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Robust approach to thermal resummation: Standard Model meets a singlet

  • Regular Article - Theoretical Physics
  • Open access
  • Published: 21 June 2021
  • Volume 2021, article number 130, (2021)
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Journal of High Energy Physics Aims and scope Submit manuscript
Robust approach to thermal resummation: Standard Model meets a singlet
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  • Philipp M. Schicho  ORCID: orcid.org/0000-0001-5869-76111,2,
  • Tuomas V. I. Tenkanen2,3,4,5 &
  • Juuso Österman  ORCID: orcid.org/0000-0002-1546-34251 
  • 515 Accesses

  • 58 Citations

  • 8 Altmetric

  • 1 Mention

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A preprint version of the article is available at arXiv.

Abstract

Perturbation theory alone fails to describe thermodynamics of the electroweak phase transition. We review a technique combining perturbative and non-perturbative methods to overcome this challenge. Accordingly, the principal theme is a tutorial of high­temperature dimensional reduction. We present an explicit derivation with a real singlet scalar and compute the thermal effective potential at two-loop order. In particular, we detail the dimensional reduction for a real-singlet extended Standard Model. The resulting effective theory will impact future non-perturbative studies based on lattice simulations as well as purely perturbative investigations.

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References

  1. R. Apreda, M. Maggiore, A. Nicolis and A. Riotto, Gravitational waves from electroweak phase transitions, Nucl. Phys. B 631 (2002) 342 [gr-qc/0107033] [INSPIRE].

  2. C. Grojean and G. Servant, Gravitational waves from phase transitions at the electroweak scale and beyond, Phys. Rev. D 75 (2007) 043507 [hep-ph/0607107] [INSPIRE].

  3. 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].

    MATH  ADS  Google Scholar 

  4. C. Caprini and D.G. Figueroa, Cosmological backgrounds of gravitational waves, Class. Quant. Grav. 35 (2018) 163001 [arXiv:1801.04268] [INSPIRE].

    Article  MathSciNet  MATH  ADS  Google Scholar 

  5. M.B. Hindmarsh, M. Lüben, J. Lumma and M. Pauly, Phase transitions in the early universe, SciPost Phys. Lect. Notes 24 (2021) 1 [arXiv:2008.09136] [INSPIRE].

    Google Scholar 

  6. LIGO Scientific and Virgo collaborations, Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116 (2016) 061102 [arXiv:1602.03837] [INSPIRE].

  7. LIGO Scientific and Virgo collaborations, GW151226: observation of gravitational waves from a 22-solar-mass binary black hole coalescence, Phys. Rev. Lett. 116 (2016) 241103 [arXiv:1606.04855] [INSPIRE].

  8. LIGO Scientific and Virgo collaborations, GW170104: observation of a 50-solar-mass binary black hole coalescence at redshift 0.2, Phys. Rev. Lett. 118 (2017) 221101 [Erratum ibid. 121 (2018) 129901] [arXiv:1706.01812] [INSPIRE].

  9. LIGO Scientific and Virgo collaborations, GW170817: observation of gravitational waves from a binary neutron star inspiral, Phys. Rev. Lett. 119 (2017) 161101 [arXiv:1710.05832] [INSPIRE].

  10. LIGO Scientific, Virgo, Fermi GBM, INTEGRAL, IceCube, AstroSat Cadmium Zinc Telluride Imager Team, IPN, Insight-Hxmt, ANTARES, Swift, AGILE Team, 1M2H Team, Dark Energy Camera GW-EM, DES, DLT40, GRAWITA, Fermi-LAT, ATCA, ASKAP, Las Cumbres Observatory Group, OzGrav, DWF ( Deeper Wider Faster Program), AST3, CAASTRO, VINROUGE, MASTER, J-GEM, GROWTH, JAGWAR, CaltechNRAO, TTU-NRAO, NuSTAR, Pan-STARRS, MAXI Team, TZAC Consortium, KU, Nordic Optical Telescope, ePESSTO, GROND, Texas Tech University, SALT Group, TOROS, BOOTES, MWA, CALET, IKI-GW Follow-up, H.E.S.S., LOFAR, LWA, HAWC, Pierre Auger, ALMA, Euro VLBI Team, Pi of Sky, Chandra Team at McGill University, DFN, ATLAS Telescopes, High Time Resolution Universe Survey, RIMAS, RATIR AND SKA South Africa/MeerKAT collaborations, Multi-messenger observations of a binary neutron star merger, Astrophys. J. Lett. 848 (2017) L12 [arXiv:1710.05833] [INSPIRE].

  11. LIGO Scientific, Virgo, Fermi-GEM and INTEGRAL collaborations, Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817 A, Astrophys. J. Lett. 848 (2017) L13 [arXiv:1710.05834] [INSPIRE].

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

  13. 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].

  14. W.-H. Ruan, Z.-K. Guo, R.-G. Cai and Y.-Z. Zhang, Taiji program: gravitational-wave sources, Int. J. Mod. Phys. A 35 (2020) 2050075 [arXiv:1807.09495] [INSPIRE].

    Article  ADS  Google Scholar 

  15. S. Kawamura et al., The Japanese space gravitational wave antenna: DECIGO, Class. Quant. Grav. 28 (2011) 094011 [INSPIRE].

    Article  ADS  Google Scholar 

  16. A. Ashoorioon and T. Konstandin, Strong electroweak phase transitions without collider traces, JHEP 07 (2009) 086 [arXiv:0904.0353] [INSPIRE].

    Article  ADS  Google Scholar 

  17. A. Alves, T. Ghosh, H.-K. Guo, K. Sinha and D. Vagie, Collider and gravitational wave complementarity in exploring the singlet extension of the Standard Model, JHEP 04 (2019) 052 [arXiv:1812.09333] [INSPIRE].

    Article  ADS  Google Scholar 

  18. A. Mazumdar and G. White, Review of cosmic phase transitions: their significance and experimental signatures, Rept. Prog. Phys. 82 (2019) 076901 [arXiv:1811.01948] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. 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].

    Article  ADS  Google Scholar 

  20. K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, Is there a hot electroweak phase transition at mH ≳ mw?, Phys. Rev. Lett. 77 (1996) 2887 [hep-ph/9605288] [INSPIRE].

  21. K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, A nonperturbative analysis of the finite T phase transition in SU(2) × U(1) electroweak theory, Nucl. Phys. B 493 (1997) 413 [hep-lat/9612006] [INSPIRE].

  22. M. Gürtler, E.-M. Ilgenfritz and A. Schiller, Where the electroweak phase transition ends, Phys. Rev. D 56 (1997) 3888 [hep-lat/9704013] [INSPIRE].

  23. F. Csikor, Z. Fodor and J. Heitger, Endpoint of the hot electroweak phase transition, Phys. Rev. Lett. 82 (1999) 21 [hep-ph/9809291] [INSPIRE].

  24. M. D’Onofrio and K. Rummukainen, Standard Model cross-over on the lattice, Phys. Rev. D 93 (2016) 025003 [arXiv:1508.07161] [INSPIRE].

    Article  ADS  Google Scholar 

  25. 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].

  26. 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].

  27. V.A. Kuzmin, V.A. Rubakov and M.E. Shaposhnikov, On the anomalous electroweak baryon number nonconservation in the early universe, Phys. Lett. B 155 (1985) 36 [INSPIRE].

    Article  ADS  Google Scholar 

  28. M. Trodden, Electroweak baryogenesis, Rev. Mod. Phys. 71 (1999) 1463 [hep-ph/9803479] [INSPIRE].

  29. D.E. Morrissey and M.J. Ramsey-Musolf, Electroweak baryogenesis, New J. Phys. 14 (2012) 125003 [arXiv:1206.2942] [INSPIRE].

    Article  ADS  Google Scholar 

  30. M.J. Ramsey-Musolf, The electroweak phase transition: a collider target, JHEP 09 (2020) 179 [arXiv:1912.07189] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. J.M. No and M. Ramsey-Musolf, Probing the Higgs portal at the LHC through resonant di-Higgs production, Phys. Rev. D 89 (2014) 095031 [arXiv:1310.6035] [INSPIRE].

    Article  ADS  Google Scholar 

  32. G.C. Dorsch, S.J. Huber, K. Mimasu and J.M. No, Echoes of the electroweak phase transition: discovering a second Higgs doublet through A0 → ZH0, Phys. Rev. Lett. 113 (2014) 211802 [arXiv:1405.5537] [INSPIRE].

    Article  ADS  Google Scholar 

  33. N. Craig, H.K. Lou, M. McCullough and A. Thalapillil, The Higgs portal above threshold, JHEP 02 (2016) 127 [arXiv:1412.0258] [INSPIRE].

    Article  ADS  Google Scholar 

  34. A.V. Kotwal, M.J. Ramsey-Musolf, J.M. No and P. Winslow, Singlet-catalyzed electroweak phase transitions in the 100 TeV frontier, Phys. Rev. D 94 (2016) 035022 [arXiv:1605.06123] [INSPIRE].

    Article  ADS  Google Scholar 

  35. T. Huang et al., Resonant di-Higgs boson production in the \( b\overline{b} WW \) channel: probing the electroweak phase transition at the LHC, Phys. Rev. D 96 (2017) 035007 [arXiv:1701.04442] [INSPIRE].

    Article  ADS  Google Scholar 

  36. C.-Y. Chen, J. Kozaczuk and I.M. Lewis, Non-resonant collider signatures of a singlet-driven electroweak phase transition, JHEP 08 (2017) 096 [arXiv:1704.05844] [INSPIRE].

    ADS  Google Scholar 

  37. N.F. Bell, M.J. Dolan, L.S. Friedrich, M.J. Ramsey-Musolf and R.R. Volkas, Two-step electroweak symmetry-breaking: theory meets experiment, JHEP 05 (2020) 050 [arXiv:2001.05335] [INSPIRE].

    Article  ADS  Google Scholar 

  38. Y. Kondo, I. Umemura and K. Yamamoto, First order phase transition in the singlet Majoron model, Phys. Lett. B 263 (1991) 93 [INSPIRE].

    Article  ADS  Google Scholar 

  39. K. Enqvist, K. Kainulainen and I. Vilja, Phase transitions in the singlet Majoron model, Nucl. Phys. B 403 (1993) 749 [INSPIRE].

    Article  ADS  Google Scholar 

  40. J.R. Espinosa and M. Quirós, The electroweak phase transition with a singlet, Phys. Lett. B 305 (1993) 98 [hep-ph/9301285] [INSPIRE].

  41. J. Choi and R.R. Volkas, Real Higgs singlet and the electroweak phase transition in the Standard Model, Phys. Lett. B 317 (1993) 385 [hep-ph/9308234] [INSPIRE].

  42. S. Profumo, M.J. Ramsey-Musolf and G. Shaughnessy, Singlet Higgs phenomenology and the electroweak phase transition, JHEP 08 (2007) 010 [arXiv:0705.2425] [INSPIRE].

    Article  ADS  Google Scholar 

  43. A. Ahriche, What is the criterion for a strong first order electroweak phase transition in singlet models?, Phys. Rev. D 75 (2007) 083522 [hep-ph/0701192] [INSPIRE].

  44. J.R. Espinosa, T. Konstandin and F. Riva, Strong electroweak phase transitions in the Standard Model with a singlet, Nucl. Phys. B 854 (2012) 592 [arXiv:1107.5441] [INSPIRE].

    Article  MATH  ADS  Google Scholar 

  45. J.M. Cline and K. Kainulainen, Electroweak baryogenesis and dark matter from a singlet Higgs, JCAP 01 (2013) 012 [arXiv:1210.4196] [INSPIRE].

    Article  ADS  Google Scholar 

  46. J.M. Cline, K. Kainulainen, P. Scott and C. Weniger, Update on scalar singlet dark matter, Phys. Rev. D 88 (2013) 055025 [Erratum ibid. 92 (2015) 039906] [arXiv:1306.4710] [INSPIRE].

  47. T. Alanne, K. Tuominen and V. Vaskonen, Strong phase transition, dark matter and vacuum stability from simple hidden sectors, Nucl. Phys. B 889 (2014) 692 [arXiv:1407.0688] [INSPIRE].

    Article  MATH  ADS  Google Scholar 

  48. S. Profumo, M.J. Ramsey-Musolf, C.L. Wainwright and P. Winslow, Singlet-catalyzed electroweak phase transitions and precision Higgs boson studies, Phys. Rev. D 91 (2015) 035018 [arXiv:1407.5342] [INSPIRE].

    Article  ADS  Google Scholar 

  49. D. Curtin, P. Meade and C.-T. Yu, Testing electroweak baryogenesis with future colliders, JHEP 11 (2014) 127 [arXiv:1409.0005] [INSPIRE].

  50. M. Kakizaki, S. Kanemura and T. Matsui, Gravitational waves as a probe of extended scalar sectors with the first order electroweak phase transition, Phys. Rev. D 92 (2015) 115007 [arXiv:1509.08394] [INSPIRE].

    Article  ADS  Google Scholar 

  51. A. Beniwal, M. Lewicki, J.D. Wells, M. White and A.G. Williams, Gravitational wave, collider and dark matter signals from a scalar singlet electroweak baryogenesis, JHEP 08 (2017) 108 [arXiv:1702.06124] [INSPIRE].

    Article  ADS  Google Scholar 

  52. G. Kurup and M. Perelstein, Dynamics of electroweak phase transition in singlet-scalar extension of the Standard Model, Phys. Rev. D 96 (2017) 015036 [arXiv:1704.03381] [INSPIRE].

    Article  ADS  Google Scholar 

  53. C.-W. Chiang, M.J. Ramsey-Musolf and E. Senaha, Standard Model with a complex scalar singlet: cosmological implications and theoretical considerations, Phys. Rev. D 97 (2018) 015005 [arXiv:1707.09960] [INSPIRE].

    Article  ADS  Google Scholar 

  54. C.-W. Chiang, Y.-T. Li and E. Senaha, Revisiting electroweak phase transition in the Standard Model with a real singlet scalar, Phys. Lett. B 789 (2019) 154 [arXiv:1808.01098] [INSPIRE].

    Article  ADS  Google Scholar 

  55. T. Alanne, T. Hugle, M. Platscher and K. Schmitz, A fresh look at the gravitational-wave signal from cosmological phase transitions, JHEP 03 (2020) 004 [arXiv:1909.11356] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  56. N. Chen, T. Li, Y. Wu and L. Bian, Complementarity of the future e+e− colliders and gravitational waves in the probe of complex singlet extension to the Standard Model, Phys. Rev. D 101 (2020) 075047 [arXiv:1911.05579] [INSPIRE].

    Article  ADS  Google Scholar 

  57. T. Alanne et al., Pseudo-Goldstone dark matter: gravitational waves and direct-detection blind spots, JHEP 10 (2020) 080 [arXiv:2008.09605] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  58. A. Papaefstathiou and G. White, The electro-weak phase transition at colliders: confronting theoretical uncertainties and complementary channels, JHEP 05 (2021) 099 [arXiv:2010.00597] [INSPIRE].

    Article  ADS  Google Scholar 

  59. K. Funakubo, A. Kakuta and K. Takenaga, The effective potential of electroweak theory with two massless Higgs doublets at finite temperature, Prog. Theor. Phys. 91 (1994) 341 [hep-ph/9310267] [INSPIRE].

  60. A.T. Davies, C.D. froggatt, G. Jenkins and R.G. Moorhouse, Baryogenesis constraints on two Higgs doublet models, Phys. Lett. B 336 (1994) 464 [INSPIRE].

  61. J.M. Cline, K. Kainulainen and A.P. Vischer, Dynamics of two Higgs doublet CP-violation and baryogenesis at the electroweak phase transition, Phys. Rev. D 54 (1996) 2451 [hep-ph/9506284] [INSPIRE].

  62. L. Fromme, S.J. Huber and M. Seniuch, Baryogenesis in the two-Higgs doublet model, JHEP 11 (2006) 038 [hep-ph/0605242] [INSPIRE].

  63. J.M. Cline, K. Kainulainen and M. Trott, Electroweak baryogenesis in two Higgs doublet models and B meson anomalies, JHEP 11 (2011) 089 [arXiv:1107.3559] [INSPIRE].

    Article  MATH  ADS  Google Scholar 

  64. G.C. Dorsch, S.J. Huber and J.M. No, A strong electroweak phase transition in the 2HDM after LHC8, JHEP 10 (2013) 029 [arXiv:1305.6610] [INSPIRE].

    Article  ADS  Google Scholar 

  65. G.C. Dorsch, S.J. Huber, T. Konstandin and J.M. No, A second Higgs doublet in the early universe: baryogenesis and gravitational waves, JCAP 05 (2017) 052 [arXiv:1611.05874] [INSPIRE].

    Article  ADS  Google Scholar 

  66. P. Basler, M. Krause, M. Mühlleitner, J. Wittbrodt and A. Wlotzka, Strong first order electroweak phase transition in the CP-conserving 2HDM revisited, JHEP 02 (2017) 121 [arXiv:1612.04086] [INSPIRE].

    Article  ADS  Google Scholar 

  67. P. Basler, M. Mühlleitner and J. Wittbrodt, The CP-violating 2HDM in light of a strong first order electroweak phase transition and implications for Higgs pair production, JHEP 03 (2018) 061 [arXiv:1711.04097] [INSPIRE].

    Article  ADS  Google Scholar 

  68. J. Bernon, L. Bian and Y. Jiang, A new insight into the phase transition in the early universe with two Higgs doublets, JHEP 05 (2018) 151 [arXiv:1712.08430] [INSPIRE].

  69. H.H. Patel and M.J. Ramsey-Musolf, Stepping into electroweak symmetry breaking: phase transitions and Higgs phenomenology, Phys. Rev. D 88 (2013) 035013 [arXiv:1212.5652] [INSPIRE].

    Article  ADS  Google Scholar 

  70. M. Chala, M. Ramos and M. Spannowsky, Gravitational wave and collider probes of a triplet Higgs sector with a low cutoff, Eur. Phys. J. C. 79 (2019) 156 [arXiv:1812.01901] [INSPIRE].

    Article  ADS  Google Scholar 

  71. S.S. AbdusSalam and T.A. Chowdhury, Scalar representations in the light of electroweak phase transition and cold dark matter phenomenology, JCAP 05 (2014) 026 [arXiv:1310.8152] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  72. M. Chala, G. Nardini and I. Sobolev, Unified explanation for dark matter and electroweak baryogenesis with direct detection and gravitational wave signatures, Phys. Rev. D 94 (2016) 055006 [arXiv:1605.08663] [INSPIRE].

    Article  ADS  Google Scholar 

  73. P. Basler, M. Mühlleitner and J. Müller, Electroweak phase transition in non-minimal Higgs sectors, JHEP 05 (2020) 016 [arXiv:1912.10477] [INSPIRE].

    Article  ADS  Google Scholar 

  74. C. Grojean, G. Servant and J.D. Wells, First-order electroweak phase transition in the Standard Model with a low cutoff, Phys. Rev. D 71 (2005) 036001 [hep-ph/0407019] [INSPIRE].

  75. D. Bödeker, L. Fromme, S.J. Huber and M. Seniuch, The baryon asymmetry in the Standard Model with a low cut-off, JHEP 02 (2005) 026 [hep-ph/0412366] [INSPIRE].

  76. C. Delaunay, C. Grojean and J.D. Wells, Dynamics of non-renormalizable electroweak symmetry breaking, JHEP 04 (2008) 029 [arXiv:0711.2511] [INSPIRE].

    Article  ADS  Google Scholar 

  77. B. Grinstein and M. Trott, Electroweak baryogenesis with a pseudo-Goldstone Higgs, Phys. Rev. D 78 (2008) 075022 [arXiv:0806.1971] [INSPIRE].

    Article  ADS  Google Scholar 

  78. F.P. Huang, Y. Wan, D.-G. Wang, Y.-F. Cai and X. Zhang, Hearing the echoes of electroweak baryogenesis with gravitational wave detectors, Phys. Rev. D 94 (2016) 041702 [arXiv:1601.01640] [INSPIRE].

    Article  ADS  Google Scholar 

  79. 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].

    Article  ADS  Google Scholar 

  80. J. de Vries, M. Postma, J. van de Vis and G. White, Electroweak baryogenesis and the Standard Model effective field theory, JHEP 01 (2018) 089 [arXiv:1710.04061] [INSPIRE].

    Article  MATH  Google Scholar 

  81. M. Chala, C. Krause and G. Nardini, Signals of the electroweak phase transition at colliders and gravitational wave observatories, JHEP 07 (2018) 062 [arXiv:1802.02168] [INSPIRE].

    Article  ADS  Google Scholar 

  82. M. Postma and G. White, Cosmological phase transitions: is effective field theory just a toy?, JHEP 03 (2021) 280 [arXiv:2012.03953] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  83. M.E. Shaposhnikov, Structure of the high temperature gauge ground state and electroweak production of the baryon asymmetry, Nucl. Phys. B 299 (1988) 797 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  84. G.R. Farrar and M.E. Shaposhnikov, Baryon asymmetry of the universe in the minimal Standard Model, Phys. Rev. Lett. 70 (1993) 2833 [Erratum ibid. 71 (1993) 210] [hep-ph/9305274] [INSPIRE].

  85. G.R. Farrar and M.E. Shaposhnikov, Baryon asymmetry of the universe in the standard electroweak theory, Phys. Rev. D 50 (1994) 774 [hep-ph/9305275] [INSPIRE].

  86. M.B. Gavela, P. Hernández, J. Orloff and O. Pène, Standard Model CP-violation and baryon asymmetry, Mod. Phys. Lett. A 9 (1994) 795 [hep-ph/9312215] [INSPIRE].

  87. M.B. Gavela, M. Lozano, J. Orloff and O. Pène, Standard Model CP-violation and baryon asymmetry. Part 1. Zero temperature, Nucl. Phys. B 430 (1994) 345 [hep-ph/9406288] [INSPIRE].

  88. T. Brauner, O. Taanila, A. Tranberg and A. Vuorinen, Temperature dependence of Standard Model CP-violation, Phys. Rev. Lett. 108 (2012) 041601 [arXiv:1110.6818] [INSPIRE].

    Article  ADS  Google Scholar 

  89. T. Brauner, O. Taanila, A. Tranberg and A. Vuorinen, Computing the temperature dependence of effective CP-violation in the Standard Model, JHEP 11 (2012) 076 [arXiv:1208.5609] [INSPIRE].

    Article  ADS  Google Scholar 

  90. D. Land and E.D. Carlson, Two stage phase transition in two Higgs models, Phys. Lett. B 292 (1992) 107 [hep-ph/9208227] [INSPIRE].

  91. S. Inoue, G. Ovanesyan and M.J. Ramsey-Musolf, Two-step electroweak baryogenesis, Phys. Rev. D 93 (2016) 015013 [arXiv:1508.05404] [INSPIRE].

    Article  ADS  Google Scholar 

  92. N. Blinov, J. Kozaczuk, D.E. Morrissey and C. Tamarit, Electroweak baryogenesis from exotic electroweak symmetry breaking, Phys. Rev. D 92 (2015) 035012 [arXiv:1504.05195] [INSPIRE].

    Article  ADS  Google Scholar 

  93. D. Croon and G. White, Exotic gravitational wave signatures from simultaneous phase transitions, JHEP 05 (2018) 210 [arXiv:1803.05438] [INSPIRE].

    Article  ADS  Google Scholar 

  94. P. Schwaller, Gravitational waves from a dark phase transition, Phys. Rev. Lett. 115 (2015) 181101 [arXiv:1504.07263] [INSPIRE].

    Article  ADS  Google Scholar 

  95. W.-C. Huang, M. Reichert, F. Sannino and Z.-W. Wang, Testing the dark confined landscape: from lattice to gravitational waves, arXiv:2012.11614 [INSPIRE].

  96. 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].

    Article  ADS  Google Scholar 

  97. D. Croon, T.E. Gonzalo and G. White, Gravitational waves from a Pati-Salam phase transition, JHEP 02 (2019) 083 [arXiv:1812.02747] [INSPIRE].

    Article  ADS  Google Scholar 

  98. W.-C. Huang, F. Sannino and Z.-W. Wang, Gravitational waves from Pati-Salam dynamics, Phys. Rev. D 102 (2020) 095025 [arXiv:2004.02332] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  99. E. Hall, T. Konstandin, R. McGehee, H. Murayama and G. Servant, Baryogenesis from a dark first-order phase transition, JHEP 04 (2020) 042 [arXiv:1910.08068] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  100. D. Croon, A. Kusenko, A. Mazumdar and G. White, Solitosynthesis and gravitational waves, Phys. Rev. D 101 (2020) 085010 [arXiv:1910.09562] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  101. D. Croon, R. Houtz and V. Sanz, Dynamical axions and gravitational waves, JHEP 07 (2019) 146 [arXiv:1904.10967] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  102. A.D. Linde, Infrared problem in thermodynamics of the Yang-Mills gas, Phys. Lett. B 96 (1980) 289 [INSPIRE].

    Article  ADS  Google Scholar 

  103. E. Braaten and R.D. Pisarski, Simple effective Lagrangian for hard thermal loops, Phys. Rev. D 45 (1992) R1827 [INSPIRE].

    Article  ADS  Google Scholar 

  104. 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. 50 (1994) 6662] [hep-ph/9212235] [INSPIRE].

  105. K. Farakos, K. Kajantie, K. Rummukainen and M.E. Shaposhnikov, 3D physics and the electroweak phase transition: a framework for lattice Monte Carlo analysis, Nucl. Phys. B 442 (1995) 317 [hep-lat/9412091] [INSPIRE].

  106. K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, The electroweak phase transition: a nonperturbative analysis, Nucl. Phys. B 466 (1996) 189 [hep-lat/9510020] [INSPIRE].

  107. P.H. Ginsparg, First order and second order phase transitions in gauge theories at finite temperature, Nucl. Phys. B 170 (1980) 388 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  108. T. Appelquist and R.D. Pisarski, High-temperature Yang-Mills theories and three-dimensional quantum chromodynamics, Phys. Rev. D 23 (1981) 2305 [INSPIRE].

    Article  ADS  Google Scholar 

  109. S. Nadkarni, Dimensional reduction in hot QCD, Phys. Rev. D 27 (1983) 917 [INSPIRE].

    Article  ADS  Google Scholar 

  110. N.P. Landsman, Limitations to dimensional reduction at high temperature, Nucl. Phys. B 322 (1989) 498 [INSPIRE].

    Article  ADS  Google Scholar 

  111. 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].

  112. E. Braaten and A. Nieto, Effective field theory approach to high temperature thermodynamics, Phys. Rev. D 51 (1995) 6990 [hep-ph/9501375] [INSPIRE].

  113. E. Braaten and A. Nieto, Free energy of QCD at high temperature, Phys. Rev. D 53 (1996) 3421 [hep-ph/9510408] [INSPIRE].

  114. K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, 3D SU(N) + adjoint Higgs theory and finite temperature QCD, Nucl. Phys. B 503 (1997) 357 [hep-ph/9704416] [INSPIRE].

  115. K. Kajantie, M. Laine, J. Peisa, A. Rajantie, K. Rummukainen and M.E. Shaposhnikov, Nonperturbative Debye mass in finite temperature QCD, Phys. Rev. Lett. 79 (1997) 3130 [hep-ph/9708207] [INSPIRE].

  116. J.O. Andersen, On effective field theories at finite temperature, Ph.D. thesis, University of Oslo, Oslo, Norway (1997) [hep-ph/9709331] [INSPIRE].

  117. K. Kajantie, M. Laine, A. Rajantie, K. Rummukainen and M. Tsypin, The phase diagram of three-dimensional SU(3) + adjoint Higgs theory, JHEP 11 (1998) 011 [hep-lat/9811004] [INSPIRE].

  118. K. Kajantie, M. Laine, K. Rummukainen and Y. Schroder, How to resum long distance contributions to the QCD pressure?, Phys. Rev. Lett. 86 (2001) 10 [hep-ph/0007109] [INSPIRE].

  119. K. Kajantie, M. Laine, K. Rummukainen and Y. Schröder, The pressure of hot QCD up to g6 ln(1/g), Phys. Rev. D 67 (2003) 105008 [hep-ph/0211321] [INSPIRE].

  120. K. Kajantie, M. Laine, K. Rummukainen and Y. Schröder, Four loop vacuum energy density of the SU(Nc) + adjoint Higgs theory, JHEP 04 (2003) 036 [hep-ph/0304048] [INSPIRE].

  121. M. Laine and M. Vepsäläinen, Mesonic correlation lengths in high temperature QCD, JHEP 02 (2004) 004 [hep-ph/0311268] [INSPIRE].

  122. A. Hietanen, K. Kajantie, M. Laine, K. Rummukainen and Y. Schröder, Plaquette expectation value and gluon condensate in three dimensions, J HEP 01 (2005) 013 [hep-lat/0412008] [INSPIRE].

  123. M. Vepsäläinen, Mesonic screening masses at high temperature and finite density, JHEP 03 (2007) 022 [hep-ph/0701250] [INSPIRE].

  124. A. Hietanen, K. Kajantie, M. Laine, K. Rummukainen and Y. Schröder, Three-dimensional physics and the pressure of hot QCD, Phys. Rev. D 79 (2009) 045018 [arXiv:0811.4664] [INSPIRE].

  125. J. Ghiglieri, A. Kurkela, M. Strickland and A. Vuorinen, Perturbative thermal QCD: formalism and applications, Phys. Rept. 880 (2020) 1 [arXiv:2002.10188] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  126. M. Gürtler, E.-M. Ilgenfritz, J. Kripfganz, H. Perlt and A. Schiller, Three-dimensional lattice studies of the electroweak phase transition at MHiggs approximates 70 GeV, Nucl. Phys. B 483 (1997) 383 [hep-lat/9605042] [INSPIRE].

  127. 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].

  128. 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].

  129. A. Gynther and M. Vepsäläinen, Pressure of the Standard Model at high temperatures, JHEP 01 (2006) 060 [hep-ph/0510375] [INSPIRE].

  130. A. Gynther and M. Vepsäläinen, Pressure of the Standard Model near the electroweak phase transition, JHEP 03 (2006) 011 [hep-ph/0512177] [INSPIRE].

  131. M. Vepsäläinen, Applications of dimensional reduction to electroweak and QCD matter, Ph.D. thesis, Helsinki U., Helsinki, Finland (2007) [arXiv:0709.2773] [INSPIRE].

  132. M. Losada, High temperature dimensional reduction of the MSSM and other multiscalar models, Phys. Rev. D 56 (1997) 2893 [hep-ph/9605266] [INSPIRE].

  133. M. Losada, The electroweak phase transition in the minimal supersymmetric Standard Model, Ph.D. thesis, Rutgers U., Piscataway, NJ, U.S.A. (1996) [hep-ph/9612337] [INSPIRE].

  134. G.R. Farrar and M. Losada, SUSY and the electroweak phase transition, Phys. Lett. B 406 (1997) 60 [hep-ph/9612346] [INSPIRE].

  135. J.M. Cline and K. Kainulainen, Supersymmetric electroweak phase transition: beyond perturbation theory, Nucl. Phys. B 482 (1996) 73 [hep-ph/9605235] [INSPIRE].

  136. J.M. Cline and K. Kainulainen, Supersymmetric electroweak phase transition: dimensional reduction versus effective potential, Nucl. Phys. B 510 (1998) 88 [hep-ph/9705201] [INSPIRE].

  137. D. Bödeker, P. John, M. Laine and M.G. Schmidt, The two loop MSSM finite temperature effective potential with stop condensation, Nucl. Phys. B 497 (1997) 387 [hep-ph/9612364] [INSPIRE].

  138. M. Laine and K. Rummukainen, A strong electroweak phase transition up to mH is about 105 GeV, Phys. Rev. Lett. 80 (1998) 5259 [hep-ph/9804255] [INSPIRE].

  139. M. Laine and K. Rummukainen, The MSSM electroweak phase transition on the lattice, Nucl. Phys. B 535 (1998) 423 [hep-lat/9804019] [INSPIRE].

  140. M. Laine and K. Rummukainen, Higgs sector CP-violation at the electroweak phase transition, Nucl. Phys. B 545 (1999) 141 [hep-ph/9811369] [INSPIRE].

  141. 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].

  142. M. Laine, G. Nardini and K. Rummukainen, Lattice study of an electroweak phase transition at mh ⋍ 126 GeV, JCAP 01 (2013) 011 [arXiv:1211.7344] [INSPIRE].

    Article  ADS  Google Scholar 

  143. J.O. Andersen, Dimensional reduction of the two Higgs doublet model at high temperature, Eur. Phys. J. C 11 (1999) 563 [hep-ph/9804280] [INSPIRE].

  144. M. Laine and K. Rummukainen, Two Higgs doublet dynamics at the electroweak phase transition: a nonperturbative study, Nucl. Phys. B 597 (2001) 23 [hep-lat/0009025] [INSPIRE].

  145. M. Karjalainen and J. Peisa, Dimensionally reduced U(1) + Higgs theory in the broken phase, Z. Phys. C 76 (1997) 319 [hep-lat/9607023] [INSPIRE].

  146. K. Kajantie, M. Karjalainen, M. Laine and J. Peisa, Masses and phase structure in the Ginzburg-Landau model, Phys. Rev. B 57 (1998) 3011 [cond-mat/9704056] [INSPIRE].

  147. K. Kajantie, M. Karjalainen, M. Laine and J. Peisa, Three-dimensional U(1) gauge + Higgs theory as an effective theory for finite temperature phase transitions, Nucl. Phys. B 520 (1998) 345 [hep-lat/9711048] [INSPIRE].

  148. J.O. Andersen, 3D effective field theory for finite temperature scalar electrodynamics, Phys. Rev. D 59 (1999) 065015 [hep-ph/9709418] [INSPIRE].

  149. A. Rajantie, SU(5) + adjoint Higgs model at finite temperature, Nucl. Phys. B 501 (1997) 521 [hep-ph/9702255] [INSPIRE].

  150. K. Jansen and M. Laine, Inverse symmetry breaking with 4D lattice simulations, Phys. Lett. B 435 (1998) 166 [hep-lat/9805024] [INSPIRE].

  151. T. Brauner, T.V.I. Tenkanen, A. Tranberg, A. Vuorinen and D.J. Weir, Dimensional reduction of the Standard Model coupled to a new singlet scalar field, JHEP 03 (2017) 007 [arXiv:1609.06230] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  152. O. Gould, J. Kozaczuk, L. Niemi, M.J. Ramsey-Musolf, T.V.I. Tenkanen and D.J. Weir, Nonperturbative analysis of the gravitational waves from a first-order electroweak phase transition, Phys. Rev . D 100 (2019) 115024 [arXiv:1903.11604] [INSPIRE].

  153. L. Niemi, H.H. Patel, M.J. Ramsey-Musolf, T.V.I. Tenkanen and D.J. Weir, Electroweak phase transition in the real triplet extension of the SM: dimensional reduction, Phys. Rev. D 100 (2019) 035002 [arXiv:1802.10500] [INSPIRE].

  154. L. Niemi, M.J. Ramsey-Musolf, T.V.I. Tenkanen and D.J. Weir, Thermodynamics of a two-step electroweak phase transition, Phys. Rev. Lett. 126 (2021) 171802 [arXiv:2005.11332] [INSPIRE].

    Article  ADS  Google Scholar 

  155. A. Helset, Dimensional reduction of the two- Higgs doublet model with a softly broken Z2 symmetry at one-loop, master’s thesis, Norwegian U. Sci. Tech., Trondheim, Norway (2017).

  156. J.O. Andersen et al., Nonperturbative analysis of the electroweak phase transition in the two Higgs doublet model, Phys. Rev. Lett. 121 (2018) 191802 [arXiv:1711.09849] [INSPIRE].

    Article  ADS  Google Scholar 

  157. T. Gorda, A. Helset, L. Niemi, T.V.I. Tenkanen and D.J. Weir, Three-dimensional effective theories for the two Higgs doublet model at high temperature, JHEP 02 (2019) 081 [arXiv:1802.05056] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  158. K. Kainulainen, V. Keus, L. Niemi, K. Rummukainen, T.V.I. Tenkanen and V. Vaskonen, On the validity of perturbative studies of the electroweak phase transition in the two Higgs doublet model, JHEP 06 (2019) 075 [arXiv:1904.01329] [INSPIRE].

    Article  ADS  Google Scholar 

  159. D. Croon, O. Gould, P. Schicho, T.V.I. Tenkanen and G. White, Theoretical uncertainties for cosmological first-order phase transitions, JHEP 04 (2021) 055 [arXiv:2009.10080] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  160. O. Gould, Real scalar phase transitions: a nonperturbative analysis, JHEP 04 (2021) 057 [arXiv:2101.05528] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  161. L. Dolan and R. Jackiw, Symmetry behavior at finite temperature, Phys. Rev. D 9 (1974) 3320 [INSPIRE].

    Article  ADS  Google Scholar 

  162. M.E. Carrington, The effective potential at finite temperature in the Standard Model, Phys. Rev. D 45 (1992) 2933 [INSPIRE].

    Article  ADS  Google Scholar 

  163. R.R. Parwani, Resummation in a hot scalar field theory, Phys. Rev. D 45 (1992) 4695 [Erratum ibid. 48 (1993) 5965] [hep-ph/9204216] [INSPIRE].

  164. W. Buchmüller, Z. Fodor, T. Helbig and D. Walliser, The weak electroweak phase transition, Annals Phys. 234 (1994) 260 [hep-ph/9303251] [INSPIRE].

  165. Z. Fodor and A. Hebecker, Finite temperature effective potential to order g4, λ2 and the el ectroweak phase transition, Nucl. Phys. B 432 (1994) 127 [hep-ph/9403219] [INSPIRE].

  166. J. Kripfganz, A. Laser and M.G. Schmidt, The high temperature two loop effective potential of the electroweak theory in a general ‘t Hooft background gauge, Phys. Lett. B 351 (1995) 266 [hep-ph/9501317] [INSPIRE].

  167. M. Laine, M. Meyer and G. Nardini, Thermal phase transition with full 2-loop effective potential, Nucl. Phys. B 920 (2017) 565 [arXiv:1702.07479] [INSPIRE].

    Article  MathSciNet  MATH  ADS  Google Scholar 

  168. A. Ekstedt and J. Löfgren, A critical look at the electroweak phase transition, JHEP 12 (2020) 136 [arXiv:2006.12614] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  169. K. Farakos, K. Kajantie, K. Rummukainen and M.E. Shaposhnikov, 3D physics and the electroweak phase transition: perturbation theory, Nucl. Phys. B 425 (1994) 67 [hep-ph/9404201] [INSPIRE].

  170. M. Laine, The two loop effective potential of the 3D SU(2) Higgs model in a general covariant gauge, Phys. Lett. B 335 (1994) 173 [hep-ph/9406268] [INSPIRE].

  171. P. Schicho, Multi-loop investigations of strong interactions at high temperatures, Ph.D. thesis, U. Bern, Bern, Switzerland (2020).

  172. L. Niemi, P. Schicho and T.V.I. Tenkanen, Singlet-assisted electroweak phase transition at two loops, arXiv:2103.07467 [INSPIRE].

  173. O. Gould and T.V.I. Tenkanen, On renormalisation scale dependence of the effective potential at high temperature, forthcoming, (2021).

  174. M. Lüscher, Chiral gauge theories revisited, Subnucl. Ser. 38 (2002) 41 [hep-th/0102028] [INSPIRE].

    Google Scholar 

  175. M. Laine, Comparison of 4D and 3D lattice results for the electroweak phase transition, Phys. Lett. B 385 (1996) 249 [hep-lat/9604011] [INSPIRE].

  176. C. Caprini et al., Detecting gravitational waves from cosmological phase transitions with LISA: an update, JCAP 03 (2020) 024 [arXiv:1910.13125] [INSPIRE].

    Article  ADS  Google Scholar 

  177. K. Schmitz, LISA sensitivity to gravitational waves from sound waves, Symmetry 12 (2020) 1477 [arXiv:2005.10789] [INSPIRE].

    Article  Google Scholar 

  178. B.M. Dillon, B.K. El-Menoufi, S.J. Huber and J.P. Manuel, Rapid holographic phase transition with brane-localized curvature, Phys. Rev . D 98 (2018) 086005 [arXiv:1708.02953] [INSPIRE].

  179. E. Megías, G. Nardini and M. Quirós, Cosmological phase transitions in warped space: gravitational waves and collider signatures, JHEP 09 (2018) 095 [arXiv:1806.04877] [INSPIRE].

    Article  MATH  ADS  Google Scholar 

  180. F.R. Ares, M. Hindmarsh, C. Hoyos and N. Jokela, Gravitational waves from a holographic phase transition, JHEP 04 (2021) 100 [arXiv:2011.12878] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  181. J.R. Espinosa, B. Gripaios, T. Konstandin and F. Riva, Electroweak baryogenesis in non-minimal composite Higgs models, JCAP 01 (2012) 012 [arXiv:1110.2876] [INSPIRE].

    Article  ADS  Google Scholar 

  182. S. Bruggisser, B. Von Harling, O. Matsedonskyi and G. Servant, Electroweak phase transition and baryogenesis in composite Higgs models, JHEP 12 (2018) 099 [arXiv:1804.07314] [INSPIRE].

    Article  ADS  Google Scholar 

  183. L. Bian, Y. Wu and K.-P. Xie, Electroweak phase transition with composite Higgs models: calculability, gravitational waves and collider searches, JHEP 12 (2019) 028 [arXiv:1909.02014] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  184. A. Katz and M. Perelstein, Higgs couplings and electroweak phase transition, JHEP 07 (2014) 108 [arXiv:1401.1827] [INSPIRE].

    Article  ADS  Google Scholar 

  185. J.S. Langer, Theory of the condensation point, Annals Phys. 41 (1967) 108 [INSPIRE].

    Article  ADS  Google Scholar 

  186. J.S. Langer, Statistical theory of the decay of metastable states, Annals Phys. 54 (1969) 258 [INSPIRE].

    Article  ADS  Google Scholar 

  187. S.R. Coleman, The fate of the false vacuum. 1. Semiclassical theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. 16 (1977) 1248] [INSPIRE].

  188. A.D. Linde, Decay of the false vacuum at finite temperature, Nucl. Phys. B 216 (1983) 421 [Erratum ibid. 223 (1983) 544] [INSPIRE].

  189. A. Kosowsky, M.S. Turner and R. Watkins, Gravitational waves from first order cosmological phase transitions, Phys. Rev. Lett. 69 (1992) 2026 [INSPIRE].

    Article  ADS  Google Scholar 

  190. 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].

  191. J. Ignatius, K. Kajantie, H. Kurki-Suonio and M. Laine, The growth of bubbles in cosmological phase transitions, Phys. Rev. D 49 (1994) 3854 [astro-ph/9309059] [INSPIRE].

  192. H. Kurki-Suonio and M. Laine, Supersonic deflagrations in cosmological phase transitions, Phys. Rev. D 51 (1995) 5431 [hep-ph/9501216] [INSPIRE].

  193. S.J. Huber and T. Konstandin, Gravitational wave production by collisions: more bubbles, JCAP 09 (2008) 022 [arXiv:0806.1828] [INSPIRE].

    Article  ADS  Google Scholar 

  194. F. Giese, T. Konstandin and J. van de Vis, Model-independent energy budget of cosmological first-order phase transitions — a sound argument to go beyond the bag model, JCAP 07 (2020) 057 [arXiv:2004.06995] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  195. D. Bödeker and G.D. Moore, Can electroweak bubble walls run away?, JCAP 05 (2009) 009 [arXiv:0903.4099] [INSPIRE].

    Article  ADS  Google Scholar 

  196. J. Kozaczuk, Bubble expansion and the viability of singlet-driven electroweak baryogenesis, JHEP 10 (2015) 135 [arXiv:1506.04741] [INSPIRE].

    Article  ADS  Google Scholar 

  197. D. Bödeker and G.D. Moore, Electroweak bubble wall speed limit, JCAP 05 (2017) 025 [arXiv:1703.08215] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  198. G.C. Dorsch, S.J. Huber and T. Konstandin, Bubble wall velocities in the Standard Model and beyond, JCAP 12 (2018) 034 [arXiv:1809.04907] [INSPIRE].

    Article  ADS  Google Scholar 

  199. S. Höche, J. Kozaczuk, A.J. Long, J. Turner and Y. Wang, Towards an all-orders calculation of the electroweak bubble wall velocity, JCAP 03 (2021) 009 [arXiv:2007.10343] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  200. R.-G. Cai and S.-J. Wang, Effective picture of bubble expansion, JCAP 03 (2021) 096 [arXiv:2011.11451] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  201. G.D. Moore and K. Rummukainen, Electroweak bubble nucleation, nonperturbatively, Phys. Rev. D 63 (2001) 045002 [hep-ph/0009132] [INSPIRE].

  202. G.D. Moore, K. Rummukainen and A. Tranberg, Nonperturbative computation of the bubble nucleation rate in the cubic anisotropy model, JHEP 04 (2001) 017 [hep-lat/0103036] [INSPIRE].

  203. 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].

    Article  ADS  Google Scholar 

  204. 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].

    Article  ADS  Google Scholar 

  205. 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 [Erratum ibid. 101 (2020) 089902] [arXiv:1704.05871] [INSPIRE].

  206. D. Cutting, M. Hindmarsh and D.J. Weir, Gravitational waves from vacuum first-order phase transitions: from the envelope to the lattice, Phys. Rev. D 97 (2018) 123513 [arXiv:1802.05712] [INSPIRE].

    Article  ADS  Google Scholar 

  207. D. Cutting, M. Hindmarsh and D.J. Weir, Vorticity, kinetic energy, and suppressed gravitational wave production in strong first order phase transitions, Phys. Rev. Lett. 125 (2020) 021302 [arXiv:1906.00480] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  208. D. Cutting, E.G. Escartin, M. Hindmarsh and D.J. Weir, Gravitational waves from vacuum first order phase transitions II: from thin to thick walls, Phys. Rev. D 103 (2021) 023531 [arXiv:2005.13537] [INSPIRE].

    Article  ADS  Google Scholar 

  209. G.A. White, A pedagogical introduction to electroweak baryogenesis, Morgan & Claypool Publishers, (2016) [INSPIRE].

  210. M. Laine, 3D effective theories for the Standard Model and extensions, in 2nd international conference on strong and electroweak matter, (1997), pg. 160 [hep-ph/9707415][INSPIRE].

  211. J.O. Andersen and M. Strickland, Resummation in hot field theories, Annals Phys. 317 (2005) 281 [hep-ph/0404164] [INSPIRE].

  212. M. Laine and A. Vuorinen, Basics of thermal field theory, Lect. Notes Phys. 925 (2016) 1 [arXiv:1701.01554] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  213. T. Matsubara, A new approach to quantum statistical mechanics, Prog. Theor. Phys. 14 (1955) 351 [INSPIRE].

    Article  MathSciNet  MATH  ADS  Google Scholar 

  214. P. Basler and M. Mühlleitner, BSMPT (Beyond the Standard Model Phase Transitions): a tool for the electroweak phase transition in extended Higgs sectors, Comput. Phys. Commun. 237 (2019) 62 [arXiv:1803.02846] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  215. C.L. Wainwright, CosmoTransitions: computing cosmological phase transition temperatures and bubble profiles with multiple fields, Comput. Phys. Commun. 183 (2012) 2006 [arXiv:1109.4189] [INSPIRE].

    Article  ADS  Google Scholar 

  216. P. Athron, C. Balázs, A. Fowlie and Y. Zhang, PhaseTracer: tracing cosmological phases and calculating transition properties, Eur. Phys. J. C 80 (2020) 567 [arXiv:2003.02859] [INSPIRE].

    Article  ADS  Google Scholar 

  217. H.H. Patel and M.J. Ramsey-Musolf, Baryon washout, electroweak phase transition, and perturbation theory, JHEP 07 (2011) 029 [arXiv:1101.4665] [INSPIRE].

    Article  MATH  ADS  Google Scholar 

  218. M. Laine, Gauge dependence of the high temperature two loop effective potential for the Higgs field, Phys. Rev. D 51 (1995) 4525 [hep-ph/9411252] [INSPIRE].

  219. A.K. Rajantie, Feynman diagrams to three loops in three-dimensional field theory, Nucl. Phys. B 480 (1996) 729 [Erratum ibid. 513 (1998) 761] [hep-ph/9606216] [INSPIRE].

  220. M. Laine, Exact relation of lattice and continuum parameters in three-dimensional SU(2) + Higgs theories, Nucl. Phys. B 451 (1995) 484 [hep-lat/9504001] [INSPIRE].

  221. M. Laine and A. Rajantie, Lattice continuum relations for 3D SU(N) + Higgs theories, Nucl. Phys. B 513 (1998) 471 [hep-lat/9705003] [INSPIRE].

  222. H.J. Rothe, Lattice gauge theories: an introduction, World Sci. Lect. Notes Phys. 43 (1992) 1.

    Article  MATH  Google Scholar 

  223. P. Athron, C. Balázs, M. Bardsley, A. Fowlie, D. Harries and G. White, BubbleProfiler: finding the field profile and action for cosmological phase transitions, Comput. Phys. Commun. 244 (2019) 448 [arXiv:1901.03714] [INSPIRE].

    Article  ADS  Google Scholar 

  224. M. Nishimura and Y. Schröder, IBP methods at finite temperature, JHEP 09 (2012) 051 [arXiv:1207.4042] [INSPIRE].

    Article  ADS  Google Scholar 

  225. M. Laine, P. Schicho and Y. Schröder, Soft thermal contributions to 3-loop gauge coupling, JHEP 05 (2018) 037 [arXiv:1803.08689] [INSPIRE].

  226. G.D. Moore, Measuring the broken phase sphaleron rate nonperturbatively, Phys. Rev. D 59 (1999) 014503 [hep-ph/9805264] [INSPIRE].

  227. B. Ruijl, T. Ueda and J. Vermaseren, FORM version 4.2, arXiv:1707.06453 [INSPIRE].

  228. P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  229. S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].

  230. P.B. Arnold and C.-X. Zhai, The three loop free energy for high temperature QED and QCD with fermions, Phys. Rev. D 51 (1995) 1906 [hep-ph/9410360] [INSPIRE].

  231. J. Osterman, Evaluation of master integrals in thermal field theory, master's thesis, University of Helsinki, Helsinki, Finland (2019).

  232. E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the Standard Model dimension six operators. Part I. Formalism and λ dependence, JHEP 10 (2013) 087 [arXiv:1308.2627] [INSPIRE].

  233. J.C. Collins and J.A.M. Vermaseren, Axodraw version 2, arXiv:1606.01177 [INSPIRE].

  234. E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the Standard Model dimension six operators. Part II. Yukawa dependence, JHEP 01 (2014) 035 [arXiv:1310.4838] [INSPIRE].

  235. R. Alonso, E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the Standard Model dimension six operators. Part III. Gauge coupling dependence and phenomenology, JHEP 04 (2014) 159 [arXiv:1312.2014] [mSPIRE].

  236. A. Andreassen, Gauge dependence of the quantum field theory effective potential, master’s thesis, Norwegian U. Sci. Tech., Trondheim, Norway (2013).

  237. A. Ekstedt and J. Löfgren, The high-temperature expansion of the thermal sunset, arXiv:2006.02179 [INSPIRE].

  238. P.B. Arnold and C.-X. Zhai, The three loop free energy for pure gauge QCD, Phys. Rev. D 50 (1994) 7603 [hep-ph/9408276] [INSPIRE].

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Authors and Affiliations

  1. Department of Physics and Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FI-00014, Helsinki, Finland

    Philipp M. Schicho & Juuso Österman

  2. AEC, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012, Bern, Switzerland

    Philipp M. Schicho & Tuomas V. I. Tenkanen

  3. Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91, Stockholm, Sweden

    Tuomas V. I. Tenkanen

  4. Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China

    Tuomas V. I. Tenkanen

  5. Shanghai Key Laboratory for Particle Physics and Cosmology, Key Laboratory for Particle Astrophysics and Cosmology (MOE), Shanghai Jiao Tong University, Shanghai, 200240, China

    Tuomas V. I. Tenkanen

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  1. Philipp M. Schicho
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  2. Tuomas V. I. Tenkanen
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  3. Juuso Österman
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Correspondence to Tuomas V. I. Tenkanen.

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Schicho, P.M., Tenkanen, T.V.I. & Österman, J. Robust approach to thermal resummation: Standard Model meets a singlet. J. High Energ. Phys. 2021, 130 (2021). https://doi.org/10.1007/JHEP06(2021)130

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  • Received: 16 April 2021

  • Accepted: 24 May 2021

  • Published: 21 June 2021

  • Version of record: 21 June 2021

  • DOI: https://doi.org/10.1007/JHEP06(2021)130

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Keywords

  • Beyond Standard Model
  • Effective Field Theories
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