Journal of High Energy Physics

, 2012:68 | Cite as

Thermal right-handed neutrino production rate in the non-relativistic regime

  • M. LaineEmail author
  • Y. Schröder


We consider the next-to-leading order thermal production rate of heavy right-handed neutrinos in the non-relativistic regime m top ≲ πT ≪ M, where m top refers to the electroweak scale. Rephrasing the problem in an OPE language and making use of different techniques than a previous analysis by Salvio et al, we confirm the general structure of their result and many of the coefficients. We also extend the analysis to the next order in the non-relativistic expansion, thereby revealing the leading non-trivial momentum dependence, as well as to NNLO in couplings, revealing the leading sensitivity to thermal resummations. Our results are expressed as a sum of simple “master” structures, which renders them a suitable starting point for determining the next-to-leading order rate also in the relativistic regime πT ∼ M.


Thermal Field Theory NLO Computations Neutrino Physics 


  1. [1]
    F.D. Steffen, Dark matter candidatesAxions, neutralinos, gravitinos and axinos, Eur. Phys. J. C 59 (2009) 557 [arXiv:0811.3347] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    A. Boyarsky, O. Ruchayskiy and M. Shaposhnikov, The role of sterile neutrinos in cosmology and astrophysics, Ann. Rev. Nucl. Part. Sci. 59 (2009) 191 [arXiv:0901.0011] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    M. Fukugita and T. Yanagida, Baryogenesis without Grand Unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].ADSGoogle Scholar
  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].ADSCrossRefGoogle Scholar
  5. [5]
    S. Davidson, E. Nardi and Y. Nir, Leptogenesis, Phys. Rept. 466 (2008) 105 [arXiv:0802.2962] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    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
  7. [7]
    A. Salvio, P. Lodone and A. Strumia, Towards leptogenesis at NLO: the right-handed neutrino interaction rate, JHEP 08 (2011) 116 [arXiv:1106.2814] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    M. Garny, A. Hohenegger and A. Kartavtsev, Medium corrections to the CP-violating parameter in leptogenesis, Phys. Rev. D 81 (2010) 085028 [arXiv:1002.0331] [INSPIRE].ADSGoogle Scholar
  9. [9]
    M. Beneke, B. Garbrecht, C. Fidler, M. Herranen and P. Schwaller, Flavoured leptogenesis in the CTP formalism, Nucl. Phys. B 843 (2011) 177 [arXiv:1007.4783] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    C.S. Fong, M. Gonzalez-Garcia and J. Racker, CP violation from scatterings with gauge bosons in leptogenesis, Phys. Lett. B 697 (2011) 463 [arXiv:1010.2209] [INSPIRE].ADSGoogle Scholar
  11. [11]
    J.-S. Gagnon and M. Shaposhnikov, Baryon asymmetry of the universe without Boltzmann or Kadanoff-Baym equations, Phys. Rev. D 83 (2011) 065021 [arXiv:1012.1126] [INSPIRE].ADSGoogle Scholar
  12. [12]
    A. Anisimov, W. Buchmüller, M. Drewes and S. Mendizabal, Quantum leptogenesis I, Annals Phys. 326 (2011) 1998 [arXiv:1012.5821] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  13. [13]
    C. Kiessig and M. Plümacher, Hard-thermal-loop corrections in leptogenesis I: CP-asymmetries, arXiv:1111.1231 [INSPIRE].
  14. [14]
    K.G. Wilson and W. Zimmermann, Operator product expansions and composite field operators in the general framework of quantum field theory, Commun. Math. Phys. 24 (1972) 87 [INSPIRE].MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. [15]
    S. Caron-Huot, Asymptotics of thermal spectral functions, Phys. Rev. D 79 (2009) 125009 [arXiv:0903.3958] [INSPIRE].ADSGoogle Scholar
  16. [16]
    M. Laine, M. Vepsäläinen and A. Vuorinen, Ultraviolet asymptotics of scalar and pseudoscalar correlators in hot Yang-Mills theory, JHEP 10 (2010) 010 [arXiv:1008.3263] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    Y. Schröder, M. Vepsäläinen, A. Vuorinen and Y. Zhu, The ultraviolet limit and sum rule for the shear correlator in hot Yang-Mills theory, JHEP 12 (2011) 035 [arXiv:1109.6548] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    T. Asaka, M. Laine and M. Shaposhnikov, On the hadronic contribution to sterile neutrino production, JHEP 06 (2006) 053 [hep-ph/0605209] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    M. Laine and M. Shaposhnikov, Sterile neutrino dark matter as a consequence of νMSM-induced lepton asymmetry, JCAP 06 (2008) 031 [arXiv:0804.4543] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    M. Le Bellac, Thermal field theory, Cambridge University Press, Cambridge U.K. (2000).Google Scholar
  21. [21]
    G. ’t Hooft and M.J.G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    P. Breitenlohner and D. Maison, Dimensional Renormalization and the Action Principle, Commun. Math. Phys. 52 (1977) 11 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    J.G. Körner, N. Nasrallah and K. Schilcher, Evaluation of the flavor changing vertex b → sH using the Breitenlohner-Maison-t Hooft-Veltman γ5 scheme, Phys. Rev. D 41 (1990) 888 [INSPIRE].ADSGoogle Scholar
  24. [24]
    A.J. Buras and P.H. Weisz, QCD nonleading corrections to weak decays in dimensional regularization andt Hooft-Veltman schemes, Nucl. Phys. B 333 (1990) 66 [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    S.A. Larin, The renormalization of the axial anomaly in dimensional regularization, Phys. Lett. B 303 (1993) 113 [hep-ph/9302240] [INSPIRE].ADSGoogle Scholar
  26. [26]
    S.A. Larin and J.A.M. Vermaseren, The \( \alpha_s^3 \) corrections to the Bjorken sum rule for polarized electroproduction and to the Gross-Llewellyn Smith sum rule, Phys. Lett. B 259 (1991) 345 [INSPIRE].ADSGoogle Scholar
  27. [27]
    P.B. Arnold and O. Espinosa, The effective potential and first order phase transitions: beyond leading-order, Phys. Rev. D 47 (1993) 3546 [Erratum ibid. D 50 (1994) 6662] [hep-ph/9212235] [INSPIRE].ADSGoogle Scholar
  28. [28]
    M. Laine, A. Vuorinen and Y. Zhu, Next-to-leading order thermal spectral functions in the perturbative domain, JHEP 09 (2011) 084 [arXiv:1108.1259] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    K. Farakos, K. Kajantie, K. Rummukainen and M.E. Shaposhnikov, 3D physics and the electroweak phase transition: perturbation theory, Nucl. Phys. B 425 (1994) 67 [hep-ph/9404201] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    J.I. Kapusta, Quantum chromodynamics at high temperature, Nucl. Phys. B 148 (1979) 461 [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.Faculty of PhysicsUniversity of BielefeldBielefeldGermany

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