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Journal of High Energy Physics

, 2019:130 | Cite as

Vacuum alignment in a composite 2HDM

  • Chengfeng Cai
  • Hong-Hao Zhang
  • Giacomo CacciapagliaEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We study in detail the vacuum structure of a composite two Higgs doublet model based on a minimal underlying theory with 3 Dirac fermions in pseudo-real representations of the condensing gauge interactions, leading to the SU(6)/Sp(6) symmetry breaking pattern. We find that, independently on the source of top mass, the most general CP-conserving vacuum is characterised by three non-vanishing angles. A special case occurs if the Yukawas are aligned, leading to a single angle. In the latter case, a Dark Matter candidate arises, protected by a global U(1) symmetry.

Keywords

Beyond Standard Model Technicolor and Composite Models 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]
    P.W. Higgs, Broken Symmetries and the Masses of Gauge Bosons, Phys. Rev. Lett. 13 (1964) 508 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    S. Weinberg, Implications of Dynamical Symmetry Breaking, Phys. Rev. D 13 (1976) 974 [INSPIRE].ADSGoogle Scholar
  3. [3]
    S. Dimopoulos and L. Susskind, Mass Without Scalars, Nucl. Phys. B 155 (1979) 237 [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    F. Sannino and K. Tuominen, Orientifold theory dynamics and symmetry breaking, Phys. Rev. D 71 (2005) 051901 [hep-ph/0405209] [INSPIRE].
  5. [5]
    S. Catterall and F. Sannino, Minimal walking on the lattice, Phys. Rev. D 76 (2007) 034504 [arXiv:0705.1664] [INSPIRE].ADSGoogle Scholar
  6. [6]
    J. Rantaharju, C. Pica and F. Sannino, Ideal Walking Dynamics via a Gauged NJLS Model, Phys. Rev. D 96 (2017) 014512 [arXiv:1704.03977] [INSPIRE].ADSGoogle Scholar
  7. [7]
    R. Foadi, M.T. Frandsen and F. Sannino, 125 GeV Higgs boson from a not so light technicolor scalar, Phys. Rev. D 87 (2013) 095001 [arXiv:1211.1083] [INSPIRE].ADSGoogle Scholar
  8. [8]
    D.B. Kaplan and H. Georgi, SU(2) × U(1) Breaking by Vacuum Misalignment, Phys. Lett. B 136 (1984) 183 [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    D.B. Kaplan, H. Georgi and S. Dimopoulos, Composite Higgs Scalars, Phys. Lett. B 136 (1984) 187 [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    J.M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    R. Contino, Y. Nomura and A. Pomarol, Higgs as a holographic pseudoGoldstone boson, Nucl. Phys. B 671 (2003) 148 [hep-ph/0306259] [INSPIRE].
  12. [12]
    R. Contino, The Higgs as a Composite Nambu-Goldstone Boson, in Physics of the large and the small, TASI 09, proceedings of the Theoretical Advanced Study Institute in Elementary Particle Physics, Boulder, Colorado, U.S.A., 1–26 June 2009, pp. 235–306 (2011) [ https://doi.org/10.1142/9789814327183_0005] [arXiv:1005.4269] [INSPIRE].
  13. [13]
    B. Bellazzini, C. Csáki and J. Serra, Composite Higgses, Eur. Phys. J. C 74 (2014) 2766 [arXiv:1401.2457] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    G. Panico and A. Wulzer, The Composite Nambu-Goldstone Higgs, Lect. Notes Phys. 913 (2016) 1 [arXiv:1506.01961] [INSPIRE].CrossRefzbMATHGoogle Scholar
  15. [15]
    G. Cacciapaglia and F. Sannino, Fundamental Composite (Goldstone) Higgs Dynamics, JHEP 04 (2014) 111 [arXiv:1402.0233] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  16. [16]
    K. Agashe, R. Contino and A. Pomarol, The Minimal composite Higgs model, Nucl. Phys. B 719 (2005) 165 [hep-ph/0412089] [INSPIRE].
  17. [17]
    F. Caracciolo, A. Parolini and M. Serone, UV Completions of Composite Higgs Models with Partial Compositeness, JHEP 02 (2013) 066 [arXiv:1211.7290] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    G. von Gersdorff, E. Pontón and R. Rosenfeld, The Dynamical Composite Higgs, JHEP 06 (2015) 119 [arXiv:1502.07340] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    E. Katz, A.E. Nelson and D.G.E. Walker, The Intermediate Higgs, JHEP 08 (2005) 074 [hep-ph/0504252] [INSPIRE].
  20. [20]
    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
  21. [21]
    M. Frigerio, A. Pomarol, F. Riva and A. Urbano, Composite Scalar Dark Matter, JHEP 07 (2012) 015 [arXiv:1204.2808] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    T.A. Ryttov and F. Sannino, Ultra Minimal Technicolor and its Dark Matter TIMP, Phys. Rev. D 78 (2008) 115010 [arXiv:0809.0713] [INSPIRE].ADSGoogle Scholar
  23. [23]
    J. Galloway, J.A. Evans, M.A. Luty and R.A. Tacchi, Minimal Conformal Technicolor and Precision Electroweak Tests, JHEP 10 (2010) 086 [arXiv:1001.1361] [INSPIRE].zbMATHGoogle Scholar
  24. [24]
    A. Hietanen, R. Lewis, C. Pica and F. Sannino, Fundamental Composite Higgs Dynamics on the Lattice: SU(2) with Two Flavors, JHEP 07 (2014) 116 [arXiv:1404.2794] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    V. Drach, A. Hietanen, C. Pica, J. Rantaharju and F. Sannino, Template Composite Dark Matter: SU(2) gauge theory with 2 fundamental flavours, PoS(LATTICE2015)234 (2016) [arXiv:1511.04370] [INSPIRE].
  26. [26]
    R. Arthur, V. Drach, M. Hansen, A. Hietanen, C. Pica and F. Sannino, SU(2) gauge theory with two fundamental flavors: A minimal template for model building, Phys. Rev. D 94 (2016) 094507 [arXiv:1602.06559] [INSPIRE].ADSGoogle Scholar
  27. [27]
    R. Arthur, V. Drach, A. Hietanen, C. Pica and F. Sannino, SU(2) Gauge Theory with Two Fundamental Flavours: Scalar and Pseudoscalar Spectrum, arXiv:1607.06654 [INSPIRE].
  28. [28]
    N. Bizot, M. Frigerio, M. Knecht and J.-L. Kneur, Nonperturbative analysis of the spectrum of meson resonances in an ultraviolet-complete composite-Higgs model, Phys. Rev. D 95 (2017) 075006 [arXiv:1610.09293] [INSPIRE].ADSGoogle Scholar
  29. [29]
    T. Ma and G. Cacciapaglia, Fundamental Composite 2HDM: SU(N) with 4 flavours, JHEP 03 (2016) 211 [arXiv:1508.07014] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    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].ADSCrossRefzbMATHGoogle Scholar
  31. [31]
    E. Bertuzzo, T.S. Ray, H. de Sandes and C.A. Savoy, On Composite Two Higgs Doublet Models, JHEP 05 (2013) 153 [arXiv:1206.2623] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. [32]
    S. De Curtis, S. Moretti, K. Yagyu and E. Yildirim, Theory and Phenomenology of Composite 2-Higgs Doublet Models, PoS(CHARGED2016)018 (2016) [arXiv:1612.05125] [INSPIRE].
  33. [33]
    M. Chala, hγγ excess and Dark Matter from Composite Higgs Models, JHEP 01 (2013) 122 [arXiv:1210.6208] [INSPIRE].
  34. [34]
    Y. Wu, T. Ma, B. Zhang and G. Cacciapaglia, Composite Dark Matter and Higgs, JHEP 11 (2017) 058 [arXiv:1703.06903] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    G. Ballesteros, A. Carmona and M. Chala, Exceptional Composite Dark Matter, Eur. Phys. J. C 77 (2017) 468 [arXiv:1704.07388] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    R. Balkin, M. Ruhdorfer, E. Salvioni and A. Weiler, Charged Composite Scalar Dark Matter, JHEP 11 (2017) 094 [arXiv:1707.07685] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  37. [37]
    H. Georgi and D.B. Kaplan, Composite Higgs and Custodial SU(2), Phys. Lett. B 145 (1984) 216 [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    A. Pomarol and R. Vega, Constraints on CP-violation in the Higgs sector from the rho parameter, Nucl. Phys. B 413 (1994) 3 [hep-ph/9305272] [INSPIRE].
  39. [39]
    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
  40. [40]
    I. Low, W. Skiba and D. Tucker-Smith, Little Higgses from an antisymmetric condensate, Phys. Rev. D 66 (2002) 072001 [hep-ph/0207243] [INSPIRE].
  41. [41]
    T. Brown, C. Frugiuele and T. Gregoire, UV friendly T-parity in the SU(6)/Sp(6) little Higgs model, JHEP 06 (2011) 108 [arXiv:1012.2060] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  42. [42]
    M.E. Peskin and T. Takeuchi, Estimation of oblique electroweak corrections, Phys. Rev. D 46 (1992) 381 [INSPIRE].ADSGoogle Scholar
  43. [43]
    E. Eichten and K.D. Lane, Dynamical Breaking of Weak Interaction Symmetries, Phys. Lett. B 90 (1980) 125 [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT, JHEP 12 (2008) 031 [arXiv:0807.0004] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    V.S. Rychkov and A. Vichi, Universal Constraints on Conformal Operator Dimensions, Phys. Rev. D 80 (2009) 045006 [arXiv:0905.2211] [INSPIRE].ADSMathSciNetGoogle Scholar
  46. [46]
    O. Antipin, E. Mølgaard and F. Sannino, Higgs Critical Exponents and Conformal Bootstrap in Four Dimensions, JHEP 06 (2015) 030 [arXiv:1406.6166] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    G. Cacciapaglia, H. Cai, T. Flacke, S.J. Lee, A. Parolini and H. Serôdio, Anarchic Yukawas and top partial compositeness: the flavour of a successful marriage, JHEP 06 (2015) 085 [arXiv:1501.03818] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    G. Panico and A. Pomarol, Flavor hierarchies from dynamical scales, JHEP 07 (2016) 097 [arXiv:1603.06609] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    G. Cacciapaglia and F. Sannino, An Ultraviolet Chiral Theory of the Top for the Fundamental Composite (Goldstone) Higgs, Phys. Lett. B 755 (2016) 328 [arXiv:1508.00016] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  50. [50]
    E.H. Simmons, Phenomenology of a Technicolor Model With Heavy Scalar Doublet, Nucl. Phys. B 312 (1989) 253 [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    S. Samuel, Bosonic Technicolor, Nucl. Phys. B 347 (1990) 625 [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    O. Antipin and M. Redi, The Half-composite Two Higgs Doublet Model and the Relaxion, JHEP 12 (2015) 031 [arXiv:1508.01112] [INSPIRE].ADSGoogle Scholar
  53. [53]
    A. Agugliaro, O. Antipin, D. Becciolini, S. De Curtis and M. Redi, UV complete composite Higgs models, Phys. Rev. D 95 (2017) 035019 [arXiv:1609.07122] [INSPIRE].ADSGoogle Scholar
  54. [54]
    D.B. Kaplan, Flavor at SSC energies: A New mechanism for dynamically generated fermion masses, Nucl. Phys. B 365 (1991) 259 [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    F. Sannino, A. Strumia, A. Tesi and E. Vigiani, Fundamental partial compositeness, JHEP 11 (2016) 029 [arXiv:1607.01659] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  56. [56]
    G.M. Pelaggi, F. Sannino, A. Strumia and E. Vigiani, Naturalness of asymptotically safe Higgs, Front. in Phys. 5 (2017) 49 [arXiv:1701.01453] [INSPIRE].CrossRefGoogle Scholar
  57. [57]
    G. Cacciapaglia, H. Gertov, F. Sannino and A.E. Thomsen, Minimal Fundamental Partial Compositeness, Phys. Rev. D 98 (2018) 015006 [arXiv:1704.07845] [INSPIRE].ADSGoogle Scholar
  58. [58]
    F. Sannino, P. Stangl, D.M. Straub and A.E. Thomsen, Flavor Physics and Flavor Anomalies in Minimal Fundamental Partial Compositeness, Phys. Rev. D 97 (2018) 115046 [arXiv:1712.07646] [INSPIRE].ADSGoogle Scholar
  59. [59]
    T. Alanne, N. Bizot, G. Cacciapaglia and F. Sannino, Classification of NLO operators for composite Higgs models, Phys. Rev. D 97 (2018) 075028 [arXiv:1801.05444] [INSPIRE].ADSGoogle Scholar
  60. [60]
    G. Ferretti and D. Karateev, Fermionic UV completions of Composite Higgs models, JHEP 03 (2014) 077 [arXiv:1312.5330] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    J. Barnard, T. Gherghetta and T.S. Ray, UV descriptions of composite Higgs models without elementary scalars, JHEP 02 (2014) 002 [arXiv:1311.6562] [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    A. Belyaev, G. Cacciapaglia, H. Cai, T. Flacke, A. Parolini and H. Serôdio, Singlets in composite Higgs models in light of the LHC 750 GeV diphoton excess, Phys. Rev. D 94 (2016) 015004 [arXiv:1512.07242] [INSPIRE].ADSGoogle Scholar
  63. [63]
    A. Belyaev et al., Di-boson signatures as Standard Candles for Partial Compositeness, JHEP 01 (2017) 094 [Erratum ibid. 12 (2017) 088] [arXiv:1610.06591] [INSPIRE].
  64. [64]
    E. Bennett et al., Sp(4) gauge theory on the lattice: towards SU(4)/Sp(4) composite Higgs (and beyond), JHEP 03 (2018) 185 [arXiv:1712.04220] [INSPIRE].CrossRefzbMATHGoogle Scholar
  65. [65]
    F. Sannino, Conformal Windows of Sp(2N) and SO(N) Gauge Theories, Phys. Rev. D 79 (2009) 096007 [arXiv:0902.3494] [INSPIRE].ADSGoogle Scholar
  66. [66]
    T.A. Ryttov and F. Sannino, Conformal House, Int. J. Mod. Phys. A 25 (2010) 4603 [arXiv:0906.0307] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  67. [67]
    G. Ferretti, Gauge theories of Partial Compositeness: Scenarios for Run-II of the LHC, JHEP 06 (2016) 107 [arXiv:1604.06467] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    C. Csáki, T. Ma and J. Shu, Maximally Symmetric Composite Higgs Models, Phys. Rev. Lett. 119 (2017) 131803 [arXiv:1702.00405] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    O. Matsedonskyi, G. Panico and A. Wulzer, Light Top Partners for a Light Composite Higgs, JHEP 01 (2013) 164 [arXiv:1204.6333] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    D. Marzocca, M. Serone and J. Shu, General Composite Higgs Models, JHEP 08 (2012) 013 [arXiv:1205.0770] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    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].ADSCrossRefzbMATHGoogle Scholar
  72. [72]
    M. Golterman and Y. Shamir, Effective potential in ultraviolet completions for composite Higgs models, Phys. Rev. D 97 (2018) 095005 [arXiv:1707.06033] [INSPIRE].ADSGoogle Scholar
  73. [73]
    A. Arbey, G. Cacciapaglia, H. Cai, A. Deandrea, S. Le Corre and F. Sannino, Fundamental Composite Electroweak Dynamics: Status at the LHC, Phys. Rev. D 95 (2017) 015028 [arXiv:1502.04718] [INSPIRE].ADSGoogle Scholar
  74. [74]
    T. Hambye, F.S. Ling, L. Lopez Honorez and J. Rocher, Scalar Multiplet Dark Matter, JHEP 07 (2009) 090 [Erratum ibid. 05 (2010) 066] [arXiv:0903.4010] [INSPIRE].
  75. [75]
    Z.-H. Yu, J.-M. Zheng, X.-J. Bi, Z. Li, D.-X. Yao and H.-H. Zhang, Constraining the interaction strength between dark matter and visible matter: II. scalar, vector and spin-3/2 dark matter, Nucl. Phys. B 860 (2012) 115 [arXiv:1112.6052] [INSPIRE].
  76. [76]
    XENON collaboration, Dark Matter Search Results from a One Ton-Year Exposure of XENON1T, Phys. Rev. Lett. 121 (2018) 111302 [arXiv:1805.12562] [INSPIRE].
  77. [77]
    LUX collaboration, Results from a search for dark matter in the complete LUX exposure, Phys. Rev. Lett. 118 (2017) 021303 [arXiv:1608.07648] [INSPIRE].
  78. [78]
    PandaX-II collaboration, Dark Matter Results From 54-Ton-Day Exposure of PandaX-II Experiment, Phys. Rev. Lett. 119 (2017) 181302 [arXiv:1708.06917] [INSPIRE].
  79. [79]
    MAGIC and Fermi-LAT collaborations, Limits to Dark Matter Annihilation Cross-Section from a Combined Analysis of MAGIC and Fermi-LAT Observations of Dwarf Satellite Galaxies, JCAP 02 (2016) 039 [arXiv:1601.06590] [INSPIRE].
  80. [80]
    J. Serra, Beyond the Minimal Top Partner Decay, JHEP 09 (2015) 176 [arXiv:1506.05110] [INSPIRE].ADSCrossRefGoogle Scholar
  81. [81]
    A. Banerjee, G. Bhattacharyya and T.S. Ray, Improving Fine-tuning in Composite Higgs Models, Phys. Rev. D 96 (2017) 035040 [arXiv:1703.08011] [INSPIRE].ADSGoogle Scholar
  82. [82]
    J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  83. [83]
    E. Witten, Global Aspects of Current Algebra, Nucl. Phys. B 223 (1983) 422 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Chengfeng Cai
    • 1
  • Hong-Hao Zhang
    • 1
  • Giacomo Cacciapaglia
    • 2
    • 3
    Email author
  1. 1.School of PhysicsSun-Yat Sen UniversityGuangzhouP.R. China
  2. 2.Université de LyonLyon Cedex 08France
  3. 3.Institut de Physique Nucléaire de Lyon, UMR5822 CNRS/IN2P3Villeurbanne CedexFrance

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