Gravitational waves from walking technicolor

Abstract

We study gravitational waves from the first-order electroweak phase transition in the SU(Nc) gauge theory with Nf/Nc ≫ 1 (“large Nf QCD”) as a candidate for the walking technicolor, which is modeled by the U(Nf ) × U(Nf ) linear sigma model with classical scale symmetry (without mass term), particularly for Nf = 8 (“one-family model”). This model exhibits spontaneous breaking of the scale symmetry as well as the U(Nf ) × U(Nf ) radiatively through the Coleman-Weinberg mechanism à la Gildener-Weinberg, thus giving rise to a light pseudo dilaton (technidilaton) to be identified with the 125 GeV Higgs. This model possess a strong first-order electroweak phase transition due to the resultant Coleman-Weinberg type potential. We estimate the bubble nucleation that exhibits an ultra supercooling and then the signal for a stochastic gravitational wave produced via the strong first-order electroweak phase transition. We show that the amplitude can be reached to the expected sensitivities of the LISA.

References

  1. [1]

    K. Yamawaki, M. Bando and K.-i. Matumoto, Scale Invariant Technicolor Model and a Technidilaton, Phys. Rev. Lett.56 (1986) 1335 [INSPIRE].

    ADS  Google Scholar 

  2. [2]

    M. Bando, K.-i. Matumoto and K. Yamawaki, Technidilaton, Phys. Lett.B 178 (1986) 308 [INSPIRE].

    ADS  Google Scholar 

  3. [3]

    T. Akiba and T. Yanagida, Hierarchic Chiral Condensate, Phys. Lett.169B (1986) 432 [INSPIRE].

    ADS  Google Scholar 

  4. [4]

    T.W. Appelquist, D. Karabali and L.C.R. Wijewardhana, Chiral Hierarchies and the Flavor Changing Neutral Current Problem in Technicolor, Phys. Rev. Lett.57 (1986) 957 [INSPIRE].

    ADS  Google Scholar 

  5. [5]

    B. Holdom, Techniodor, Phys. Lett.150B (1985) 301 [INSPIRE].

    ADS  Google Scholar 

  6. [6]

    S. Weinberg, Implications of Dynamical Symmetry Breaking, Phys. Rev.D 13 (1976) 974 [INSPIRE].

    ADS  Google Scholar 

  7. [7]

    L. Susskind, Dynamics of Spontaneous Symmetry Breaking in the Weinberg-Salam Theory, Phys. Rev.D 20 (1979) 2619 [INSPIRE].

    ADS  Google Scholar 

  8. [8]

    S. Matsuzaki and K. Yamawaki, Walking on the ladder: 125 GeV technidilaton, or Conformal Higgs, JHEP12 (2015) 053 [Erratum ibid.11 (2016) 158] [arXiv:1508.07688] [INSPIRE].

  9. [9]

    W.E. Caswell, Asymptotic Behavior of Nonabelian Gauge Theories to Two Loop Order, Phys. Rev. Lett.33 (1974) 244 [INSPIRE].

    ADS  Google Scholar 

  10. [10]

    T. Banks and A. Zaks, On the Phase Structure of Vector-Like Gauge Theories with Massless Fermions, Nucl. Phys.B 196 (1982) 189 [INSPIRE].

    ADS  Google Scholar 

  11. [11]

    T. Appelquist, J. Terning and L.C.R. Wijewardhana, The Zero temperature chiral phase transition in SU(N) gauge theories, Phys. Rev. Lett.77 (1996) 1214 [hep-ph/9602385] [INSPIRE].

  12. [12]

    LatKMI collaboration, Walking signals in Nf = 8 QCD on the lattice, Phys. Rev.D 87 (2013) 094511 [arXiv:1302.6859] [INSPIRE].

  13. [13]

    LSD collaboration, Lattice simulations with eight flavors of domain wall fermions in SU(3) gauge theory, Phys. Rev.D 90 (2014) 114502 [arXiv:1405.4752] [INSPIRE].

  14. [14]

    A. Hasenfratz, D. Schaich and A. Veernala, Nonperturbative β function of eight-flavor SU(3) gauge theory, JHEP06 (2015) 143 [arXiv:1410.5886] [INSPIRE].

    ADS  Google Scholar 

  15. [15]

    LatKMI collaboration, Light composite scalar in eight-flavor QCD on the lattice, Phys. Rev.D 89 (2014) 111502 [arXiv:1403.5000] [INSPIRE].

  16. [16]

    LatKMI collaboration, Light flavor-singlet scalars and walking signals in Nf = 8 QCD on the lattice, Phys. Rev.D 96 (2017) 014508 [arXiv:1610.07011] [INSPIRE].

  17. [17]

    T. Appelquist et al., Strongly interacting dynamics and the search for new physics at the LHC, Phys. Rev.D 93 (2016) 114514 [arXiv:1601.04027] [INSPIRE].

    ADS  Google Scholar 

  18. [18]

    Lattice Strong Dynamics collaboration, Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavors, Phys. Rev.D 99 (2019) 014509 [arXiv:1807.08411] [INSPIRE].

  19. [19]

    C.T. Hill and E.H. Simmons, Strong dynamics and electroweak symmetry breaking, Phys. Rept.381 (2003) 235 [Erratum ibid.390 (2004) 553] [hep-ph/0203079] [INSPIRE].

  20. [20]

    R.D. Pisarski and F. Wilczek, Remarks on the Chiral Phase Transition in Chromodynamics, Phys. Rev.D 29 (1984) 338 [INSPIRE].

    ADS  Google Scholar 

  21. [21]

    E. Witten, Cosmic Separation of Phases, Phys. Rev.D 30 (1984) 272 [INSPIRE].

    ADS  Google Scholar 

  22. [22]

    eLISA collaboration, The Gravitational Universe, arXiv:1305.5720 [INSPIRE].

  23. [23]

    LISA collaboration, Laser Interferometer Space Antenna, arXiv:1702.00786 [INSPIRE].

  24. [24]

    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].

  25. [25]

    S. Sato et al., The status of DECIGO, J. Phys. Conf. Ser.840 (2017) 012010 [INSPIRE].

    Google Scholar 

  26. [26]

    S. Matsuzaki and K. Yamawaki, Dilaton Chiral Perturbation Theory: Determining the Mass and Decay Constant of the Technidilaton on the Lattice, Phys. Rev. Lett.113 (2014) 082002 [arXiv:1311.3784] [INSPIRE].

    ADS  Google Scholar 

  27. [27]

    M. Golterman and Y. Shamir, Low-energy effective action for pions and a dilatonic meson, Phys. Rev.D 94 (2016) 054502 [arXiv:1603.04575] [INSPIRE].

    ADS  Google Scholar 

  28. [28]

    A. Kasai, K.-i. Okumura and H. Suzuki, A dilaton-pion mass relation, arXiv:1609.02264 [INSPIRE].

  29. [29]

    T. Appelquist, J. Ingoldby and M. Piai, Dilaton EFT Framework For Lattice Data, JHEP07 (2017) 035 [arXiv:1702.04410] [INSPIRE].

    ADS  MATH  Google Scholar 

  30. [30]

    M. Hansen, K. Langæble and F. Sannino, Extending Chiral Perturbation Theory with an Isosinglet Scalar, Phys. Rev.D 95 (2017) 036005 [arXiv:1610.02904] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  31. [31]

    Y. Meurice, Linear σ-model for multiflavor gauge theories, Phys. Rev.D 96 (2017) 114507 [arXiv:1709.09264] [INSPIRE].

    ADS  Google Scholar 

  32. [32]

    LSD collaboration, Linear Sigma EFT for Nearly Conformal Gauge Theories, Phys. Rev.D 98 (2018) 114510 [arXiv:1809.02624] [INSPIRE].

  33. [33]

    Y. Chen, M. Huang and Q.-S. Yan, Gravitation waves from QCD and electroweak phase transitions, JHEP05 (2018) 178 [arXiv:1712.03470] [INSPIRE].

    ADS  Google Scholar 

  34. [34]

    E. Gildener and S. Weinberg, Symmetry Breaking and Scalar Bosons, Phys. Rev.D 13 (1976) 3333 [INSPIRE].

    ADS  Google Scholar 

  35. [35]

    A.J. Paterson, Coleman-Weinberg Symmetry Breaking in the Chiral SU(N ) × SU(N ) Linear σ-model, Nucl. Phys.B 190 (1981) 188 [INSPIRE].

    ADS  Google Scholar 

  36. [36]

    K. Tsumura, M. Yamada and Y. Yamaguchi, Gravitational wave from dark sector with dark pion, JCAP07 (2017) 044 [arXiv:1704.00219] [INSPIRE].

    ADS  Google Scholar 

  37. [37]

    L. Marzola, A. Racioppi and V. Vaskonen, Phase transition and gravitational wave phenomenology of scalar conformal extensions of the Standard Model, Eur. Phys. J.C 77 (2017) 484 [arXiv:1704.01034] [INSPIRE].

    ADS  Google Scholar 

  38. [38]

    M. Aoki, H. Goto and J. Kubo, Gravitational Waves from Hidden QCD Phase Transition, Phys. Rev.D 96 (2017) 075045 [arXiv:1709.07572] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  39. [39]

    D. Croon, V. Sanz and G. White, Model Discrimination in Gravitational Wave spectra from Dark Phase Transitions, JHEP08 (2018) 203 [arXiv:1806.02332] [INSPIRE].

    ADS  Google Scholar 

  40. [40]

    T. Prokopec, J. Rezacek and B. Świezżewska, Gravitational waves from conformal symmetry breaking, JCAP02 (2019) 009 [arXiv:1809.11129] [INSPIRE].

    MathSciNet  Google Scholar 

  41. [41]

    LatKMI collaboration, Walking and conformal dynamics in many-flavor QCD, PoS(LATTICE2015)213 (2016) [arXiv:1601.02287] [INSPIRE].

  42. [42]

    Y. Aoki et al., Flavor-singlet spectrum in multi-flavor QCD, EPJ Web Conf.175 (2018) 08023 [arXiv:1710.06549] [INSPIRE].

    Google Scholar 

  43. [43]

    V.A. Miransky and K. Yamawaki, Conformal phase transition in gauge theories, Phys. Rev.D 55 (1997) 5051 [Erratum ibid.D 56 (1997) 3768] [hep-th/9611142] [INSPIRE].

  44. [44]

    Y. Kikukawa, M. Kohda and J. Yasuda, First-order restoration of SU(Nf ) × SU(Nf ) chiral symmetry with large Nfand Electroweak phase transition, Phys. Rev.D 77 (2008) 015014 [arXiv:0709.2221] [INSPIRE].

    ADS  Google Scholar 

  45. [45]

    J. Jia, S. Matsuzaki and K. Yamawaki, Walking technipions at the LHC, Phys. Rev.D 87 (2013) 016006 [arXiv:1207.0735] [INSPIRE].

    ADS  Google Scholar 

  46. [46]

    S. Weinberg, Gauge and Global Symmetries at High Temperature, Phys. Rev.D 9 (1974) 3357 [INSPIRE].

    ADS  Google Scholar 

  47. [47]

    L. Dolan and R. Jackiw, Symmetry Behavior at Finite Temperature, Phys. Rev.D 9 (1974) 3320 [INSPIRE].

    ADS  Google Scholar 

  48. [48]

    D.J. Gross, R.D. Pisarski and L.G. Yaffe, QCD and Instantons at Finite Temperature, Rev. Mod. Phys.53 (1981) 43 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  49. [49]

    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].

  50. [50]

    J. Ellis, M. Lewicki and J.M. No, On the Maximal Strength of a First-Order Electroweak Phase Transition and its Gravitational Wave Signal, arXiv:1809.08242 [INSPIRE].

  51. [51]

    C. Caprini et al., Science with the space-based interferometer eLISA. II: Gravitational waves from cosmological phase transitions, JCAP04 (2016) 001 [arXiv:1512.06239] [INSPIRE].

  52. [52]

    S.R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev.D 15 (1977) 2929 [Erratum ibid.D 16 (1977) 1248] [INSPIRE].

  53. [53]

    C.G. Callan Jr. and S.R. Coleman, The Fate of the False Vacuum. 2. First Quantum Corrections, Phys. Rev.D 16 (1977) 1762 [INSPIRE].

  54. [54]

    A.D. Linde, Decay of the False Vacuum at Finite Temperature, Nucl. Phys.B 216 (1983) 421 [Erratum ibid.B 223 (1983) 544] [INSPIRE].

  55. [55]

    V. Brdar, A.J. Helmboldt and J. Kubo, Gravitational Waves from First-Order Phase Transitions: LIGO as a Window to Unexplored Seesaw Scales, JCAP02 (2019) 021 [arXiv:1810.12306] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  56. [56]

    L. Leitao and A. Megevand, Gravitational waves from a very strong electroweak phase transition, JCAP05 (2016) 037 [arXiv:1512.08962] [INSPIRE].

    ADS  Google Scholar 

  57. [57]

    R.-G. Cai, M. Sasaki and S.-J. Wang, The gravitational waves from the first-order phase transition with a dimension-six operator, JCAP08 (2017) 004 [arXiv:1707.03001] [INSPIRE].

    ADS  Google Scholar 

  58. [58]

    D. Bödeker and G.D. Moore, Electroweak Bubble Wall Speed Limit, JCAP05 (2017) 025 [arXiv:1703.08215] [INSPIRE].

  59. [59]

    D. Bödeker and G.D. Moore, Can electroweak bubble walls run away?, JCAP05 (2009) 009 [arXiv:0903.4099] [INSPIRE].

  60. [60]

    D.J. Weir, Gravitational waves from a first order electroweak phase transition: a brief review, Phil. Trans. Roy. Soc. Lond.A 376 (2018) 20170126 [arXiv:1705.01783] [INSPIRE].

    ADS  MATH  Google Scholar 

  61. [61]

    R. Jinno and M. Takimoto, Gravitational waves from bubble dynamics: Beyond the Envelope, JCAP01 (2019) 060 [arXiv:1707.03111] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  62. [62]

    K. Hashino, R. Jinno, M. Kakizaki, S. Kanemura, T. Takahashi and M. Takimoto, Selecting models of first-order phase transitions using the synergy between collider and gravitational-wave experiments, Phys. Rev.D 99 (2019) 075011 [arXiv:1809.04994] [INSPIRE].

    ADS  Google Scholar 

  63. [63]

    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].

    ADS  Google Scholar 

  64. [64]

    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].

    ADS  Google Scholar 

  65. [65]

    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].

    ADS  Google Scholar 

  66. [66]

    J.T. Giblin Jr. and J.B. Mertens, Vacuum Bubbles in the Presence of a Relativistic Fluid, JHEP12 (2013) 042 [arXiv:1310.2948] [INSPIRE].

    ADS  Google Scholar 

  67. [67]

    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].

    ADS  Google Scholar 

  68. [68]

    J.R. Espinosa, T. Konstandin, J.M. No and G. Servant, Energy Budget of Cosmological First-order Phase Transitions, JCAP06 (2010) 028 [arXiv:1004.4187] [INSPIRE].

    ADS  Google Scholar 

  69. [69]

    C. Caprini, R. Durrer and G. Servant, The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition, JCAP12 (2009) 024 [arXiv:0909.0622] [INSPIRE].

    ADS  Google Scholar 

  70. [70]

    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, JCAP06 (2012) 027 [arXiv:1201.0983] [INSPIRE].

    ADS  Google Scholar 

  71. [71]

    A. Kosowsky, A. Mack and T. Kahniashvili, Gravitational radiation from cosmological turbulence, Phys. Rev.D 66 (2002) 024030 [astro-ph/0111483] [INSPIRE].

  72. [72]

    J.M. Cornwall, R. Jackiw and E. Tomboulis, Effective Action for Composite Operators, Phys. Rev.D 10 (1974) 2428 [INSPIRE].

    ADS  MATH  Google Scholar 

  73. [73]

    R. Jinno and M. Takimoto, Gravitational waves from bubble collisions: An analytic derivation, Phys. Rev.D 95 (2017) 024009 [arXiv:1605.01403] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  74. [74]

    S. Kuroyanagi, K. Nakayama and J. Yokoyama, Prospects of determination of reheating temperature after inflation by DECIGO, PTEP2015 (2015) 013E02 [arXiv:1410.6618] [INSPIRE].

  75. [75]

    K. Yagi and N. Seto, Detector configuration of DECIGO/BBO and identification of cosmological neutron-star binaries, Phys. Rev.D 83 (2011) 044011 [Erratum ibid.D 95 (2017) 109901] [arXiv:1101.3940] [INSPIRE].

  76. [76]

    K. Hashino, M. Kakizaki, S. Kanemura and T. Matsui, Synergy between measurements of gravitational waves and the triple-Higgs coupling in probing the first-order electroweak phase transition, Phys. Rev.D 94 (2016) 015005 [arXiv:1604.02069] [INSPIRE].

    ADS  Google Scholar 

Download references

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

Affiliations

Authors

Corresponding author

Correspondence to Hiroshi Ohki.

Additional information

ArXiv ePrint: 1811.05670

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/.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Miura, K., Ohki, H., Otani, S. et al. Gravitational waves from walking technicolor. J. High Energ. Phys. 2019, 194 (2019). https://doi.org/10.1007/JHEP10(2019)194

Download citation

Keywords

  • Technicolor and Composite Models
  • Beyond Standard Model
  • Higgs Physics
  • Cosmology of Theories beyond the SM