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Source terms for electroweak baryogenesis in the vev-insertion approximation beyond leading order

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Abstract

In electroweak baryogenesis the baryon asymmetry of the universe is created during the electroweak phase transition. The quantum transport equations governing the dynamics of the plasma particles can be derived in the vev-insertion approximation, which treats the vev-dependent part of the particle masses as a perturbation. We calculate the next-to-leading order (NLO) contribution to the CP-violating source term and CP-conserving relaxation rate, corresponding to Feynman diagrams for the self-energies with four mass insertions. We consider both a pair of Weyl fermions and a pair of complex scalars, that scatter off the bubble wall. We find: (i) The NLO correction becomes large for \( \mathcal{O} \)(1) couplings. If only the Standard Model (SM) Higgs obtains a vev during the phase transition, this implies the vev-insertion approximation breaks down for top quarks. (ii) The resonant enhancement of the source term and relaxation rate, that exists at leading order in the limit of degenerate thermal masses for the fermions/scalars, persists at NLO.

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References

  1. [1]

    A. Arhrib, P.M. Ferreira and R. Santos, Are There Hidden Scalars in LHC Higgs Results ?, JHEP03 (2014) 053 [arXiv:1311.1520] [INSPIRE].

  2. [2]

    C.-Y. Chen, S. Dawson and M. Sher, Heavy Higgs Searches and Constraints on Two Higgs Doublet Models, Phys. Rev.D 88 (2013) 015018 [Erratum ibid.D 88 (2013) 039901] [arXiv:1305.1624] [INSPIRE].

  3. [3]

    W.-F. Chang, T. Modak and J.N. Ng, Signal for a light singlet scalar at the LHC, Phys. Rev.D 97 (2018) 055020 [arXiv:1711.05722] [INSPIRE].

  4. [4]

    CMS collaboration, A Search for Beyond Standard Model Light Bosons Decaying into Muon Pairs, CMS-PAS-HIG-16-035 (2016).

  5. [5]

    C. Englert et al., Precision Measurements of Higgs Couplings: Implications for New Physics Scales, J. Phys.G 41 (2014) 113001 [arXiv:1403.7191] [INSPIRE].

  6. [6]

    I. Brivio and M. Trott, The Standard Model as an Effective Field Theory, Phys. Rept.793 (2019) 1 [arXiv:1706.08945] [INSPIRE].

  7. [7]

    T. Han and Y. Li, Genuine CP-odd Observables at the LHC, Phys. Lett.B 683 (2010) 278 [arXiv:0911.2933] [INSPIRE].

  8. [8]

    F. Boudjema, R.M. Godbole, D. Guadagnoli and K.A. Mohan, Lab-frame observables for probing the top-Higgs interaction, Phys. Rev.D 92 (2015) 015019 [arXiv:1501.03157] [INSPIRE].

  9. [9]

    J. Ellis, Discrete Glimpses of the Physics Landscape after the Higgs Discovery, J. Phys. Conf. Ser.631 (2015) 012001 [arXiv:1501.05418] [INSPIRE].

  10. [10]

    A. Askew, P. Jaiswal, T. Okui, H.B. Prosper and N. Sato, Prospect for measuring the CP phase in the hττ coupling at the LHC, Phys. Rev.91 (2015) 075014 [arXiv:1501.03156] [INSPIRE].

  11. [11]

    F. Demartin, F. Maltoni, K. Mawatari and M. Zaro, Higgs production in association with a single top quark at the LHC, Eur. Phys. J.C 75 (2015) 267 [arXiv:1504.00611] [INSPIRE].

  12. [12]

    T. Chupp, P. Fierlinger, M. Ramsey-Musolf and J. Singh, Electric dipole moments of atoms, molecules, nuclei and particles, Rev. Mod. Phys.91 (2019) 015001 [arXiv:1710.02504] [INSPIRE].

  13. [13]

    C. Balázs, G. White and J. Yue, Effective field theory, electric dipole moments and electroweak baryogenesis, JHEP03 (2017) 030 [arXiv:1612.01270] [INSPIRE].

  14. [14]

    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, JHEP02 (2016) 011 [arXiv:1510.00725] [INSPIRE].

  15. [15]

    V. Cirigliano, W. Dekens, J. de Vries and E. Mereghetti, Constraining the top-Higgs sector of the Standard Model Effective Field Theory, Phys. Rev.D 94 (2016) 034031 [arXiv:1605.04311] [INSPIRE].

  16. [16]

    J. de Vries, M. Postma, J. van de Vis and G. White, Electroweak Baryogenesis and the Standard Model Effective Field Theory, JHEP01 (2018) 089 [arXiv:1710.04061] [INSPIRE].

  17. [17]

    ACME collaboration, Improved limit on the electric dipole moment of the electron, Nature562 (2018) 355 [INSPIRE].

  18. [18]

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

  19. [19]

    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].

  20. [20]

    T. Konstandin, Quantum Transport and Electroweak Baryogenesis, Phys. Usp.56 (2013) 747.

  21. [21]

    L. Kadanoff and G. Baym, Quantum Statistical Mechanics, Benjamin, New York, U.S.A. (1962).

  22. [22]

    T. Prokopec, M.G. Schmidt and S. Weinstock, Transport equations for chiral fermions to order h bar and electroweak baryogenesis. Part 1, Annals Phys.314 (2004) 208 [hep-ph/0312110] [INSPIRE].

  23. [23]

    E.A. Calzetta and B.-L.B. Hu, Nonequilibrium Quantum Field Theory, Cambridge University Press, (2008).

  24. [24]

    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].

  25. [25]

    A. Riotto, The more relaxed supersymmetric electroweak baryogenesis, Phys. Rev.D 58 (1998) 095009 [hep-ph/9803357] [INSPIRE].

  26. [26]

    C. Lee, V. Cirigliano and M.J. Ramsey-Musolf, Resonant relaxation in electroweak baryogenesis, Phys. Rev.D 71 (2005) 075010 [hep-ph/0412354] [INSPIRE]

  27. [27]

    T. Konstandin, T. Prokopec and M.G. Schmidt, Kinetic description of fermion flavor mixing and CP-violating sources for baryogenesis, Nucl. Phys.B 716 (2005) 373 [hep-ph/0410135] [INSPIRE].

  28. [28]

    A.I. Bochkarev, S.V. Kuzmin and M.E. Shaposhnikov, Electroweak baryogenesis and the Higgs boson mass problem, Phys. Lett.B 244 (1990) 275 [INSPIRE].

  29. [29]

    N. Turok and J. Zadrozny, Phase transitions in the two doublet model, Nucl. Phys.B 369 (1992) 729 [INSPIRE].

  30. [30]

    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].

  31. [31]

    J.M. Cline and P.-A. Lemieux, Electroweak phase transition in two Higgs doublet models, Phys. Rev.D 55 (1997) 3873 [hep-ph/9609240] [INSPIRE].

  32. [32]

    J.M. Cline, K. Kainulainen and M. Trott, Electroweak Baryogenesis in Two Higgs Doublet Models and B meson anomalies, JHEP11 (2011) 089 [arXiv:1107.3559] [INSPIRE].

  33. [33]

    G.C. Dorsch, S.J. Huber, T. Konstandin and J.M. No, A Second Higgs Doublet in the Early Universe: Baryogenesis and Gravitational Waves, JCAP05 (2017) 052 [arXiv:1611.05874] [INSPIRE].

  34. [34]

    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].

  35. [35]

    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, JHEP02 (2019) 081 [arXiv:1802.05056] [INSPIRE].

  36. [36]

    X. Zhang, S.K. Lee, K. Whisnant and B.L. Young, Phenomenology of a nonstandard top quark Yukawa coupling, Phys. Rev.D 50 (1994) 7042 [hep-ph/9407259] [INSPIRE].

  37. [37]

    D. Bödeker, L. Fromme, S.J. Huber and M. Seniuch, The baryon asymmetry in the standard model with a low cut-off, JHEP02 (2005) 026 [hep-ph/0412366] [INSPIRE].

  38. [38]

    H.-K. Guo, Y.-Y. Li, T. Liu, M. Ramsey-Musolf and J. Shu, Lepton-Flavored Electroweak Baryogenesis, Phys. Rev.D 96 (2017) 115034 [arXiv:1609.09849] [INSPIRE].

  39. [39]

    C.-W. Chiang, K. Fuyuto and E. Senaha, Electroweak Baryogenesis with Lepton Flavor Violation, Phys. Lett.B 762 (2016) 315 [arXiv:1607.07316] [INSPIRE].

  40. [40]

    V. Cirigliano, C. Lee, M.J. Ramsey-Musolf and S. Tulin, Flavored Quantum Boltzmann Equations, Phys. Rev.D 81 (2010) 103503 [arXiv:0912.3523] [INSPIRE].

  41. [41]

    J.S. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys.2 (1961) 407 [INSPIRE].

  42. [42]

    L.V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz.47 (1964) 1515 [INSPIRE].

  43. [43]

    K.-c. Chou, Z.-b. Su, B.-l. Hao and L. Yu, Equilibrium and Nonequilibrium Formalisms Made Unified, Phys. Rept.118 (1985) 1 [INSPIRE].

  44. [44]

    P.S. Bhupal Dev, P. Millington, A. Pilaftsis and D. Teresi, Kadanoff-Baym approach to flavour mixing and oscillations in resonant leptogenesis, Nucl. Phys.B 891 (2015) 128 [arXiv:1410.6434] [INSPIRE].

  45. [45]

    T. Liu, M.J. Ramsey-Musolf and J. Shu, Electroweak Beautygenesis: From b → s CP-violation to the Cosmic Baryon Asymmetry, Phys. Rev. Lett.108 (2012) 221301 [arXiv:1109.4145] [INSPIRE].

  46. [46]

    D.J.H. Chung, B. Garbrecht, M.J. Ramsey-Musolf and S. Tulin, Lepton-mediated electroweak baryogenesis, Phys. Rev.D 81 (2010) 063506 [arXiv:0905.4509] [INSPIRE].

  47. [47]

    M. Joyce, T. Prokopec and N. Turok, Nonlocal electroweak baryogenesis. Part 1: Thin wall regime, Phys. Rev.D 53 (1996) 2930 [hep-ph/9410281] [INSPIRE].

  48. [48]

    M. Joyce, T. Prokopec and N. Turok, Efficient electroweak baryogenesis from lepton transport, Phys. Lett.B 338 (1994) 269 [hep-ph/9401352] [INSPIRE].

  49. [48]

    J. De Vries, M. Postma and J. van de Vis, The role of leptons in electroweak baryogenesis, JHEP04 (2019) 024 [arXiv:1811.11104] [INSPIRE].

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Correspondence to Jorinde van de Vis.

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ArXiv ePrint: 1910.11794

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Postma, M., van de Vis, J. Source terms for electroweak baryogenesis in the vev-insertion approximation beyond leading order. J. High Energ. Phys. 2020, 90 (2020). https://doi.org/10.1007/JHEP02(2020)090

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Keywords

  • Cosmology of Theories beyond the SM
  • Beyond Standard Model
  • CP violation