Simulations of domain walls in Two Higgs Doublet Models


The Two Higgs Doublet Model predicts the emergence of 3 distinct domain wall solutions arising from the breaking of 3 accidental global symmetries, Z2, CP1 and CP2, at the electroweak scale for specific choices of the model parameters. We present numerical kink solutions to the field equations in all three cases along with dynamical simulations of the models in (2+1) and (3+1) dimensions. For each kink solution we define an associated topological current. In all three cases simulations produce a network of domain walls which deviates from power law scaling in Minkowski and FRW simulations. This deviation is attributed to a winding of the electroweak group parameters around the domain walls in our simulations. We observe a local violation of the neutral vacuum condition on the domain walls in our simulations. This violation is attributed to relative electroweak transformations across the domain walls which is a general feature emerging from random initial conditions.

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  1. [1]

    E.J. Copeland, M. Sami and S. Tsujikawa, Dynamics of dark energy, Int. J. Mod. Phys. D 15 (2006) 1753 [hep-th/0603057] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  2. [2]

    J.R. Ellis, J.S. Hagelin, D.V. Nanopoulos, K.A. Olive and M. Srednicki, Supersymmetric Relics from the Big Bang, Nucl. Phys. B 238 (1984) 453 [INSPIRE].

    ADS  Article  Google Scholar 

  3. [3]

    A. Pilaftsis, Heavy Majorana neutrinos and baryogenesis, Int. J. Mod. Phys. A 14 (1999) 1811 [hep-ph/9812256] [INSPIRE].

  4. [4]

    W. Buchmüller, R.D. Peccei and T. Yanagida, Leptogenesis as the origin of matter, Ann. Rev. Nucl. Part. Sci. 55 (2005) 311 [hep-ph/0502169] [INSPIRE].

  5. [5]

    G. Lazarides, Q. Shafi and C. Wetterich, Proton Lifetime and Fermion Masses in an SO(10) Model, Nucl. Phys. B 181 (1981) 287 [INSPIRE].

    ADS  Article  Google Scholar 

  6. [6]

    P. Nath and P. Fileviez Perez, Proton stability in grand unified theories, in strings and in branes, Phys. Rept. 441 (2007) 191 [hep-ph/0601023] [INSPIRE].

  7. [7]

    A. Djouadi, The anatomy of electro-weak symmetry breaking. II. The Higgs bosons in the minimal supersymmetric model, Phys. Rept. 459 (2008) 1 [hep-ph/0503173] [INSPIRE].

  8. [8]

    P. Minkowski, μeγ at a Rate of One Out of 109 Muon Decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].

  9. [9]

    T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131 (1979) 95 [INSPIRE].

    Google Scholar 

  10. [10]

    R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Nonconservation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].

    ADS  Article  Google Scholar 

  11. [11]

    J. Schechter and J.W.F. Valle, Neutrino Masses in SU(2) × U(1) Theories, Phys. Rev. D 22 (1980) 2227 [INSPIRE].

    ADS  Article  Google Scholar 

  12. [12]

    Super-Kamiokande collaboration, Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 81 (1998) 1562 [hep-ex/9807003] [INSPIRE].

  13. [13]

    SNO collaboration, Measurement of the rate of νe + d → p + p + e interactions produced by 8B solar neutrinos at the Sudbury Neutrino Observatory, Phys. Rev. Lett. 87 (2001) 071301 [nucl-ex/0106015] [INSPIRE].

  14. [14]

    T.D. Lee, A Theory of Spontaneous T Violation, Phys. Rev. D 8 (1973) 1226 [INSPIRE].

    ADS  Article  Google Scholar 

  15. [15]

    G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva, Theory and phenomenology of two-Higgs-doublet models, Phys. Rept. 516 (2012) 1 [arXiv:1106.0034] [INSPIRE].

    ADS  Article  Google Scholar 

  16. [16]

    A. Pilaftsis and C.E.M. Wagner, Higgs bosons in the minimal supersymmetric standard model with explicit CP-violation, Nucl. Phys. B 553 (1999) 3 [hep-ph/9902371] [INSPIRE].

  17. [17]

    B. Grzadkowski, O.M. Ogreid and P. Osland, Natural Multi-Higgs Model with Dark Matter and CP-violation, Phys. Rev. D 80 (2009) 055013 [arXiv:0904.2173] [INSPIRE].

  18. [18]

    B. Grzadkowski, O.M. Ogreid, P. Osland, A. Pukhov and M. Purmohammadi, Exploring the CP-Violating Inert-Doublet Model, JHEP 06 (2011) 003 [arXiv:1012.4680] [INSPIRE].

    ADS  Article  Google Scholar 

  19. [19]

    V. Keus, S.F. King, S. Moretti and K. Yagyu, CP Violating Two-Higgs-Doublet Model: Constraints and LHC Predictions, JHEP 04 (2016) 048 [arXiv:1510.04028] [INSPIRE].

    ADS  Google Scholar 

  20. [20]

    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].

  21. [21]

    V. Keus, S.F. King, S. Moretti and D. Sokolowska, Dark Matter with Two Inert Doublets plus One Higgs Doublet, JHEP 11 (2014) 016 [arXiv:1407.7859] [INSPIRE].

    ADS  Article  Google Scholar 

  22. [22]

    M. Hindmarsh, R. Kirk, J.M. No and S.M. West, Dark Matter with Topological Defects in the Inert Doublet Model, JCAP 05 (2015) 048 [arXiv:1412.4821] [INSPIRE].

    ADS  Article  Google Scholar 

  23. [23]

    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].

    ADS  Article  Google Scholar 

  24. [24]

    M. Carena, J. Ellis, J.S. Lee, A. Pilaftsis and C.E.M. Wagner, CP Violation in Heavy MSSM Higgs Scenarios, JHEP 02 (2016) 123 [arXiv:1512.00437] [INSPIRE].

    ADS  Article  Google Scholar 

  25. [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. [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. [27]

    ATLAS and CMS collaborations, Combined Measurement of the Higgs Boson Mass in pp Collisions at \( \sqrt{s} \) = 7 and 8 TeV with the ATLAS and CMS Experiments, Phys. Rev. Lett. 114 (2015) 191803 [arXiv:1503.07589] [INSPIRE].

  28. [28]

    A. Djouadi, The anatomy of electro-weak symmetry breaking. I: The Higgs boson in the standard model, Phys. Rept. 457 (2008) 1 [hep-ph/0503172] [INSPIRE].

  29. [29]

    ATLAS and CMS collaborations, Measurements of the Higgs boson production and decay rates and constraints on its couplings from a combined ATLAS and CMS analysis of the LHC pp collision data at \( \sqrt{s} \) = 7 and 8 TeV, JHEP 08 (2016) 045 [arXiv:1606.02266] [INSPIRE].

  30. [30]

    R.A. Battye, G.D. Brawn and A. Pilaftsis, Vacuum Topology of the Two Higgs Doublet Model, JHEP 08 (2011) 020 [arXiv:1106.3482] [INSPIRE].

    ADS  Article  Google Scholar 

  31. [31]

    M. Eto, M. Kurachi and M. Nitta, Constraints on two Higgs doublet models from domain walls, Phys. Lett. B 785 (2018) 447 [arXiv:1803.04662] [INSPIRE].

    ADS  Article  Google Scholar 

  32. [32]

    M. Eto, M. Kurachi and M. Nitta, Non-Abelian strings and domain walls in two Higgs doublet models, JHEP 08 (2018) 195 [arXiv:1805.07015] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  33. [33]

    N. Chen, T. Li, Z. Teng and Y. Wu, Collapsing domain walls in the two-Higgs-doublet model and deep insights from the EDM, JHEP 10 (2020) 081 [arXiv:2006.06913] [INSPIRE].

    ADS  Article  Google Scholar 

  34. [34]

    T. Garagounis and M. Hindmarsh, Scaling in numerical simulations of domain walls, Phys. Rev. D 68 (2003) 103506 [hep-ph/0212359] [INSPIRE].

  35. [35]

    A. Vilenkin and E. Shellard, Cosmic strings and other topological defects, Cambridge monographs on mathematical physics, Cambridge University Press, Cambridge, (1994).

  36. [36]

    T.W.B. Kibble, G. Lazarides and Q. Shafi, Walls Bounded by Strings, Phys. Rev. D 26 (1982) 435 [INSPIRE].

    ADS  Article  Google Scholar 

  37. [37]

    K. Nakayama, F. Takahashi and N. Yokozaki, Gravitational waves from domain walls and their implications, Phys. Lett. B 770 (2017) 500 [arXiv:1612.08327] [INSPIRE].

    ADS  Article  Google Scholar 

  38. [38]

    R.A. Battye and A. Moss, Scaling dynamics of domain walls in the cubic anisotropy model, Phys. Rev. D 74 (2006) 023528 [hep-th/0605057] [INSPIRE].

  39. [39]

    R.A. Battye, J.A. Pearson, S. Pike and P.M. Sutcliffe, Formation and evolution of kinky vortons, JCAP 09 (2009) 039 [arXiv:0908.1865] [INSPIRE].

    ADS  Article  Google Scholar 

  40. [40]

    R.A. Battye and J.A. Pearson, Charge, junctions and the scaling dynamics of domain wall networks, Phys. Rev. D 82 (2010) 125001 [arXiv:1010.2328] [INSPIRE].

    ADS  Article  Google Scholar 

  41. [41]

    A. Lazanu, C.J.A.P. Martins and E.P.S. Shellard, Contribution of domain wall networks to the CMB power spectrum, Phys. Lett. B 747 (2015) 426 [arXiv:1505.03673] [INSPIRE].

    ADS  Article  Google Scholar 

  42. [42]

    Y. Zeldovich, I. Kobzarev and L.B. Okun, Cosmological Consequences of the Spontaneous Breakdown of Discrete Symmetry, Zh. Eksp. Teor. Fiz. 67 (1974) 3 [INSPIRE].

    ADS  Google Scholar 

  43. [43]

    S.E. Larsson, S. Sarkar and P.L. White, Evading the cosmological domain wall problem, Phys. Rev. D 55 (1997) 5129 [hep-ph/9608319] [INSPIRE].

  44. [44]

    W.H. Press, B.S. Ryden and D.N. Spergel, Dynamical Evolution of Domain Walls in an Expanding Universe, Astrophys. J. 347 (1989) 590 [INSPIRE].

    ADS  Article  Google Scholar 

  45. [45]

    L. Bian and N. Chen, Higgs pair productions in the CP-violating two-Higgs-doublet model, JHEP 09 (2016) 069 [arXiv:1607.02703] [INSPIRE].

    ADS  Article  Google Scholar 

  46. [46]

    D. Azevedo, P. Ferreira, M.M. Mühlleitner, R. Santos and J. Wittbrodt, Models with extended Higgs sectors at future e+e colliders, Phys. Rev. D 99 (2019) 055013 [arXiv:1808.00755] [INSPIRE].

  47. [47]

    P. Basler, M. Mühlleitner and J. Müller, Electroweak Phase Transition in Non-Minimal Higgs Sectors, JHEP 05 (2020) 016 [arXiv:1912.10477] [INSPIRE].

    ADS  Article  Google Scholar 

  48. [48]

    I.P. Ivanov, Minkowski space structure of the Higgs potential in 2HDM. II. Minima, symmetries, and topology, Phys. Rev. D 77 (2008) 015017 [arXiv:0710.3490] [INSPIRE].

  49. [49]

    P.M. Ferreira, H.E. Haber and J.P. Silva, Generalized CP symmetries and special regions of parameter space in the two-Higgs-doublet model, Phys. Rev. D 79 (2009) 116004 [arXiv:0902.1537] [INSPIRE].

    ADS  Article  Google Scholar 

  50. [50]

    P.S. Bhupal Dev and A. Pilaftsis, Maximally Symmetric Two Higgs Doublet Model with Natural Standard Model Alignment, JHEP 12 (2014) 024 [Erratum ibid. 11 (2015) 147] [arXiv:1408.3405] [INSPIRE].

  51. [51]

    A. Pilaftsis, On the Classification of Accidental Symmetries of the Two Higgs Doublet Model Potential, Phys. Lett. B 706 (2012) 465 [arXiv:1109.3787] [INSPIRE].

    ADS  Article  Google Scholar 

  52. [52]

    N. Darvishi and A. Pilaftsis, Natural Alignment in Multi-Higgs Doublet Models, PoS CORFU2019 (2020) 064 [arXiv:2004.04505] [INSPIRE].

  53. [53]

    M. Maniatis, A. von Manteuffel and O. Nachtmann, CP violation in the general two-Higgs-doublet model: A geometric view, Eur. Phys. J. C 57 (2008) 719 [arXiv:0707.3344] [INSPIRE].

    ADS  Article  Google Scholar 

  54. [54]

    C.C. Nishi, CP violation conditions in N-Higgs-doublet potentials, Phys. Rev. D 74 (2006) 036003 [Erratum ibid. 76 (2007) 119901] [hep-ph/0605153] [INSPIRE].

  55. [55]

    L. Sousa and P.P. Avelino, Evolution of domain wall networks: The Press-Ryden-Spergel algorithm, Phys. Rev. D 81 (2010) 087305 [arXiv:1101.3350] [INSPIRE].

  56. [56]

    J.R.C.C.C. Correia and C.J.A.P. Martins, General purpose graphics-processing-unit implementation of cosmological domain wall network evolution, Phys. Rev. E 96 (2017) 043310 [arXiv:1710.10420] [INSPIRE].

  57. [57]

    N. Darvishi and A. Pilaftsis, Quartic Coupling Unification in the Maximally Symmetric 2HDM, Phys. Rev. D 99 (2019) 115014 [arXiv:1904.06723] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  58. [58]

    A. Arbey, F. Mahmoudi, O. Stal and T. Stefaniak, Status of the Charged Higgs Boson in Two Higgs Doublet Models, Eur. Phys. J. C 78 (2018) 182 [arXiv:1706.07414] [INSPIRE].

    ADS  Article  Google Scholar 

  59. [59]

    A. Arbey, T. Hurth, F. Mahmoudi, D.M. Santos and S. Neshatpour, Update on the bs anomalies, Phys. Rev. D 100 (2019) 015045 [arXiv:1904.08399] [INSPIRE].

  60. [60]

    P. Osland, P.N. Pandita and L. Selbuz, Trilinear Higgs couplings in the two Higgs doublet model with CP-violation, Phys. Rev. D 78 (2008) 015003 [arXiv:0802.0060] [INSPIRE].

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Battye, R.A., Pilaftsis, A. & Viatic, D.G. Simulations of domain walls in Two Higgs Doublet Models. J. High Energ. Phys. 2021, 105 (2021).

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  • Higgs Physics
  • Spontaneous Symmetry Breaking
  • Cosmology of Theories beyond the SM
  • CP violation