Electroweak baryogenesis with anomalous Higgs couplings


We investigate feasibility of efficient baryogenesis at the electroweak scale within the effective field theory framework based on a non-linear realisation of the electroweak gauge symmetry. In this framework the LHC Higgs boson is described by a singlet scalar field, which, therefore, admits new interactions. Assuming that Higgs couplings with the eletroweak gauge bosons are as in the Standard Model, we demonstrate that the Higgs cubic coupling and the CP-violating Higgs-top quark anomalous couplings alone may drive the a strongly first-order phase transition. The distinguished feature of this transition is that the anomalous Higgs vacuum expectation value is generally non-zero in both phases. We identify a range of anomalous couplings, consistent with current experimental data, where sphaleron rates are sufficiently fast in the ‘symmetric’ phase and are suppressed in the ‘broken’ phase and demonstrate that the desired baryon asymmetry can indeed be generated in this framework. This range of the Higgs anomalous couplings can be further constrained from the LHC Run 2 data and be probed at high luminosity LHC and beyond.

A preprint version of the article is available at ArXiv.


  1. [1]

    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].

  2. [2]

    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].

  3. [3]

    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].

    ADS  Article  Google Scholar 

  4. [4]

    M.E. Shaposhnikov, Possible appearance of the baryon asymmetry of the universe in an electroweak theory, JETP Lett. 44 (1986) 465 [Pisma Zh. Eksp. Teor. Fiz. 44 (1986) 364] [INSPIRE].

  5. [5]

    M.E. Shaposhnikov, Baryon asymmetry of the universe in standard electroweak theory, Nucl. Phys. B 287 (1987) 757 [INSPIRE].

    ADS  Article  Google Scholar 

  6. [6]

    A.G. Cohen, D.B. Kaplan and A.E. Nelson, Spontaneous baryogenesis at the weak phase transition, Phys. Lett. B 263 (1991) 86 [INSPIRE].

    ADS  Article  Google Scholar 

  7. [7]

    A.E. Nelson, D.B. Kaplan and A.G. Cohen, Why there is something rather than nothing: matter from weak interactions, Nucl. Phys. B 373 (1992) 453 [INSPIRE].

    ADS  Article  Google Scholar 

  8. [8]

    K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, Is there a hot electroweak phase transition at m H larger or equal to m W ?, Phys. Rev. Lett. 77 (1996) 2887 [hep-ph/9605288] [INSPIRE].

    ADS  Article  Google Scholar 

  9. [9]

    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].

    ADS  Article  Google Scholar 

  10. [10]

    M.B. Gavela, P. Hernández, J. Orloff, O. Pene and C. Quimbay, Standard model CP-violation and baryon asymmetry. Part 2: finite temperature, Nucl. Phys. B 430 (1994) 382 [hep-ph/9406289] [INSPIRE].

    ADS  Article  Google Scholar 

  11. [11]

    P. Huet and E. Sather, Electroweak baryogenesis and standard model CP-violation, Phys. Rev. D 51 (1995) 379 [hep-ph/9404302] [INSPIRE].

    ADS  Google Scholar 

  12. [12]

    R. Cooke, M. Pettini, R.A. Jorgenson, M.T. Murphy and C.C. Steidel, Precision measures of the primordial abundance of deuterium, Astrophys. J. 781 (2014) 31 [arXiv:1308.3240] [INSPIRE].

    ADS  Article  Google Scholar 

  13. [13]

    Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, arXiv:1502.01589 [INSPIRE].

  14. [14]

    A.G. Cohen, D.B. Kaplan and A.E. Nelson, Progress in electroweak baryogenesis, Ann. Rev. Nucl. Part. Sci. 43 (1993) 27 [hep-ph/9302210] [INSPIRE].

    ADS  Article  Google Scholar 

  15. [15]

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

    ADS  Article  Google Scholar 

  16. [16]

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

    ADS  Article  Google Scholar 

  17. [17]

    X. Zhang and B.L. Young, Effective Lagrangian approach to electroweak baryogenesis: Higgs mass limit and electric dipole moments of fermion, Phys. Rev. D 49 (1994) 563 [hep-ph/9309269] [INSPIRE].

    ADS  Google Scholar 

  18. [18]

    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].

    ADS  Google Scholar 

  19. [19]

    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].

    MathSciNet  Article  Google Scholar 

  20. [20]

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

    ADS  Article  Google Scholar 

  21. [21]

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

    ADS  Google Scholar 

  22. [22]

    F.P. Huang and C.S. Li, Electroweak baryogenesis in the framework of the effective field theory, Phys. Rev. D 92 (2015) 075014 [arXiv:1507.08168] [INSPIRE].

    ADS  Google Scholar 

  23. [23]

    J. Ellis, V. Sanz and T. You, The effective standard model after LHC Run I, JHEP 03 (2015) 157 [arXiv:1410.7703] [INSPIRE].

    Article  Google Scholar 

  24. [24]

    D.J.H. Chung, A.J. Long and L.-T. Wang, 125 GeV Higgs boson and electroweak phase transition model classes, Phys. Rev. D 87 (2013) 023509 [arXiv:1209.1819] [INSPIRE].

    ADS  Google Scholar 

  25. [25]

    J. Shu and Y. Zhang, Impact of a CP-violating Higgs sector: from LHC to baryogenesis, Phys. Rev. Lett. 111 (2013) 091801 [arXiv:1304.0773] [INSPIRE].

    ADS  Article  Google Scholar 

  26. [26]

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

    ADS  Article  Google Scholar 

  27. [27]

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

    ADS  Article  Google Scholar 

  28. [28]

    W. Chao and M.J. Ramsey-Musolf, Electroweak baryogenesis, electric dipole moments and Higgs diphoton decays, JHEP 10 (2014) 180 [arXiv:1406.0517] [INSPIRE].

    ADS  Article  Google Scholar 

  29. [29]

    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].

    ADS  Google Scholar 

  30. [30]

    F.P. Huang, P.-H. Gu, P.-F. Yin, Z.-H. Yu and X. Zhang, Testing the electroweak phase transition and electroweak baryogenesis at LHC and CEPC, arXiv:1511.03969 [INSPIRE].

  31. [31]

    P. Huang, A. Joglekar, B. Li and C.E.M. Wagner, Probing the electroweak phase transition at the LHC, Phys. Rev. D 93 (2016) 055049 [arXiv:1512.00068] [INSPIRE].

    Google Scholar 

  32. [32]

    P.H. Damgaard, A. Haarr, D. O’Connell and A. Tranberg, Effective field theory and electroweak baryogenesis in the singlet-extended standard model, JHEP 02 (2016) 107 [arXiv:1512.01963] [INSPIRE].

    ADS  Article  Google Scholar 

  33. [33]

    A. Kobakhidze, Standard model with a distorted Higgs sector and the enhanced Higgs diphoton decay rate, arXiv:1208.5180 [INSPIRE].

  34. [34]

    S. Ferrara, A. Masiero and M. Porrati, Nonlinear realizations of SU(2) × U(1) in the MSSM: model independent analysis and g − 2 of W bosons, Phys. Lett. B 301 (1993) 358 [hep-ph/9212211] [INSPIRE].

    ADS  Article  Google Scholar 

  35. [35]

    A. Kobakhidze and M. Talia, The effective MSSM, Phys. Lett. B 751 (2015) 251 [arXiv:1508.04068] [INSPIRE].

    ADS  Article  Google Scholar 

  36. [36]

    T. Appelquist and M.S. Chanowitz, Unitarity bound on the scale of fermion mass generation, Phys. Rev. Lett. 59 (1987) 2405 [Erratum ibid. 60 (1988) 1589] [INSPIRE].

  37. [37]

    D. Binosi and A. Quadri, Scalar resonances in the non-linearly realized electroweak theory, JHEP 02 (2013) 020 [arXiv:1210.2637] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  38. [38]

    A. Kobakhidze, L. Wu and J. Yue, Anomalous top-Higgs couplings and top polarisation in single top and Higgs associated production at the LHC, JHEP 10 (2014) 100 [arXiv:1406.1961] [INSPIRE].

    ADS  Article  Google Scholar 

  39. [39]

    S.M. Barr and A. Zee, Electric dipole moment of the electron and of the neutron, Phys. Rev. Lett. 65 (1990) 21 [Erratum ibid. 65 (1990) 2920] [INSPIRE].

  40. [40]

    J.J. Hudson, D.M. Kara, I.J. Smallman, B.E. Sauer, M.R. Tarbutt and E.A. Hinds, Improved measurement of the shape of the electron, Nature 473 (2011) 493 [INSPIRE].

    ADS  Article  Google Scholar 

  41. [41]

    ACME collaboration, J. Baron et al., Order of magnitude smaller limit on the electric dipole moment of the electron, Science 343 (2014) 269 [arXiv:1310.7534] [INSPIRE].

  42. [42]

    Y.T. Chien, V. Cirigliano, W. Dekens, J. de Vries and E. Mereghetti, Direct and indirect constraints on CP-violating Higgs-quark and Higgs-gluon interactions, JHEP 02 (2016) 011 [arXiv:1510.00725] [INSPIRE].

    ADS  Article  Google Scholar 

  43. [43]

    N.S. Manton, Topology in the Weinberg-Salam theory, Phys. Rev. D 28 (1983) 2019 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  44. [44]

    F.R. Klinkhamer and N.S. Manton, A saddle point solution in the Weinberg-Salam theory, Phys. Rev. D 30 (1984) 2212 [INSPIRE].

    ADS  Google Scholar 

  45. [45]

    P. Huet and A.E. Nelson, Electroweak baryogenesis in supersymmetric models, Phys. Rev. D 53 (1996) 4578 [hep-ph/9506477] [INSPIRE].

    ADS  Google Scholar 

  46. [46]

    P. Huet and A.E. Nelson, CP violation and electroweak baryogenesis in extensions of the standard model, Phys. Lett. B 355 (1995) 229 [hep-ph/9504427] [INSPIRE].

    ADS  Article  Google Scholar 

  47. [47]

    G.D. Moore, Computing the strong sphaleron rate, Phys. Lett. B 412 (1997) 359 [hep-ph/9705248] [INSPIRE].

    ADS  Article  Google Scholar 

  48. [48]

    P.B. Arnold and L.D. McLerran, Sphalerons, small fluctuations and baryon number violation in electroweak theory, Phys. Rev. D 36 (1987) 581 [INSPIRE].

    ADS  Google Scholar 

  49. [49]

    L. Carson, X. Li, L.D. McLerran and R.-T. Wang, Exact computation of the small fluctuation determinant around a sphaleron, Phys. Rev. D 42 (1990) 2127 [INSPIRE].

    ADS  Google Scholar 

  50. [50]

    G.W. Anderson and L.J. Hall, The electroweak phase transition and baryogenesis, Phys. Rev. D 45 (1992) 2685 [INSPIRE].

    ADS  Google Scholar 

  51. [51]

    G.D. Moore, Electroweak bubble wall friction: analytic results, JHEP 03 (2000) 006 [hep-ph/0001274] [INSPIRE].

    ADS  Article  Google Scholar 

  52. [52]

    A. Megevand and A.D. Sanchez, Velocity of electroweak bubble walls, Nucl. Phys. B 825 (2010) 151 [arXiv:0908.3663] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  53. [53]

    J. Ellis, D.S. Hwang, K. Sakurai and M. Takeuchi, Disentangling Higgs-top couplings in associated production, JHEP 04 (2014) 004 [arXiv:1312.5736] [INSPIRE].

    ADS  Article  Google Scholar 

  54. [54]

    J. Yue, Enhanced thj signal at the LHC with hγγ decay and CP-violating top-Higgs coupling, Phys. Lett. B 744 (2015) 131 [arXiv:1410.2701] [INSPIRE].

    ADS  Article  Google Scholar 

  55. [55]

    F. Demartin, F. Maltoni, K. Mawatari, B. Page and M. Zaro, Higgs characterisation at NLO in QCD: CP properties of the top-quark Yukawa interaction, Eur. Phys. J. C 74 (2014) 3065 [arXiv:1407.5089] [INSPIRE].

    ADS  Article  Google Scholar 

  56. [56]

    F. Maltoni, D. Pagani and I. Tsinikos, Associated production of a top-quark pair with vector bosons at NLO in QCD: impact on \( t\overline{t}H \) searches at the LHC, JHEP 02 (2016) 113 [arXiv:1507.05640] [INSPIRE].

    ADS  Article  Google Scholar 

  57. [57]

    C. Degrande, J.M. Gerard, C. Grojean, F. Maltoni and G. Servant, Probing top-Higgs non-standard interactions at the LHC, JHEP 07 (2012) 036 [Erratum ibid. 03 (2013) 032] [arXiv:1205.1065] [INSPIRE].

  58. [58]

    S. Biswas, E. Gabrielli and B. Mele, Single top and Higgs associated production as a probe of the Htt coupling sign at the LHC, JHEP 01 (2013) 088 [arXiv:1211.0499] [INSPIRE].

    ADS  Article  Google Scholar 

  59. [59]

    P. Agrawal, S. Bandyopadhyay and S.P. Das, Multilepton signatures of the Higgs boson through its production in association with a top-quark pair, Phys. Rev. D 88 (2013) 093008 [arXiv:1308.3043] [INSPIRE].

    ADS  Google Scholar 

  60. [60]

    C. Englert and E. Re, Bounding the top Yukawa coupling with Higgs-associated single-top production, Phys. Rev. D 89 (2014) 073020 [arXiv:1402.0445] [INSPIRE].

    ADS  Google Scholar 

  61. [61]

    S. Biswas, R. Frederix, E. Gabrielli and B. Mele, Enhancing the \( t\overline{t}H \) signal through top-quark spin polarization effects at the LHC, JHEP 07 (2014) 020 [arXiv:1403.1790] [INSPIRE].

    ADS  Article  Google Scholar 

  62. [62]

    J. Chang, K. Cheung, J.S. Lee and C.-T. Lu, Probing the top-Yukawa coupling in associated Higgs production with a single top quark, JHEP 05 (2014) 062 [arXiv:1403.2053] [INSPIRE].

    ADS  Article  Google Scholar 

  63. [63]

    B. Bhattacharya, A. Datta and D. London, Probing new physics in Higgs couplings to fermions using an angular analysis, Phys. Lett. B 736 (2014) 421 [arXiv:1407.0695] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  64. [64]

    L. Wu, Enhancing thj production from top-Higgs FCNC couplings, JHEP 02 (2015) 061 [arXiv:1407.6113] [INSPIRE].

    ADS  Article  Google Scholar 

  65. [65]

    S. Khatibi and M.M. Najafabadi, Exploring the anomalous Higgs-top couplings, Phys. Rev. D 90 (2014) 074014 [arXiv:1409.6553] [INSPIRE].

    ADS  Google Scholar 

  66. [66]

    X.-G. He, G.-N. Li and Y.-J. Zheng, Probing Higgs boson CP properties with \( t\overline{t}H \) at the LHC and the 100 TeV pp collider, Int. J. Mod. Phys. A 30 (2015) 1550156 [arXiv:1501.00012] [INSPIRE].

    ADS  Article  Google Scholar 

  67. [67]

    Y. Chen, D. Stolarski and R. Vega-Morales, Golden probe of the top Yukuwa coupling, Phys. Rev. D 92 (2015) 053003 [arXiv:1505.01168] [INSPIRE].

    ADS  Google Scholar 

  68. [68]

    N. Moretti, P. Petrov, S. Pozzorini and M. Spannowsky, Measuring the signal strength in \( t\overline{t}H \) with \( H\to b\overline{b} \), Phys. Rev. D 93 (2016) 014019 [arXiv:1510.08468] [INSPIRE].

    ADS  Google Scholar 

  69. [69]

    U. Baur, T. Plehn and D.L. Rainwater, Probing the Higgs selfcoupling at hadron colliders using rare decays, Phys. Rev. D 69 (2004) 053004 [hep-ph/0310056] [INSPIRE].

    ADS  Google Scholar 

  70. [70]

    M.J. Dolan, C. Englert and M. Spannowsky, Higgs self-coupling measurements at the LHC, JHEP 10 (2012) 112 [arXiv:1206.5001] [INSPIRE].

    ADS  Article  Google Scholar 

  71. [71]

    J. Baglio, A. Djouadi, R. Gröber, M.M. Mühlleitner, J. Quevillon and M. Spira, The measurement of the Higgs self-coupling at the LHC: theoretical status, JHEP 04 (2013) 151 [arXiv:1212.5581] [INSPIRE].

    ADS  Article  Google Scholar 

  72. [72]

    M.J. Dolan, C. Englert and M. Spannowsky, New physics in LHC Higgs boson pair production, Phys. Rev. D 87 (2013) 055002 [arXiv:1210.8166] [INSPIRE].

    ADS  Google Scholar 

  73. [73]

    V. Barger, L.L. Everett, C.B. Jackson and G. Shaughnessy, Higgs-pair production and measurement of the triscalar coupling at LHC(8, 14), Phys. Lett. B 728 (2014) 433 [arXiv:1311.2931] [INSPIRE].

    ADS  Article  Google Scholar 

  74. [74]

    A.J. Barr, M.J. Dolan, C. Englert and M. Spannowsky, Di-Higgs final states augMT2ed — selecting hh events at the high luminosity LHC, Phys. Lett. B 728 (2014) 308 [arXiv:1309.6318] [INSPIRE].

    ADS  Article  Google Scholar 

  75. [75]

    R. Frederix et al., Higgs pair production at the LHC with NLO and parton-shower effects, Phys. Lett. B 732 (2014) 142 [arXiv:1401.7340] [INSPIRE].

    ADS  Article  Google Scholar 

  76. [76]

    N. Liu, S. Hu, B. Yang and J. Han, Impact of top-Higgs couplings on di-Higgs production at future colliders, JHEP 01 (2015) 008 [arXiv:1408.4191] [INSPIRE].

    ADS  Google Scholar 

  77. [77]

    A. Azatov, R. Contino, G. Panico and M. Son, Effective field theory analysis of double Higgs boson production via gluon fusion, Phys. Rev. D 92 (2015) 035001 [arXiv:1502.00539] [INSPIRE].

    ADS  Google Scholar 

  78. [78]

    C.-T. Lu, J. Chang, K. Cheung and J.S. Lee, An exploratory study of Higgs-boson pair production, JHEP 08 (2015) 133 [arXiv:1505.00957] [INSPIRE].

    ADS  Article  Google Scholar 

  79. [79]

    S.R. Coleman and E.J. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking, Phys. Rev. D 7 (1973) 1888 [INSPIRE].

    ADS  Google Scholar 

  80. [80]

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

    ADS  Google Scholar 

  81. [81]

    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].

    ADS  Google Scholar 

  82. [82]

    J. Elias-Miro, J.R. Espinosa and T. Konstandin, Taming infrared divergences in the effective potential, JHEP 08 (2014) 034 [arXiv:1406.2652] [INSPIRE].

    ADS  Article  Google Scholar 

  83. [83]

    S.P. Martin, Taming the Goldstone contributions to the effective potential, Phys. Rev. D 90 (2014) 016013 [arXiv:1406.2355] [INSPIRE].

    ADS  Google Scholar 

  84. [84]

    A. Pilaftsis and D. Teresi, Symmetry-improved 2PI approach to the Goldstone-boson IR problem of the SM effective potential, Nucl. Phys. B 906 (2016) 381 [arXiv:1511.05347] [INSPIRE].

    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



Corresponding author

Correspondence to Archil Kobakhidze.

Additional information

ArXiv ePrint: 1512.08922

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kobakhidze, A., Wu, L. & Yue, J. Electroweak baryogenesis with anomalous Higgs couplings. J. High Energ. Phys. 2016, 11 (2016). https://doi.org/10.1007/JHEP04(2016)011

Download citation


  • Cosmology of Theories beyond the SM
  • Higgs Physics