaboration, G. Aad et al., Search for the Standard Model Higgs boson in the diphoton decay channel with 4.9 fb −1 of pp collisions at \( \sqrt {s} = {7} \) TeV with ATLAS, Phys. Rev. Lett. 108 (2012) 111803 [arXiv:1202.1414] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    CMS collaboration, S. Chatrchyan et al., Search for the standard model Higgs boson decaying into two photons in pp collisions at \( \sqrt {s} = {7} \) TeV, Phys. Lett. B 710 (2012) 403 [arXiv:1202.1487] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    W. Fisher for the CDF and D0 collaborations, Seeking the Brout-Englert-Higgs Boson: New Results from Tevatron Experiments, talk given at Rencontres de Moriond 2012, La Thuile (Aosta), Italy, 7 march 2012,
  31. [31]
    A. Azatov, R. Contino and J. Galloway, Model-Independent Bounds on a Light Higgs, JHEP 04 (2012) 127 [arXiv:1202.3415] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    J. Espinosa, C. Grojean and M. Muhlleitner, Composite Higgs Search at the LHC, JHEP 05 (2010) 065 [arXiv:1003.3251] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    J. Espinosa, C. Grojean and M. Muhlleitner, Composite Higgs under LHC Experimental Scrutiny, EPJ Web Conf. 28 (2012) 08004 [arXiv:1202.1286] [INSPIRE].CrossRefGoogle Scholar
  34. [34]
    J. Espinosa, C. Grojean, M. Muhlleitner and M. Trott, Fingerprinting Higgs Suspects at the LHC, JHEP 05 (2012) 097 [arXiv:1202.3697] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    S. Weinberg, Precise relations between the spectra of vector and axial vector mesons, Phys. Rev. Lett. 18 (1967) 507 [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    R. Contino, The Higgs as a Composite Nambu-Goldstone Boson, arXiv:1005.4269 [INSPIRE].
  37. [37]
    CMS collaboration, S. Chatrchyan et al., Search for heavy bottom-like quarks in 4.9 inverse femtobarns of pp collisions at \( \sqrt {s} = {7} \) TeV, JHEP 05 (2012) 123 [arXiv:1204.1088] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    CMS collaboration, S. Chatrchyan et al., Search for heavy, top-like quark pair production in the dilepton final state in pp collisions at \( \sqrt {s} = {7} \) TeV, arXiv:1203.5410 [INSPIRE].
  39. [39]
    G. Ecker, J. Gasser, H. Leutwyler, A. Pich and E. de Rafael, Chiral Lagrangians for Massive Spin 1 Fields, Phys. Lett. B 223 (1989) 425 [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    R. Contino, T. Kramer, M. Son and R. Sundrum, Warped/composite phenomenology simplified, JHEP 05 (2007) 074 [hep-ph/0612180] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    R. Contino, D. Marzocca, D. Pappadopulo and R. Rattazzi, On the effect of resonances in composite Higgs phenomenology, JHEP 10 (2011) 081 [arXiv:1109.1570] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    K. Agashe, R. Contino, L. Da Rold and A. Pomarol, A Custodial symmetry for \( Zb\overline b \), Phys. Lett. B 641 (2006) 62 [hep-ph/0605341] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    M.E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections, Phys. Rev. D 46 (1992) 381 [INSPIRE].ADSGoogle Scholar
  44. [44]
    A. Orgogozo and S. Rychkov, Exploring T and S parameters in Vector Meson Dominance Models of Strong Electroweak Symmetry Breaking, JHEP 03 (2012) 046 [arXiv:1111.3534] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    E. Witten, Some Inequalities Among Hadron Masses, Phys. Rev. Lett. 51 (1983) 2351 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  46. [46]
    M. Serone, Holographic Methods and Gauge-Higgs Unification in Flat Extra Dimensions, New J. Phys. 12 (2010) 075013 [arXiv:0909.5619] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    G. Panico, M. Safari and M. Serone, Simple and Realistic Composite Higgs Models in Flat Extra Dimensions, JHEP 02 (2011) 103 [arXiv:1012.2875] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    G. Altarelli and R. Barbieri, Vacuum polarization effects of new physics on electroweak processes, Phys. Lett. B 253 (1991) 161 [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    G. Altarelli, R. Barbieri and S. Jadach, Toward a model independent analysis of electroweak data, Nucl. Phys. B 369 (1992) 3 [Erratum ibid. B 376 (1992) 444] [INSPIRE].
  50. [50]
    G. Altarelli, R. Barbieri and F. Caravaglios, Nonstandard analysis of electroweak precision data, Nucl. Phys. B 405 (1993) 3 [INSPIRE].ADSGoogle Scholar
  51. [51]
    Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    A. Wulzer, Modeling and Testing a Composite Higgs, talk at Workshop on Strongly Coupled Physics Beyond the Standard Model, ICTP, Trieste, Itlay, 25–27 January 2012.Google Scholar
  53. [53]
    B. Gripaios, A. Pomarol, F. Riva and J. Serra, Beyond the Minimal Composite Higgs Model, JHEP 04 (2009) 070 [arXiv:0902.1483] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    J. Mrazek, A. Pomarol, R. Rattazzi, M. Redi, J. Serra and A. Wulzer, The Other Natural Two Higgs Doublet Model, Nucl. Phys. B 853 (2011) 1 [arXiv:1105.5403] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    O. Matsedonskyi, G. Panico and A. Wulzer, Light Top Partners for a Light Composite Higgs, arXiv:1204.6333 [INSPIRE].
  56. [56]
    M. Redi and A. Tesi, Implications of a Light Higgs in Composite Models, arXiv:1205.0232 [INSPIRE].
  57. [57]
    R. Barbieri, A. Pomarol, R. Rattazzi and A. Strumia, Electroweak symmetry breaking after LEP-1 and LEP-2, Nucl. Phys. B 703 (2004) 127 [hep-ph/0405040] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    M.S. Carena, E. Ponton, J. Santiago and C.E. Wagner, Light Kaluza Klein States in Randall-Sundrum Models with Custodial SU(2), Nucl. Phys. B 759 (2006) 202 [hep-ph/0607106] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  59. [59]
    M.S. Carena, E. Ponton, J. Santiago and C. Wagner, Electroweak constraints on warped models with custodial symmetry, Phys. Rev. D 76 (2007) 035006 [hep-ph/0701055] [INSPIRE].ADSGoogle Scholar
  60. [60]
    R. Barbieri, B. Bellazzini, V.S. Rychkov and A. Varagnolo, The Higgs boson from an extended symmetry, Phys. Rev. D 76 (2007) 115008 [arXiv:0706.0432] [INSPIRE].ADSGoogle Scholar
  61. [61]
    CDF and D0 collaboration, T.E.W. Group, Combination of CDF and D0 Results on the Mass of the Top Quark, arXiv:0903.2503 [INSPIRE].
  62. [62]
    K. Aoki, Z. Hioki, M. Konuma, R. Kawabe and T. Muta, Electroweak Theory. Framework of On-Shell Renormalization and Study of Higher Order Effects, Prog. Theor. Phys. Suppl. 73 (1982) 1 [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.SISSA and INFNTriesteItaly
  2. 2.ICTPTriesteItaly

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