Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
N. Craig, A. Katz, M. Strassler and R. Sundrum, Naturalness in the Dark at the LHC, JHEP 07 (2015) 105 [arXiv:1501.05310] [INSPIRE].
G. Burdman, Z. Chacko, H.-S. Goh and R. Harnik, Folded supersymmetry and the LEP paradox, JHEP 02 (2007) 009 [hep-ph/0609152] [INSPIRE].
A. Falkowski, S. Pokorski and M. Schmaltz, Twin SUSY, Phys. Rev. D 74 (2006) 035003 [hep-ph/0604066] [INSPIRE].
S. Chang, L.J. Hall and N. Weiner, A Supersymmetric twin Higgs, Phys. Rev. D 75 (2007) 035009 [hep-ph/0604076] [INSPIRE].
N. Craig and K. Howe, Doubling down on naturalness with a supersymmetric twin Higgs, JHEP 03 (2014) 140 [arXiv:1312.1341] [INSPIRE].
A. Katz, A. Mariotti, S. Pokorski, D. Redigolo and R. Ziegler, SUSY Meets Her Twin, JHEP 01 (2017) 142 [arXiv:1611.08615] [INSPIRE].
M. Badziak and K. Harigaya, Supersymmetric D-term Twin Higgs, JHEP 06 (2017) 065 [arXiv:1703.02122] [INSPIRE].
M. Badziak and K. Harigaya, Minimal Non-Abelian Supersymmetric Twin Higgs, JHEP 10 (2017) 109 [arXiv:1707.09071] [INSPIRE].
M. Badziak and K. Harigaya, Asymptotically Free Natural Supersymmetric Twin Higgs Model, Phys. Rev. Lett. 120 (2018) 211803 [arXiv:1711.11040] [INSPIRE].
P. Batra and Z. Chacko, A Composite Twin Higgs Model, Phys. Rev. D 79 (2009) 095012 [arXiv:0811.0394] [INSPIRE].
M. Geller and O. Telem, Holographic Twin Higgs Model, Phys. Rev. Lett. 114 (2015) 191801 [arXiv:1411.2974] [INSPIRE].
R. Barbieri, D. Greco, R. Rattazzi and A. Wulzer, The Composite Twin Higgs scenario, JHEP 08 (2015) 161 [arXiv:1501.07803] [INSPIRE].
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].
C. Csáki, M. Geller, O. Telem and A. Weiler, The Flavor of the Composite Twin Higgs, JHEP 09 (2016) 146 [arXiv:1512.03427] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].
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].
R. Barbieri, L.J. Hall and K. Harigaya, Minimal Mirror Twin Higgs, JHEP 11 (2016) 172 [arXiv:1609.05589] [INSPIRE].
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].
N. Craig, S. Koren and T. Trott, Cosmological Signals of a Mirror Twin Higgs, JHEP 05 (2017) 038 [arXiv:1611.07977] [INSPIRE].
C. Csáki, E. Kuflik and S. Lombardo, Viable Twin Cosmology from Neutrino Mixing, Phys. Rev. D 96 (2017) 055013 [arXiv:1703.06884] [INSPIRE].
Z. Chacko, D. Curtin, M. Geller and Y. Tsai, Cosmological Signatures of a Mirror Twin Higgs, JHEP 09 (2018) 163 [arXiv:1803.03263] [INSPIRE].
M. Farina, Asymmetric Twin Dark Matter, JCAP 11 (2015) 017 [arXiv:1506.03520] [INSPIRE].
N. Craig and A. Katz, The Fraternal WIMP Miracle, JCAP 10 (2015) 054 [arXiv:1505.07113] [INSPIRE].
I. Garcia Garcia, R. Lasenby and J. March-Russell, Twin Higgs WIMP Dark Matter, Phys. Rev. D 92 (2015) 055034 [arXiv:1505.07109] [INSPIRE].
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].
V. Prilepina and Y. Tsai, Reconciling Large And Small-Scale Structure In Twin Higgs Models, JHEP 09 (2017) 033 [arXiv:1611.05879] [INSPIRE].
F. Csikor, Z. Fodor and J. Heitger, Endpoint of the hot electroweak phase transition, Phys. Rev. Lett. 82 (1999) 21 [hep-ph/9809291] [INSPIRE].
C. Kilic and S. Swaminathan, Can A Pseudo-Nambu-Goldstone Higgs Lead To Symmetry Non-Restoration?, JHEP 01 (2016) 002 [arXiv:1508.05121] [INSPIRE].
M.S. Turner and F. Wilczek, Relic gravitational waves and extended inflation, Phys. Rev. Lett. 65 (1990) 3080 [INSPIRE].
A. Kosowsky, M.S. Turner and R. Watkins, Gravitational radiation from colliding vacuum bubbles, Phys. Rev. D 45 (1992) 4514 [INSPIRE].
A. Kosowsky, M.S. Turner and R. Watkins, Gravitational waves from first order cosmological phase transitions, Phys. Rev. Lett. 69 (1992) 2026 [INSPIRE].
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].
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].
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].
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].
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].
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].
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].
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].
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].
A. Kosowsky, A. Mack and T. Kahniashvili, Gravitational radiation from cosmological turbulence, Phys. Rev. D 66 (2002) 024030 [astro-ph/0111483] [INSPIRE].
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].
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].
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].
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].
M. Trodden, Electroweak baryogenesis, Rev. Mod. Phys. 71 (1999) 1463 [hep-ph/9803479] [INSPIRE].
D.E. Morrissey and M.J. Ramsey-Musolf, Electroweak baryogenesis, New J. Phys. 14 (2012) 125003 [arXiv:1206.2942] [INSPIRE].
R. Barbieri and G.F. Giudice, Upper Bounds on Supersymmetric Particle Masses, Nucl. Phys. B 306 (1988) 63 [INSPIRE].
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].
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].
S. Bruggisser, B. Von Harling, O. Matsedonskyi and G. Servant, Electroweak Phase Transition and Baryogenesis in Composite Higgs Models, arXiv:1804.07314 [INSPIRE].
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].
D. Comelli and J.R. Espinosa, Bosonic thermal masses in supersymmetry, Phys. Rev. D 55 (1997) 6253 [hep-ph/9606438] [INSPIRE].
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].
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].
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].
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].
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].
J.R. Espinosa, Dominant two loop corrections to the MSSM finite temperature effective potential, Nucl. Phys. B 475 (1996) 273 [hep-ph/9604320] [INSPIRE].
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].
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].
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].
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].
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].
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].
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].
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].
P. Fendley, The Effective Potential and the Coupling Constant at High Temperature, Phys Lett. B 196 (1987) 175 [INSPIRE].
A.D. Linde, Infrared Problem in Thermodynamics of the Yang-Mills Gas, Phys. Lett. B 96 (1980) 289 [INSPIRE].
D.J. Gross, R.D. Pisarski and L.G. Yaffe, QCD and Instantons at Finite Temperature, Rev. Mod. Phys. 53 (1981) 43 [INSPIRE].
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].
A.D. Linde, Fate of the False Vacuum at Finite Temperature: Theory and Applications, Phys. Lett. B 100 (1981) 37 [INSPIRE].
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].
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].
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].
P.J. Steinhardt, Relativistic Detonation Waves and Bubble Growth in False Vacuum Decay, Phys. Rev. D 25 (1982) 2074 [INSPIRE].
S.J. Huber and T. Konstandin, Gravitational Wave Production by Collisions: More Bubbles, JCAP 09 (2008) 022 [arXiv:0806.1828] [INSPIRE].
R. Jinno and M. Takimoto, Gravitational waves from bubble collisions: An analytic derivation, Phys. Rev. D 95 (2017) 024009 [arXiv:1605.01403] [INSPIRE].
R. Jinno and M. Takimoto, Gravitational waves from bubble dynamics: Beyond the Envelope, arXiv:1707.03111 [INSPIRE].
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].
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
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1810.00574
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Fujikura, K., Kamada, K., Nakai, Y. et al. Phase transitions in twin Higgs models. J. High Energ. Phys. 2018, 18 (2018). https://doi.org/10.1007/JHEP12(2018)018
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2018)018