Journal of High Energy Physics

, 2019:14 | Cite as

Precision study of GeV-scale resonant leptogenesis

  • J. Ghiglieri
  • M. LaineEmail author
Open Access
Regular Article - Theoretical Physics


Low-scale leptogenesis is most efficient in the limit of an extreme mass degeneracy of right-handed neutrino flavours. Two variants of this situation are of particular interest: large neutrino Yukawa couplings, which boost the prospects of experimental scrutiny, and small ones, which may lead to large lepton asymmetries surviving down to T < 5 GeV. We study benchmarks of these cases within a “complete” framework which tracks both helicity states of right-handed neutrinos as well as their kinetic non-equilibrium, and includes a number of effects not accounted for previously. For two right-handed flavours with GeV-scale masses, Yukawa couplings up to |h| ∼ 0.7×10−5 are found to be viable for baryogenesis, with ΔM/M ∼ 10−8 as the optimal degeneracy. Late-time lepton asymmetries are most favourably produced with ΔM/M ∼ 10−11. We show that the system reaches a stationary state at T < 15 GeV, in which lepton asymmetries can be more than 103 times larger than the baryon asymmetry, reach flavour equilibrium, and balance against helicity asymmetries.


Thermal Field Theory Neutrino Physics CP violation Resummation 


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.


  1. [1]
    M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    V.A. Kuzmin, V.A. Rubakov and M.E. Shaposhnikov, On the anomalous electroweak baryon number nonconservation in the early universe, Phys. Lett. 155B (1985) 36 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    D. Bödeker and M. Wörmann, Non-relativistic leptogenesis, JCAP 02 (2014) 016 [arXiv:1311.2593] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  4. [4]
    S. Biondini, N. Brambilla and A. Vairo, CP asymmetry in heavy Majorana neutrino decays at finite temperature: the hierarchical case, JHEP 09 (2016) 126 [arXiv:1608.01979] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    D. Bödeker and M. Sangel, Lepton asymmetry rate from quantum field theory: NLO in the hierarchical limit, JCAP 06 (2017) 052 [arXiv:1702.02155] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  6. [6]
    J. Racker, Unitarity and CP-violation in leptogenesis at NLO: general considerations and top Yukawa contributions, arXiv:1811.00280 [INSPIRE].
  7. [7]
    E.J. Chun et al., Probing leptogenesis, Int. J. Mod. Phys. A 33 (2018) 1842005 [arXiv:1711.02865] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    P. Hernández, M. Kekic and J. Lopez-Pavon, N eff in low-scale seesaw models versus the lightest neutrino mass, Phys. Rev. D 90 (2014) 065033 [arXiv:1406.2961] [INSPIRE].ADSGoogle Scholar
  9. [9]
    E.K. Akhmedov, V.A. Rubakov and A.Yu. Smirnov, Baryogenesis via neutrino oscillations, Phys. Rev. Lett. 81 (1998) 1359 [hep-ph/9803255] [INSPIRE].
  10. [10]
    T. Asaka and M. Shaposhnikov, The νMSM, dark matter and baryon asymmetry of the universe, Phys. Lett. B 620 (2005) 17 [hep-ph/0505013] [INSPIRE].
  11. [11]
    M. Shaposhnikov, The νMSM, leptonic asymmetries and properties of singlet fermions, JHEP 08 (2008) 008 [arXiv:0804.4542] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    T. Asaka, S. Eijima and H. Ishida, Kinetic equations for baryogenesis via sterile neutrino oscillation, JCAP 02 (2012) 021 [arXiv:1112.5565] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    L. Canetti, M. Drewes, T. Frossard and M. Shaposhnikov, Dark Matter, baryogenesis and neutrino oscillations from right handed neutrinos, Phys. Rev. D 87 (2013) 093006 [arXiv:1208.4607] [INSPIRE].ADSGoogle Scholar
  14. [14]
    M. Shaposhnikov, A possible symmetry of the νMSM, Nucl. Phys. B 763 (2007) 49 [hep-ph/0605047] [INSPIRE].
  15. [15]
    J. Ghiglieri and M. Laine, Neutrino dynamics below the electroweak crossover, JCAP 07 (2016) 015 [arXiv:1605.07720] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    T. Hambye and D. Teresi, Higgs doublet decay as the origin of the baryon asymmetry, Phys. Rev. Lett. 117 (2016) 091801 [arXiv:1606.00017] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    M. Drewes, B. Garbrecht, D. Gueter and J. Klarić, Leptogenesis from oscillations of heavy neutrinos with large mixing angles, JHEP 12 (2016) 150 [arXiv:1606.06690] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    P. Hernández, M. Kekic, J. López-Pavón, J. Racker and J. Salvado, Testable baryogenesis in seesaw models, JHEP 08 (2016) 157 [arXiv:1606.06719] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    S. Eijima and M. Shaposhnikov, Fermion number violating effects in low scale leptogenesis, Phys. Lett. B 771 (2017) 288 [arXiv:1703.06085] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    J. Ghiglieri and M. Laine, GeV-scale hot sterile neutrino oscillations: a derivation of evolution equations, JHEP 05 (2017) 132 [arXiv:1703.06087] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    T. Asaka, S. Eijima, H. Ishida, K. Minogawa and T. Yoshii, Initial condition for baryogenesis via neutrino oscillation, Phys. Rev. D 96 (2017) 083010 [arXiv:1704.02692] [INSPIRE].ADSGoogle Scholar
  22. [22]
    T. Hambye and D. Teresi, Baryogenesis from L-violating Higgs-doublet decay in the density-matrix formalism, Phys. Rev. D 96 (2017) 015031 [arXiv:1705.00016] [INSPIRE].ADSGoogle Scholar
  23. [23]
    A. Abada, G. Arcadi, V. Domcke and M. Lucente, Neutrino masses, leptogenesis and dark matter from small lepton number violation?, JCAP 12 (2017) 024 [arXiv:1709.00415] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    S. Eijima, M. Shaposhnikov and I. Timiryasov, Freeze-out of baryon number in low-scale leptogenesis, JCAP 11 (2017) 030 [arXiv:1709.07834] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    S. Antusch, E. Cazzato, M. Drewes, O. Fischer, B. Garbrecht, D. Gueter and J. Klarić, Probing leptogenesis at future colliders, JHEP 09 (2018) 124 [arXiv:1710.03744] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    J. Ghiglieri and M. Laine, GeV-scale hot sterile neutrino oscillations: a numerical solution, JHEP 02 (2018) 078 [arXiv:1711.08469] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    S. Eijima, M. Shaposhnikov and I. Timiryasov, Parameter space of baryogenesis in the νMSM, arXiv:1808.10833 [INSPIRE].
  28. [28]
    A. Abada, G. Arcadi, V. Domcke, M. Drewes, J. Klaric and M. Lucente, Low-scale leptogenesis with three heavy neutrinos, JHEP 01 (2019) 164 [arXiv:1810.12463] [INSPIRE].CrossRefGoogle Scholar
  29. [29]
    M. D’Onofrio, K. Rummukainen and A. Tranberg, Sphaleron rate in the Minimal Standard Model, Phys. Rev. Lett. 113 (2014) 141602 [arXiv:1404.3565] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    M. Laine and M. Meyer, Standard Model thermodynamics across the electroweak crossover, JCAP 07 (2015) 035 [arXiv:1503.04935] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    M. D’Onofrio and K. Rummukainen, Standard model cross-over on the lattice, Phys. Rev. D 93 (2016) 025003 [arXiv:1508.07161] [INSPIRE].ADSGoogle Scholar
  32. [32]
    A. Anisimov, D. Besak and D. Bödeker, Thermal production of relativistic Majorana neutrinos: strong enhancement by multiple soft scattering, JCAP 03 (2011) 042 [arXiv:1012.3784] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    D. Besak and D. Bödeker, Thermal production of ultrarelativistic right-handed neutrinos: Complete leading-order results, JCAP 03 (2012) 029 [arXiv:1202.1288] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    I. Ghisoiu and M. Laine, Right-handed neutrino production rate at T > 160 GeV, JCAP 12 (2014) 032 [arXiv:1411.1765] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    J. Ghiglieri and M. Laine, Improved determination of sterile neutrino dark matter spectrum, JHEP 11 (2015) 171 [arXiv:1506.06752] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    D. Bödeker, M. Sangel and M. Wörmann, Equilibration, particle production and self-energy, Phys. Rev. D 93 (2016) 045028 [arXiv:1510.06742] [INSPIRE].ADSMathSciNetGoogle Scholar
  37. [37]
    S.Yu. Khlebnikov and M.E. Shaposhnikov, Melting of the Higgs vacuum: conserved numbers at high temperature, Phys. Lett. B 387 (1996) 817 [hep-ph/9607386] [INSPIRE].
  38. [38]
    D. Bödeker and M. Laine, Kubo relations and radiative corrections for lepton number washout, JCAP 05 (2014) 041 [arXiv:1403.2755] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  39. [39]
    D. Bödeker and M. Sangel, Order g 2 susceptibilities in the symmetric phase of the Standard Model, JCAP 04 (2015) 040 [arXiv:1501.03151] [INSPIRE].CrossRefGoogle Scholar
  40. [40]
    H.A. Weldon, Effective fermion masses of order gT in high-temperature gauge theories with exact chiral invariance, Phys. Rev. D 26 (1982) 2789 [INSPIRE].ADSGoogle Scholar
  41. [41]
    L. Lello, D. Boyanovsky and R.D. Pisarski, Production of heavy sterile neutrinos from vector boson decay at electroweak temperatures, Phys. Rev. D 95 (2017) 043524 [arXiv:1609.07647] [INSPIRE].ADSGoogle Scholar
  42. [42]
    P. Aurenche, F. Gelis and H. Zaraket, A simple sum rule for the thermal gluon spectral function and applications, JHEP 05 (2002) 043 [hep-ph/0204146] [INSPIRE].
  43. [43]
    S. Caron-Huot, O(g) plasma effects in jet quenching, Phys. Rev. D 79 (2009) 065039 [arXiv:0811.1603] [INSPIRE].ADSGoogle Scholar
  44. [44]
    J. Ghiglieri and D. Teaney, Parton energy loss and momentum broadening at NLO in high temperature QCD plasmas, Int. J. Mod. Phys. E 24 (2015) 1530013 [arXiv:1502.03730] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  45. [45]
    J. Ghiglieri, G.D. Moore and D. Teaney, Jet-medium interactions at NLO in a weakly-coupled quark-gluon plasma, JHEP 03 (2016) 095 [arXiv:1509.07773] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    R.D. Pisarski, Scattering amplitudes in hot gauge theories, Phys. Rev. Lett. 63 (1989) 1129 [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    J. Frenkel and J.C. Taylor, High temperature limit of thermal QCD, Nucl. Phys. B 334 (1990) 199 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    E. Braaten and R.D. Pisarski, Soft amplitudes in hot gauge theories: a general analysis, Nucl. Phys. B 337 (1990) 569 [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    J.C. Taylor and S.M.H. Wong, The effective action of hard thermal loops in QCD, Nucl. Phys. B 346 (1990) 115 [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    D. Nötzold and G. Raffelt, Neutrino dispersion at finite temperature and density, Nucl. Phys. B 307 (1988) 924 [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    M.C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, Updated fit to three neutrino mixing: status of leptonic CP-violation, JHEP 11 (2014) 052 [arXiv:1409.5439] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    J.A. Casas and A. Ibarra, Oscillating neutrinos and μe, γ, Nucl. Phys. B 618 (2001) 171 [hep-ph/0103065] [INSPIRE].
  53. [53]
    A. Donini, P. Hernández, J. López-Pavón, M. Maltoni and T. Schwetz, The minimal 3 + 2 neutrino model versus oscillation anomalies, JHEP 07 (2012) 161 [arXiv:1205.5230] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    Planck collaboration, Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].
  55. [55]
    X.-D. Shi and G.M. Fuller, A new dark matter candidate: nonthermal sterile neutrinos, Phys. Rev. Lett. 82 (1999) 2832 [astro-ph/9810076] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Theoretical Physics DepartmentCERNGeneva 23Switzerland
  2. 2.AEC, Institute for Theoretical PhysicsUniversity of BernBernSwitzerland

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