Journal of High Energy Physics

, 2018:18 | Cite as

Phase transitions in twin Higgs models

  • Kohei FujikuraEmail author
  • Kohei Kamada
  • Yuichiro Nakai
  • Masahide Yamaguchi
Open Access
Regular Article - Theoretical Physics


We study twin Higgs models at non-zero temperature and discuss cosmological phase transitions as well as their implications on electroweak baryogenesis and gravitational waves. It is shown that the expectation value of the Higgs field at the critical temperature of the electroweak phase transition is much smaller than the critical temperature, which indicates two important facts: (i) the electroweak phase transition cannot be analyzed perturbatively (ii) the electroweak baryogenesis is hardly realized in the typical realizations of twin Higgs models. We also analyze the phase transition associated with the global symmetry breaking, through which the Standard Model Higgs is identified with one of the pseudo-Nambu-Goldstone bosons in terms of its linear realization, with and without supersymmetry. For this phase transition, we show that, only in the supersymmetric case, there are still some parameter spaces, in which the perturbative approach is validated and the phase transition is the first order. We find that the stochastic gravitational wave background is generated through this first order phase transition, but it is impossible to be detected by DECIGO or BBO in the linear realization and the decoupling limit. The detection of stochastic gravitational wave background with the feature of first order phase transition, therefore, will give strong constraints on twin Higgs models.


Beyond Standard Model Thermal Field Theory 


Open Access

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  1. [1]
    Z. Chacko, H.-S. Goh and R. Harnik, The Twin Higgs: Natural electroweak breaking from mirror symmetry, Phys. Rev. Lett. 96 (2006) 231802 [hep-ph/0506256] [INSPIRE].
  2. [2]
    N. Craig, A. Katz, M. Strassler and R. Sundrum, Naturalness in the Dark at the LHC, JHEP 07 (2015) 105 [arXiv:1501.05310] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    G. Burdman, Z. Chacko, H.-S. Goh and R. Harnik, Folded supersymmetry and the LEP paradox, JHEP 02 (2007) 009 [hep-ph/0609152] [INSPIRE].
  4. [4]
    A. Falkowski, S. Pokorski and M. Schmaltz, Twin SUSY, Phys. Rev. D 74 (2006) 035003 [hep-ph/0604066] [INSPIRE].
  5. [5]
    S. Chang, L.J. Hall and N. Weiner, A Supersymmetric twin Higgs, Phys. Rev. D 75 (2007) 035009 [hep-ph/0604076] [INSPIRE].
  6. [6]
    N. Craig and K. Howe, Doubling down on naturalness with a supersymmetric twin Higgs, JHEP 03 (2014) 140 [arXiv:1312.1341] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    A. Katz, A. Mariotti, S. Pokorski, D. Redigolo and R. Ziegler, SUSY Meets Her Twin, JHEP 01 (2017) 142 [arXiv:1611.08615] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  8. [8]
    M. Badziak and K. Harigaya, Supersymmetric D-term Twin Higgs, JHEP 06 (2017) 065 [arXiv:1703.02122] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    M. Badziak and K. Harigaya, Minimal Non-Abelian Supersymmetric Twin Higgs, JHEP 10 (2017) 109 [arXiv:1707.09071] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    M. Badziak and K. Harigaya, Asymptotically Free Natural Supersymmetric Twin Higgs Model, Phys. Rev. Lett. 120 (2018) 211803 [arXiv:1711.11040] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    P. Batra and Z. Chacko, A Composite Twin Higgs Model, Phys. Rev. D 79 (2009) 095012 [arXiv:0811.0394] [INSPIRE].
  12. [12]
    M. Geller and O. Telem, Holographic Twin Higgs Model, Phys. Rev. Lett. 114 (2015) 191801 [arXiv:1411.2974] [INSPIRE].
  13. [13]
    R. Barbieri, D. Greco, R. Rattazzi and A. Wulzer, The Composite Twin Higgs scenario, JHEP 08 (2015) 161 [arXiv:1501.07803] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    M. Low, A. Tesi and L.-T. Wang, Twin Higgs mechanism and a composite Higgs boson, Phys. Rev. D 91 (2015) 095012 [arXiv:1501.07890] [INSPIRE].
  15. [15]
    C. Csáki, M. Geller, O. Telem and A. Weiler, The Flavor of the Composite Twin Higgs, JHEP 09 (2016) 146 [arXiv:1512.03427] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].
  17. [17]
    R.H. Cyburt, B.D. Fields, K.A. Olive and T.-H. Yeh, Big Bang Nucleosynthesis: 2015, Rev. Mod. Phys. 88 (2016) 015004 [arXiv:1505.01076] [INSPIRE].
  18. [18]
    R. Barbieri, L.J. Hall and K. Harigaya, Minimal Mirror Twin Higgs, JHEP 11 (2016) 172 [arXiv:1609.05589] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    Z. Chacko, N. Craig, P.J. Fox and R. Harnik, Cosmology in Mirror Twin Higgs and Neutrino Masses, JHEP 07 (2017) 023 [arXiv:1611.07975] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    N. Craig, S. Koren and T. Trott, Cosmological Signals of a Mirror Twin Higgs, JHEP 05 (2017) 038 [arXiv:1611.07977] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  21. [21]
    C. Csáki, E. Kuflik and S. Lombardo, Viable Twin Cosmology from Neutrino Mixing, Phys. Rev. D 96 (2017) 055013 [arXiv:1703.06884] [INSPIRE].
  22. [22]
    Z. Chacko, D. Curtin, M. Geller and Y. Tsai, Cosmological Signatures of a Mirror Twin Higgs, JHEP 09 (2018) 163 [arXiv:1803.03263] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    M. Farina, Asymmetric Twin Dark Matter, JCAP 11 (2015) 017 [arXiv:1506.03520] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    N. Craig and A. Katz, The Fraternal WIMP Miracle, JCAP 10 (2015) 054 [arXiv:1505.07113] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    I. Garcia Garcia, R. Lasenby and J. March-Russell, Twin Higgs WIMP Dark Matter, Phys. Rev. D 92 (2015) 055034 [arXiv:1505.07109] [INSPIRE].
  26. [26]
    M. Freytsis, S. Knapen, D.J. Robinson and Y. Tsai, Gamma-rays from Dark Showers with Twin Higgs Models, JHEP 05 (2016) 018 [arXiv:1601.07556] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    V. Prilepina and Y. Tsai, Reconciling Large And Small-Scale Structure In Twin Higgs Models, JHEP 09 (2017) 033 [arXiv:1611.05879] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    F. Csikor, Z. Fodor and J. Heitger, Endpoint of the hot electroweak phase transition, Phys. Rev. Lett. 82 (1999) 21 [hep-ph/9809291] [INSPIRE].
  29. [29]
    C. Kilic and S. Swaminathan, Can A Pseudo-Nambu-Goldstone Higgs Lead To Symmetry Non-Restoration?, JHEP 01 (2016) 002 [arXiv:1508.05121] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    M.S. Turner and F. Wilczek, Relic gravitational waves and extended inflation, Phys. Rev. Lett. 65 (1990) 3080 [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    A. Kosowsky, M.S. Turner and R. Watkins, Gravitational radiation from colliding vacuum bubbles, Phys. Rev. D 45 (1992) 4514 [INSPIRE].
  32. [32]
    A. Kosowsky, M.S. Turner and R. Watkins, Gravitational waves from first order cosmological phase transitions, Phys. Rev. Lett. 69 (1992) 2026 [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    A. Kosowsky and M.S. Turner, Gravitational radiation from colliding vacuum bubbles: envelope approximation to many bubble collisions, Phys. Rev. D 47 (1993) 4372 [astro-ph/9211004] [INSPIRE].
  34. [34]
    M.S. Turner, E.J. Weinberg and L.M. Widrow, Bubble nucleation in first order inflation and other cosmological phase transitions, Phys. Rev. D 46 (1992) 2384 [INSPIRE].
  35. [35]
    M. Hindmarsh, S.J. Huber, K. Rummukainen and D.J. Weir, Gravitational waves from the sound of a first order phase transition, Phys. Rev. Lett. 112 (2014) 041301 [arXiv:1304.2433] [INSPIRE].
  36. [36]
    J.T. Giblin and J.B. Mertens, Gravitional radiation from first-order phase transitions in the presence of a fluid, Phys. Rev. D 90 (2014) 023532 [arXiv:1405.4005] [INSPIRE].
  37. [37]
    M. Hindmarsh, S.J. Huber, K. Rummukainen and D.J. Weir, Numerical simulations of acoustically generated gravitational waves at a first order phase transition, Phys. Rev. D 92 (2015) 123009 [arXiv:1504.03291] [INSPIRE].
  38. [38]
    M. Hindmarsh, S.J. Huber, K. Rummukainen and D.J. Weir, Shape of the acoustic gravitational wave power spectrum from a first order phase transition, Phys. Rev. D 96 (2017) 103520 [arXiv:1704.05871] [INSPIRE].
  39. [39]
    M. Kamionkowski, A. Kosowsky and M.S. Turner, Gravitational radiation from first order phase transitions, Phys. Rev. D 49 (1994) 2837 [astro-ph/9310044] [INSPIRE].
  40. [40]
    C. Caprini and R. Durrer, Gravitational waves from stochastic relativistic sources: Primordial turbulence and magnetic fields, Phys. Rev. D 74 (2006) 063521 [astro-ph/0603476] [INSPIRE].
  41. [41]
    C. Caprini, R. Durrer and G. Servant, The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition, JCAP 12 (2009) 024 [arXiv:0909.0622] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    A. Kosowsky, A. Mack and T. Kahniashvili, Gravitational radiation from cosmological turbulence, Phys. Rev. D 66 (2002) 024030 [astro-ph/0111483] [INSPIRE].
  43. [43]
    G. Gogoberidze, T. Kahniashvili and A. Kosowsky, The Spectrum of Gravitational Radiation from Primordial Turbulence, Phys. Rev. D 76 (2007) 083002 [arXiv:0705.1733] [INSPIRE].
  44. [44]
    P. Niksa, M. Schlederer and G. Sigl, Gravitational Waves produced by Compressible MHD Turbulence from Cosmological Phase Transitions, Class. Quant. Grav. 35 (2018) 144001 [arXiv:1803.02271] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  45. [45]
    N. Seto, S. Kawamura and T. Nakamura, Possibility of direct measurement of the acceleration of the universe using 0.1-Hz band laser interferometer gravitational wave antenna in space, Phys. Rev. Lett. 87 (2001) 221103 [astro-ph/0108011] [INSPIRE].
  46. [46]
    G.M. Harry, P. Fritschel, D.A. Shaddock, W. Folkner and E.S. Phinney, Laser interferometry for the big bang observer, Class. Quant. Grav. 23 (2006) 4887 [Erratum ibid. 23 (2006) 7361] [INSPIRE].
  47. [47]
    M. Trodden, Electroweak baryogenesis, Rev. Mod. Phys. 71 (1999) 1463 [hep-ph/9803479] [INSPIRE].
  48. [48]
    D.E. Morrissey and M.J. Ramsey-Musolf, Electroweak baryogenesis, New J. Phys. 14 (2012) 125003 [arXiv:1206.2942] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    R. Barbieri and G.F. Giudice, Upper Bounds on Supersymmetric Particle Masses, Nucl. Phys. B 306 (1988) 63 [INSPIRE].
  50. [50]
    L. Delle Rose, C. Marzo and A. Urbano, On the fate of the Standard Model at finite temperature, JHEP 05 (2016) 050 [arXiv:1507.06912] [INSPIRE].CrossRefGoogle Scholar
  51. [51]
    S. Bruggisser, B. Von Harling, O. Matsedonskyi and G. Servant, Baryon Asymmetry from a Composite Higgs Boson, Phys. Rev. Lett. 121 (2018) 131801 [arXiv:1803.08546] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    S. Bruggisser, B. Von Harling, O. Matsedonskyi and G. Servant, Electroweak Phase Transition and Baryogenesis in Composite Higgs Models, arXiv:1804.07314 [INSPIRE].
  53. [53]
    D. Croon, V. Sanz and G. White, Model Discrimination in Gravitational Wave spectra from Dark Phase Transitions, JHEP 08 (2018) 203 [arXiv:1806.02332] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    D. Comelli and J.R. Espinosa, Bosonic thermal masses in supersymmetry, Phys. Rev. D 55 (1997) 6253 [hep-ph/9606438] [INSPIRE].
  55. [55]
    M. Dine, R.G. Leigh, P.Y. Huet, A.D. Linde and D.A. Linde, Towards the theory of the electroweak phase transition, Phys. Rev. D 46 (1992) 550 [hep-ph/9203203] [INSPIRE].
  56. [56]
    K. Rummukainen, M. Tsypin, K. Kajantie, M. Laine and M.E. Shaposhnikov, The Universality class of the electroweak theory, Nucl. Phys. B 532 (1998) 283 [hep-lat/9805013] [INSPIRE].
  57. [57]
    K. Farakos, K. Kajantie, K. Rummukainen and M.E. Shaposhnikov, 3-D physics and the electroweak phase transition: Perturbation theory, Nucl. Phys. B 425 (1994) 67 [hep-ph/9404201] [INSPIRE].
  58. [58]
    K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, Generic rules for high temperature dimensional reduction and their application to the standard model, Nucl. Phys. B 458 (1996) 90 [hep-ph/9508379] [INSPIRE].
  59. [59]
    K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, High temperature dimensional reduction and parity violation, Phys. Lett. B 423 (1998) 137 [hep-ph/9710538] [INSPIRE].
  60. [60]
    J.R. Espinosa, Dominant two loop corrections to the MSSM finite temperature effective potential, Nucl. Phys. B 475 (1996) 273 [hep-ph/9604320] [INSPIRE].
  61. [61]
    R.R. Parwani, Resummation in a hot scalar field theory, Phys. Rev. D 45 (1992) 4695 [Erratum ibid. D 48 (1993) 5965] [hep-ph/9204216] [INSPIRE].
  62. [62]
    P.B. Arnold and O. Espinosa, The Effective potential and first order phase transitions: Beyond leading-order, Phys. Rev. D 47 (1993) 3546 [Erratum ibid. D 50 (1994) 6662] [hep-ph/9212235] [INSPIRE].
  63. [63]
    K. Funakubo and E. Senaha, Two-loop effective potential, thermal resummation and first-order phase transitions: Beyond the high-temperature expansion, Phys. Rev. D 87 (2013) 054003 [arXiv:1210.1737] [INSPIRE].
  64. [64]
    M. Laine and M. Losada, Two loop dimensional reduction and effective potential without temperature expansions, Nucl. Phys. B 582 (2000) 277 [hep-ph/0003111] [INSPIRE].
  65. [65]
    J. Ellis, M. Lewicki and J.M. No, On the Maximal Strength of a First-Order Electroweak Phase Transition and its Gravitational Wave Signal, submitted to JCAP (2018) [arXiv:1809.08242] [INSPIRE].
  66. [66]
    C. Wainwright, S. Profumo and M.J. Ramsey-Musolf, Gravity Waves from a Cosmological Phase Transition: Gauge Artifacts and Daisy Resummations, Phys. Rev. D 84 (2011) 023521 [arXiv:1104.5487] [INSPIRE].
  67. [67]
    C.-W. Chiang and E. Senaha, On gauge dependence of gravitational waves from a first-order phase transition in classical scale-invariant U(1) models, Phys. Lett. B 774 (2017) 489 [arXiv:1707.06765] [INSPIRE].
  68. [68]
    M. Quirós, Finite temperature field theory and phase transitions, in Proceedings, Summer School in High-energy physics and cosmology, Trieste, Italy, June 29-July 17, 1998, pp. 187-259 (1999) [hep-ph/9901312] [INSPIRE].
  69. [69]
    P. Fendley, The Effective Potential and the Coupling Constant at High Temperature, Phys Lett. B 196 (1987) 175 [INSPIRE].
  70. [70]
    A.D. Linde, Infrared Problem in Thermodynamics of the Yang-Mills Gas, Phys. Lett. B 96 (1980) 289 [INSPIRE].
  71. [71]
    D.J. Gross, R.D. Pisarski and L.G. Yaffe, QCD and Instantons at Finite Temperature, Rev. Mod. Phys. 53 (1981) 43 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  72. [72]
    P.B. Arnold, The Electroweak phase transition: Part 1. Review of perturbative methods, in 8th International Seminar on High-energy Physics (Quarks 94), Vladimir, Russia, May 11-18, 1994, pp. 71-86 (1994) [hep-ph/9410294] [INSPIRE].
  73. [73]
    A.D. Linde, Fate of the False Vacuum at Finite Temperature: Theory and Applications, Phys. Lett. B 100 (1981) 37 [INSPIRE].
  74. [74]
    R.-G. Cai, M. Sasaki and S.-J. Wang, The gravitational waves from the first-order phase transition with a dimension-six operator, JCAP 08 (2017) 004 [arXiv:1707.03001] [INSPIRE].ADSCrossRefGoogle Scholar
  75. [75]
    P. Binetruy, A. Bohe, C. Caprini and J.-F. Dufaux, Cosmological Backgrounds of Gravitational Waves and eLISA/NGO: Phase Transitions, Cosmic Strings and Other Sources, JCAP 06 (2012) 027 [arXiv:1201.0983] [INSPIRE].ADSCrossRefGoogle Scholar
  76. [76]
    C. Caprini et al., Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions, JCAP 04 (2016) 001 [arXiv:1512.06239] [INSPIRE].
  77. [77]
    P.J. Steinhardt, Relativistic Detonation Waves and Bubble Growth in False Vacuum Decay, Phys. Rev. D 25 (1982) 2074 [INSPIRE].
  78. [78]
    S.J. Huber and T. Konstandin, Gravitational Wave Production by Collisions: More Bubbles, JCAP 09 (2008) 022 [arXiv:0806.1828] [INSPIRE].ADSCrossRefGoogle Scholar
  79. [79]
    R. Jinno and M. Takimoto, Gravitational waves from bubble collisions: An analytic derivation, Phys. Rev. D 95 (2017) 024009 [arXiv:1605.01403] [INSPIRE].
  80. [80]
    R. Jinno and M. Takimoto, Gravitational waves from bubble dynamics: Beyond the Envelope, arXiv:1707.03111 [INSPIRE].
  81. [81]
    R. Jinno, S. Lee, H. Seong and M. Takimoto, Gravitational waves from first-order phase transitions: Towards model separation by bubble nucleation rate, JCAP 11 (2017) 050 [arXiv:1708.01253] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Kohei Fujikura
    • 1
    Email author
  • Kohei Kamada
    • 2
    • 3
  • Yuichiro Nakai
    • 4
  • Masahide Yamaguchi
    • 1
  1. 1.Department of PhysicsTokyo Institute of TechnologyTokyoJapan
  2. 2.Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS)DaejeonKorea
  3. 3.Research Center for the Early Universe (RESCEU), Graduate School of ScienceThe University of TokyoTokyoJapan
  4. 4.Department of Physics and AstronomyRutgers UniversityPiscatawayU.S.A.

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