Dark matter relic abundance and light sterile neutrinos

  • Yi-Lei Tang
  • Shou-hua Zhu
Open Access
Regular Article - Theoretical Physics


In this paper, we calculate the relic abundance of the dark matter particles when they can annihilate into sterile neutrinos with the mass ≲ 100 GeV in a simple model. Unlike the usual standard calculations, the sterile neutrino may fall out of the thermal equilibrium with the thermal bath before the dark matter freezes out. In such a case, if the Yukawa coupling y N between the Higgs and the sterile neutrino is small, this process gives rise to a larger ΩDM h 2 so we need a larger coupling between the dark matter and the sterile neutrino for a correct relic abundance.


Beyond Standard Model Cosmology of Theories beyond the SM Neutrino Physics 


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]
    G. Bertone, D. Hooper and J. Silk, Particle dark matter: evidence, candidates and constraints, Phys. Rept. 405 (2005) 279 [hep-ph/0404175] [INSPIRE].
  2. [2]
    E.W. Kolb and M.S. Turner, The early universe, Front. Phys. 69 (1990) 1 [INSPIRE].ADSMATHGoogle Scholar
  3. [3]
    P. Minkowski, μeγ at a rate of one out of 109 muon decays?, Phys. Lett. B 67 (1977) 421 [INSPIRE].
  4. [4]
    T. Yanagida, Horizontal symmetry and masses of neutrinos, in the proceedings of the Workshop on unified theory and baryon number in the universe, O. Sawada and A. Sugamoto eds., KEK, Tsukuba, Japan (1979).Google Scholar
  5. [5]
    M. Gell-Mann, P. Ramond, R. Slansky, Complex spinors and unified theories, in Supergravity, D.Z. Freedman and P.van Nieuwenhuizen eds., North Holland, Amsterdam, The Netherlands (1979).Google Scholar
  6. [6]
    S.L. Glashow, The future of elementary particle physics, in Quarks and leptons, Cargèse lectures, M. Lévy et al. eds., Plenum Press, New York, U.S.A. (1980).Google Scholar
  7. [7]
    R.N. Mohapatra and G. Senjanović, Neutrino Mass and Spontaneous Parity Violation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    A. Strumia, Baryogenesis via leptogenesis, in the proceedings of the Summer School on Theoretical Physics, 84th Session, August 1-26, Les Houches, France (2005), hep-ph/0608347 [INSPIRE].
  9. [9]
    D. Wyler and L. Wolfenstein, Massless neutrinos in left-right symmetric models, Nucl. Phys. B 218 (1983) 205 [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    R.N. Mohapatra and J.W.F. Valle, Neutrino mass and baryon number nonconservation in superstring models, Phys. Rev. D 34 (1986) 1642 [INSPIRE].ADSGoogle Scholar
  11. [11]
    E. Ma, Lepton number nonconservation in E 6 superstring models, Phys. Lett. B 191 (1987) 287 [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    R.N. Mohapatra, Mechanism for understanding small neutrino mass in superstring theories, Phys. Rev. Lett. 56 (1986) 561 [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    E. Witten, Symmetry breaking patterns in superstring models, Nucl. Phys. B 258 (1985) 75 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    M. Malinsky, J.C. Romao and J.W.F. Valle, Novel supersymmetric SO(10) seesaw mechanism, Phys. Rev. Lett. 95 (2005) 161801 [hep-ph/0506296] [INSPIRE].
  15. [15]
    S. Khalil, TeV-scale gauged B-L symmetry with inverse seesaw mechanism, Phys. Rev. D 82 (2010) 077702 [arXiv:1004.0013] [INSPIRE].ADSGoogle Scholar
  16. [16]
    M. Pospelov, A. Ritz and M.B. Voloshin, Secluded WIMP dark matter, Phys. Lett. B 662 (2008) 53 [arXiv:0711.4866] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    N. Arkani-Hamed, D.P. Finkbeiner, T.R. Slatyer and N. Weiner, A theory of dark matter, Phys. Rev. D 79 (2009) 015014 [arXiv:0810.0713] [INSPIRE].ADSGoogle Scholar
  18. [18]
    S. Okawa, M. Tanabashi and M. Yamanaka, Relic abundance in a secluded dark matter scenario with a massive mediator, arXiv:1607.08520 [INSPIRE].
  19. [19]
    R. Allahverdi, S. Bornhauser, B. Dutta and K. Richardson-McDaniel, Prospects for indirect detection of sneutrino dark matter with IceCube, Phys. Rev. D 80 (2009) 055026 [arXiv:0907.1486] [INSPIRE].ADSGoogle Scholar
  20. [20]
    R. Allahverdi, S. Campbell and B. Dutta, Extragalactic and galactic gamma-rays and neutrinos from annihilating dark matter, Phys. Rev. D 85 (2012) 035004 [arXiv:1110.6660] [INSPIRE].ADSGoogle Scholar
  21. [21]
    R. Allahverdi, B. Dutta, K. Richardson-McDaniel and Y. Santoso, Sneutrino dark matter and the observed anomalies in cosmic rays, Phys. Lett. B 677 (2009) 172 [arXiv:0902.3463] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    R. Allahverdi, S.S. Campbell, B. Dutta and Y. Gao, Dark matter indirect detection signals and the nature of neutrinos in the supersymmetric U(1)BL extension of the standard model, Phys. Rev. D 90 (2014) 073002 [arXiv:1405.6253] [INSPIRE].ADSGoogle Scholar
  23. [23]
    V. González-Macías, J.I. Illana and J. Wudka, A realistic model for dark matter interactions in the neutrino portal paradigm, JHEP 05 (2016) 171 [arXiv:1601.05051] [INSPIRE].
  24. [24]
    M. Escudero, N. Rius and V. Sanz, Sterile neutrino portal to dark matter II: exact dark symmetry, arXiv:1607.02373 [INSPIRE].
  25. [25]
    V. González-Macías, J. Illana and J. Wudka, Dark matter and the neutrino portal paradigm, J. Phys. Conf. Ser. 761 (2016) 012082 [arXiv:1608.06267] [INSPIRE].CrossRefGoogle Scholar
  26. [26]
    V. Gonzalez Macias and J. Wudka, Effective theories for dark matter interactions and the neutrino portal paradigm, JHEP 07 (2015) 161 [arXiv:1506.03825] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    S. Gopalakrishna, A. de Gouvêa and W. Porod, Right-handed sneutrinos as nonthermal dark matter, JCAP 05 (2006) 005 [hep-ph/0602027] [INSPIRE].
  28. [28]
    S. Dodelson and L.M. Widrow, Sterile-neutrinos as dark matter, Phys. Rev. Lett. 72 (1994) 17 [hep-ph/9303287] [INSPIRE].
  29. [29]
    R. Adhikari et al., A white paper on keV sterile neutrino dark matter, arXiv:1602.04816 [INSPIRE].
  30. [30]
    A. Biswas and A. Gupta, Freeze-in production of sterile neutrino dark matter in U(1)B−L model, JCAP 09 (2016) 044 [arXiv:1607.01469] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    Y.-L. Tang and S.-h. Zhu, Dark matter annihilation into right-handed neutrinos and the galactic center γ-ray excess, arXiv:1512.02899 [INSPIRE].
  32. [32]
    S. Davidson, E. Nardi and Y. Nir, Leptogenesis, Phys. Rept. 466 (2008) 105 [arXiv:0802.2962] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    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
  34. [34]
    M. Quirós, Finite temperature field theory and phase transitions, hep-ph/9901312 [INSPIRE].
  35. [35]
    L. Dolan and R. Jackiw, Symmetry behavior at finite temperature, Phys. Rev. D 9 (1974) 3320 [INSPIRE].ADSGoogle Scholar
  36. [36]
    C.P. Kiessig, M. Plümacher and M.H. Thoma, Decay of a Yukawa fermion at finite temperature and applications to leptogenesis, Phys. Rev. D 82 (2010) 036007 [arXiv:1003.3016] [INSPIRE].ADSGoogle Scholar
  37. [37]
    G.F. Giudice, A. Notari, M. Raidal, A. Riotto and A. Strumia, Towards a complete theory of thermal leptogenesis in the SM and MSSM, Nucl. Phys. B 685 (2004) 89 [hep-ph/0310123] [INSPIRE].
  38. [38]
    S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, Numerical recipes in c: the art of scientific computing, 2nd edition, W.H. Press, U.S.A. (1992).Google Scholar
  39. [39]
    G. Hairer, Solving ordinary differential equations II, Springer, Berlin Germany (2010).Google Scholar
  40. [40]
    G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs4.1: two dark matter candidates, Comput. Phys. Commun. 192 (2015) 322 [arXiv:1407.6129] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    A. Belyaev, N.D. Christensen and A. Pukhov, CalcHEP 3.4 for collider physics within and beyond the Standard Model, Comput. Phys. Commun. 184 (2013) 1729 [arXiv:1207.6082] [INSPIRE].
  42. [42]
    A. Alloul, N.D. Christensen, C. Degrande, C. Duhr and B. Fuks, FeynRules 2.0A complete toolbox for tree-level phenomenology, Comput. Phys. Commun. 185 (2014) 2250 [arXiv:1310.1921] [INSPIRE].
  43. [43]
    C.O. Dib and C.S. Kim, Discovering sterile neutrinos ligther than M W at the LHC, Phys. Rev. D 92 (2015) 093009 [arXiv:1509.05981] [INSPIRE].ADSGoogle Scholar
  44. [44]
    ATLAS collaboration, Search for heavy Majorana neutrinos with the ATLAS detector in pp collisions at \( \sqrt{s}=8 \) TeV, JHEP 07 (2015) 162 [arXiv:1506.06020] [INSPIRE].
  45. [45]
    CMS collaboration, Search for heavy Majorana neutrinos in μ ± μ ± + jets events in proton-proton collisions at \( \sqrt{s}=8 \) TeV, Phys. Lett. B 748 (2015) 144 [arXiv:1501.05566] [INSPIRE].
  46. [46]
    S. Antusch and O. Fischer, Testing sterile neutrino extensions of the standard model at future lepton colliders, JHEP 05 (2015) 053 [arXiv:1502.05915] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    F.F. Deppisch, P.S. Bhupal Dev and A. Pilaftsis, Neutrinos and collider physics, New J. Phys. 17 (2015) 075019 [arXiv:1502.06541] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    A. Das, P.S. Bhupal Dev and N. Okada, Direct bounds on electroweak scale pseudo-Dirac neutrinos from \( \sqrt{s}=8 \) TeV LHC data, Phys. Lett. B 735 (2014) 364 [arXiv:1405.0177] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    S. Antusch, E. Cazzato and O. Fischer, Displaced vertex searches for sterile neutrinos at future lepton colliders, JHEP 12 (2016) 007 [arXiv:1604.02420] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    S. Antusch and O. Fischer, Non-unitarity of the leptonic mixing matrix: Present bounds and future sensitivities, JHEP 10 (2014) 094 [arXiv:1407.6607] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    A. Das and N. Okada, Improved bounds on the heavy neutrino productions at the LHC, Phys. Rev. D 93 (2016) 033003 [arXiv:1510.04790] [INSPIRE].ADSGoogle Scholar
  52. [52]
    A. Das and N. Okada, Inverse seesaw neutrino signatures at the LHC and ILC, Phys. Rev. D 88 (2013) 113001 [arXiv:1207.3734] [INSPIRE].ADSGoogle Scholar
  53. [53]
    A. Das, P. Konar and S. Majhi, Production of heavy neutrino in next-to-leading order QCD at the LHC and beyond, JHEP 06 (2016) 019 [arXiv:1604.00608] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XVI. Cosmological parameters, Astron. Astrophys. 571 (2014) A16 [arXiv:1303.5076] [INSPIRE].
  55. [55]
    Particle Data Group collaboration, C. Patrignani et al., Review of particle physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].

Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Center for High Energy PhysicsPeking UniversityBeijingChina
  2. 2.Institute of Theoretical Physics & State Key Laboratory of Nuclear Physics and TechnologyPeking UniversityBeijingChina
  3. 3.Collaborative Innovation Center of Quantum MatterBeijingChina

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