Advertisement

Symmetries and mass degeneracies in the scalar sector

  • Howard E. Haber
  • O. M. OgreidEmail author
  • P. Osland
  • M. N. Rebelo
Open Access
Regular Article - Theoretical Physics

Abstract

We explore some aspects of models with two and three SU(2) scalar doublets that lead to mass degeneracies among some of the physical scalars. In Higgs sectors with two scalar doublets, the exact degeneracy of scalar masses, without an artificial fine-tuning of the scalar potential parameters, is possible only in the case of the inert doublet model (IDM), where the scalar potential respects a global U(1) symmetry that is not broken by the vacuum. In the case of three doublets, we introduce and analyze the replicated inert doublet model, which possesses two inert doublets of scalars. We then generalize this model to obtain a scalar potential, first proposed by Ivanov and Silva, with a CP4 symmetry that guarantees the existence of pairwise degenerate scalar states among two pairs of neutral scalars and two pairs of charged scalars. Here, CP4 is a generalized CP symmetry with the property that (CP4)n is the identity operator only for integer n values that are multiples of 4. The form of the CP4-symmetric scalar potential is simplest when expressed in the Higgs basis, where the neutral scalar field vacuum expectation value resides entirely in one of the scalar doublet fields. The symmetries of the model permit a term in the scalar potential with a complex coefficient that cannot be removed by any redefinition of the scalar fields within the class of Higgs bases (in which case, we say that no real Higgs basis exists). A striking feature of the CP4-symmetric model is that it preserves CP even in the absence of a real Higgs basis, as illustrated by the cancellation of the contributions to the CP violating form factors of the effective ZZZ and ZWW vertices.

Keywords

Beyond Standard Model CP violation Higgs Physics 

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]
    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]
    J.F. Gunion, Y. Jiang and S. Kraml, Could two NMSSM Higgs bosons be present near 125 GeV?, Phys. Rev. D 86 (2012) 071702 [arXiv:1207.1545] [INSPIRE].ADSGoogle Scholar
  4. [4]
    J.F. Gunion, Y. Jiang and S. Kraml, Diagnosing Degenerate Higgs Bosons at 125 GeV, Phys. Rev. Lett. 110 (2013) 051801 [arXiv:1208.1817] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    P.M. Ferreira, R. Santos, H.E. Haber and J.P. Silva, Mass-degenerate Higgs bosons at 125 GeV in the two-Higgs-doublet model, Phys. Rev. D 87 (2013) 055009 [arXiv:1211.3131] [INSPIRE].ADSGoogle Scholar
  6. [6]
    A. Drozd, B. Grzadkowski, J.F. Gunion and Y. Jiang, Two-Higgs-Doublet Models and Enhanced Rates for a 125 GeV Higgs, JHEP 05 (2013) 072 [arXiv:1211.3580] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    Y. Grossman, Z. Surujon and J. Zupan, How to test for mass degenerate Higgs resonances, JHEP 03 (2013) 176 [arXiv:1301.0328] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    S. Munir, L. Roszkowski and S. Trojanowski, Simultaneous enhancement in γγ, \( b\overline{b} \) and τ + τ rates in the NMSSM with nearly degenerate scalar and pseudoscalar Higgs bosons, Phys. Rev. D 88 (2013) 055017 [arXiv:1305.0591] [INSPIRE].ADSGoogle Scholar
  9. [9]
    A. Efrati, D. Grossman and Y. Hochberg, A tale of two Higgs, JHEP 09 (2013) 118 [arXiv:1302.7215] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    A. David, J. Heikkilä and G. Petrucciani, Searching for degenerate Higgs bosons, Eur. Phys. J. C 75 (2015) 49 [arXiv:1409.6132] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    X.-F. Han, L. Wang and J.M. Yang, Higgs pair signal enhanced in the 2HDM with two degenerate 125 GeV Higgs bosons, Mod. Phys. Lett. A 31 (2016) 1650178 [arXiv:1509.02453] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    ATLAS and CMS collaborations, Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at \( \sqrt{s}=7 \) and 8 TeV, JHEP 08 (2016) 045 [arXiv:1606.02266] [INSPIRE].
  13. [13]
    CMS collaboration, Combined measurements of Higgs boson couplings in proton-proton collisions at \( \sqrt{s}=13 \) TeV, submitted to Eur. Phys. J. (2018) [arXiv:1809.10733] [INSPIRE].
  14. [14]
    ATLAS collaboration, Combined measurements of Higgs boson production and decay using up to 80 fb −1 of proton-proton collision data at \( \sqrt{s}=13 \) TeV collected with the ATLAS experiment, ATLAS-CONF-2018-031.
  15. [15]
    L. Bian, N. Chen, W. Su, Y. Wu and Y. Zhang, Future prospects of mass-degenerate Higgs bosons in the CP -conserving two-Higgs-doublet model, Phys. Rev. D 97 (2018) 115007 [arXiv:1712.01299] [INSPIRE].ADSGoogle Scholar
  16. [16]
    J.F. Donoghue and L.F. Li, Properties of Charged Higgs Bosons, Phys. Rev. D 19 (1979) 945 [INSPIRE].ADSGoogle Scholar
  17. [17]
    H. Georgi and D.V. Nanopoulos, Suppression of Flavor Changing Effects From Neutral Spinless Meson Exchange in Gauge Theories, Phys. Lett. B 82 (1979) 95 [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    F.J. Botella and J.P. Silva, Jarlskog-like invariants for theories with scalars and fermions, Phys. Rev. D 51 (1995) 3870 [hep-ph/9411288] [INSPIRE].
  19. [19]
    G.C. Branco, L. Lavoura and J.P. Silva, CP Violation, Oxford University Press, Oxford, U.K. (1999) [INSPIRE].Google Scholar
  20. [20]
    S. Davidson and H.E. Haber, Basis-independent methods for the two-Higgs-doublet model, Phys. Rev. D 72 (2005) 035004 [Erratum ibid. D 72 (2005) 099902] [hep-ph/0504050] [INSPIRE].
  21. [21]
    O.M. Ogreid, P. Osland and M.N. Rebelo, A Simple Method to detect spontaneous CP-violation in multi-Higgs models, JHEP 08 (2017) 005 [arXiv:1701.04768] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson, The Higgs Hunters Guide, Westview Press, Boulder, CO (2000) [INSPIRE].Google Scholar
  23. [23]
    G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva, Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1 [arXiv:1106.0034] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    J.M. Gerard and M. Herquet, A Twisted custodial symmetry in the two-Higgs-doublet model, Phys. Rev. Lett. 98 (2007) 251802 [hep-ph/0703051] [INSPIRE].
  25. [25]
    H.E. Haber and D. O’Neil, Basis-independent methods for the two-Higgs-doublet model III: The CP-conserving limit, custodial symmetry and the oblique parameters S, T, U, Phys. Rev. D 83 (2011) 055017 [arXiv:1011.6188] [INSPIRE].ADSGoogle Scholar
  26. [26]
    B. Grzadkowski, M. Maniatis and J. Wudka, The bilinear formalism and the custodial symmetry in the two-Higgs-doublet model, JHEP 11 (2011) 030 [arXiv:1011.5228] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  27. [27]
    C.C. Nishi, Custodial SO(4) symmetry and CP-violation in N-Higgs-doublet potentials, Phys. Rev. D 83 (2011) 095005 [arXiv:1103.0252] [INSPIRE].ADSGoogle Scholar
  28. [28]
    E. Ma, Verifiable radiative seesaw mechanism of neutrino mass and dark matter, Phys. Rev. D 73 (2006) 077301 [hep-ph/0601225] [INSPIRE].
  29. [29]
    R. Barbieri, L.J. Hall and V.S. Rychkov, Improved naturalness with a heavy Higgs: An Alternative road to LHC physics, Phys. Rev. D 74 (2006) 015007 [hep-ph/0603188] [INSPIRE].
  30. [30]
    I.P. Ivanov and J.P. Silva, CP-conserving multi-Higgs model with irremovable complex coefficients, Phys. Rev. D 93 (2016) 095014 [arXiv:1512.09276] [INSPIRE].ADSGoogle Scholar
  31. [31]
    M. Köpke, Investigation of the GCP Structure of Three-Higgs-Doublet Models and a General Method to Derive Boundedness Constraints for Multi-Higgs Potentials, MSc Thesis, Karlsruhe Instititue of Theoretical Physics (KIT), 14 February 2018 [INSPIRE].
  32. [32]
    I.P. Ivanov, C.C. Nishi, J.P. Silva and A. Trautner, Basis-invariant conditions for CP symmetry of order 4, arXiv:1810.13396 [INSPIRE].
  33. [33]
    N. Craig, J. Galloway and S. Thomas, Searching for Signs of the Second Higgs Doublet, arXiv:1305.2424 [INSPIRE].
  34. [34]
    H.E. Haber, The Higgs data and the Decoupling Limit, in Proceedings, 1st Toyama International Workshop on Higgs as a Probe of New Physics 2013 (HPNP2013), Toyama, Japan, February 13–16, 2013 [arXiv:1401.0152] [INSPIRE].
  35. [35]
    D.M. Asner et al., ILC Higgs White Paper, in Proceedings, 2013 Community Summer Study on the Future of U.S. Particle Physics: Snowmass on the Mississippi (CSS2013), Minneapolis, MN, U.S.A., July 29–August 6, 2013 (2013) [arXiv:1310.0763] [INSPIRE].
  36. [36]
    M. Carena, I. Low, N.R. Shah and C.E.M. Wagner, Impersonating the Standard Model Higgs Boson: Alignment without Decoupling, JHEP 04 (2014) 015 [arXiv:1310.2248] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    M. Carena, H.E. Haber, I. Low, N.R. Shah and C.E.M. Wagner, Complementarity between Nonstandard Higgs Boson Searches and Precision Higgs Boson Measurements in the MSSM, Phys. Rev. D 91 (2015) 035003 [arXiv:1410.4969] [INSPIRE].ADSGoogle Scholar
  38. [38]
    P.S. Bhupal Dev and A. Pilaftsis, Maximally Symmetric Two Higgs Doublet Model with Natural Standard Model Alignment, JHEP 12 (2014) 024 [Erratum ibid. 11 (2015) 147] [arXiv:1408.3405] [INSPIRE].
  39. [39]
    J. Bernon, J.F. Gunion, H.E. Haber, Y. Jiang and S. Kraml, Scrutinizing the alignment limit in two-Higgs-doublet models: m h = 125 GeV, Phys. Rev. D 92 (2015) 075004 [arXiv:1507.00933] [INSPIRE].ADSGoogle Scholar
  40. [40]
    J. Bernon, J.F. Gunion, H.E. Haber, Y. Jiang and S. Kraml, Scrutinizing the alignment limit in two-Higgs-doublet models. II. m H = 125 GeV, Phys. Rev. D 93 (2016) 035027 [arXiv:1511.03682] [INSPIRE].
  41. [41]
    A. Pilaftsis, Symmetries for standard model alignment in multi-Higgs doublet models, Phys. Rev. D 93 (2016) 075012 [arXiv:1602.02017] [INSPIRE].ADSGoogle Scholar
  42. [42]
    L. Lavoura and J.P. Silva, Fundamental CP-violating quantities in a SU(2) × U(1) model with many Higgs doublets, Phys. Rev. D 50 (1994) 4619 [hep-ph/9404276] [INSPIRE].
  43. [43]
    T.D. Lee, A Theory of Spontaneous T Violation, Phys. Rev. D 8 (1973) 1226 [INSPIRE].ADSGoogle Scholar
  44. [44]
    G.C. Branco and M.N. Rebelo, The Higgs Mass in a Model With Two Scalar Doublets and Spontaneous CP Violation, Phys. Lett. B 160 (1985) 117 [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    G.C. Branco, M.N. Rebelo and J.I. Silva-Marcos, CP-odd invariants in models with several Higgs doublets, Phys. Lett. B 614 (2005) 187 [hep-ph/0502118] [INSPIRE].
  46. [46]
    J.F. Gunion and H.E. Haber, Conditions for CP-violation in the general two-Higgs-doublet model, Phys. Rev. D 72 (2005) 095002 [hep-ph/0506227] [INSPIRE].
  47. [47]
    B. Grzadkowski, O.M. Ogreid and P. Osland, Spontaneous CP-violation in the 2HDM: physical conditions and the alignment limit, Phys. Rev. D 94 (2016) 115002 [arXiv:1609.04764] [INSPIRE].ADSGoogle Scholar
  48. [48]
    A. Mendez and A. Pomarol, Signals of CP-violation in the Higgs sector, Phys. Lett. B 272 (1991) 313 [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    H.E. Haber and D. O’Neil, Basis-independent methods for the two-Higgs-doublet model. II. The Significance of tanβ, Phys. Rev. D 74 (2006) 015018 [Erratum ibid. D 74 (2006) 059905] [hep-ph/0602242] [INSPIRE].
  50. [50]
    B. Grzadkowski, O.M. Ogreid and P. Osland, Measuring CP-violation in Two-Higgs-Doublet models in light of the LHC Higgs data, JHEP 11 (2014) 084 [arXiv:1409.7265] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    G.C. Branco, I. de Medeiros Varzielas and S.F. King, Invariant approach to \( \mathcal{C}\mathcal{P} \) in unbroken Δ(27), Nucl. Phys. B 899 (2015) 14 [arXiv:1505.06165] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  52. [52]
    I. de Medeiros Varzielas, S.F. King, C. Luhn and T. Neder, CP-odd invariants for multi-Higgs models: applications with discrete symmetry, Phys. Rev. D 94 (2016) 056007 [arXiv:1603.06942] [INSPIRE].ADSMathSciNetGoogle Scholar
  53. [53]
    I. de Medeiros Varzielas, S.F. King, C. Luhn and T. Neder, Spontaneous CP-violation in multi-Higgs potentials with triplets of Δ(3n 2) and Δ(6n 2), JHEP 11 (2017) 136 [arXiv:1706.07606] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    N.G. Deshpande and E. Ma, Pattern of Symmetry Breaking with Two Higgs Doublets, Phys. Rev. D 18 (1978) 2574 [INSPIRE].ADSGoogle Scholar
  55. [55]
    I.P. Ivanov, Minkowski space structure of the Higgs potential in 2HDM. II. Minima, symmetries and topology, Phys. Rev. D 77 (2008) 015017 [arXiv:0710.3490] [INSPIRE].
  56. [56]
    P.M. Ferreira, H.E. Haber and J.P. Silva, Generalized CP symmetries and special regions of parameter space in the two-Higgs-doublet model, Phys. Rev. D 79 (2009) 116004 [arXiv:0902.1537] [INSPIRE].ADSGoogle Scholar
  57. [57]
    P.M. Ferreira, H.E. Haber, M. Maniatis, O. Nachtmann and J.P. Silva, Geometric picture of generalized-CP and Higgs-family transformations in the two-Higgs-doublet model, Int. J. Mod. Phys. A 26 (2011) 769 [arXiv:1010.0935] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  58. [58]
    R.A. Battye, G.D. Brawn and A. Pilaftsis, Vacuum Topology of the Two Higgs Doublet Model, JHEP 08 (2011) 020 [arXiv:1106.3482] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  59. [59]
    A. Pilaftsis, On the Classification of Accidental Symmetries of the Two Higgs Doublet Model Potential, Phys. Lett. B 706 (2012) 465 [arXiv:1109.3787] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    R.D. Peccei and H.R. Quinn, Constraints Imposed by CP Conservation in the Presence of Instantons, Phys. Rev. D 16 (1977) 1791 [INSPIRE].ADSGoogle Scholar
  61. [61]
    S. Weinberg, A New Light Boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    F. Wilczek, Problem of Strong P and T Invariance in the Presence of Instantons, Phys. Rev. Lett. 40 (1978) 279 [INSPIRE].ADSCrossRefGoogle Scholar
  63. [63]
    H.E. Haber and O. Stal, New LHC benchmarks for the \( \mathcal{C}\mathcal{P} \) -conserving two-Higgs-doublet model, Eur. Phys. J. C 75 (2015) 491 [Erratum ibid. C 76 (2016) 312] [arXiv:1507.04281] [INSPIRE].
  64. [64]
    L.J. Hall and M.B. Wise, Flavor changing Higgs boson couplings, Nucl. Phys. B 187 (1981) 397 [INSPIRE].ADSCrossRefGoogle Scholar
  65. [65]
    K. Olaussen, P. Osland and M.A. Solberg, Symmetry and Mass Degeneration in Multi-Higgs-Doublet Models, JHEP 07 (2011) 020 [arXiv:1007.1424] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  66. [66]
    A. Aranda, I.P. Ivanov and E. Jiménez, When the C in CP does not matter: anatomy of order-4 CP eigenstates and their Yukawa interactions, Phys. Rev. D 95 (2017) 055010 [arXiv:1608.08922] [INSPIRE].ADSGoogle Scholar
  67. [67]
    H. Ishimori, T. Kobayashi, H. Ohki, H. Okada, Y. Shimizu and M. Tanimoto, An introduction to non-Abelian discrete symmetries for particle physicists, Lect. Notes Phys. 858 (2012) 1 [INSPIRE].MathSciNetzbMATHGoogle Scholar
  68. [68]
    I.P. Ivanov and E. Vdovin, Discrete symmetries in the three-Higgs-doublet model, Phys. Rev. D 86 (2012) 095030 [arXiv:1206.7108] [INSPIRE].ADSGoogle Scholar
  69. [69]
    I.P. Ivanov and E. Vdovin, Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model, Eur. Phys. J. C 73 (2013) 2309 [arXiv:1210.6553] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    P.M. Ferreira, I.P. Ivanov, E. Jiménez, R. Pasechnik and H. Serôdio, CP4 miracle: shaping Yukawa sector with CP symmetry of order four, JHEP 01 (2018) 065 [arXiv:1711.02042] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    I.P. Ivanov, Radiative neutrino masses from order-4 CP symmetry, JHEP 02 (2018) 025 [arXiv:1712.02101] [INSPIRE].ADSCrossRefGoogle Scholar
  72. [72]
    I.P. Ivanov and M. Laletin, Multi-Higgs models with CP-symmetries of increasingly high order, Phys. Rev. D 98 (2018) 015021 [arXiv:1804.03083] [INSPIRE].ADSGoogle Scholar
  73. [73]
    B. Grzadkowski, O.M. Ogreid and P. Osland, CP-Violation in the ZZZ and ZWW vertices at e + e colliders in Two-Higgs-Doublet Models, JHEP 05 (2016) 025 [Erratum ibid. 11 (2017) 002] [arXiv:1603.01388] [INSPIRE].
  74. [74]
    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
  75. [75]
    J.F. Nieves and P.B. Pal, Electromagnetic properties of neutral and charged spin 1 particles, Phys. Rev. D 55 (1997) 3118 [hep-ph/9611431] [INSPIRE].
  76. [76]
    G.J. Gounaris, J. Layssac and F.M. Renard, Signatures of the anomalous Zγ and ZZ production at the lepton and hadron colliders, Phys. Rev. D 61 (2000) 073013 [hep-ph/9910395] [INSPIRE].
  77. [77]
    G.J. Gounaris, J. Layssac and F.M. Renard, Off-shell structure of the anomalous Z and γ self-couplings, Phys. Rev. D 62 (2000) 073012 [Addendum ibid. D 65 (2002) 017302] [hep-ph/0005269] [INSPIRE].
  78. [78]
    U. Baur and D.L. Rainwater, Probing neutral gauge boson self-interactions in ZZ production at hadron colliders, Phys. Rev. D 62 (2000) 113011 [hep-ph/0008063] [INSPIRE].
  79. [79]
    T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
  80. [80]
    H.K. Dreiner, H.E. Haber and S.P. Martin, Two-component spinor techniques and Feynman rules for quantum field theory and supersymmetry, Phys. Rept. 494 (2010) 1 [arXiv:0812.1594] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  81. [81]
    M.P. Bento, H.E. Haber, J.C. Romão and J.P. Silva, Multi-Higgs doublet models: physical parametrization, sum rules and unitarity bounds, JHEP 11 (2017) 095 [arXiv:1708.09408] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  82. [82]
    H.E. Haber and Y. Nir, \( Z\to {A}^0{A}^0\nu \overline{\nu} \) and e + e A 0 A 0 Z in two Higgs doublet models, Phys. Lett. B 306 (1993) 327 [hep-ph/9302228] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Santa Cruz Institute for Particle PhysicsSanta CruzU.S.A.
  2. 2.Western Norway University of Applied SciencesBergenNorway
  3. 3.Department of Physics and TechnologyUniversity of BergenBergenNorway
  4. 4.Departamento de Física and Centro de Física Teórica de Partículas (CFTP)Instituto Superior TécnicoLisboaPortugal

Personalised recommendations