Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
F.D. Steffen, Dark matter candidates — Axions, neutralinos, gravitinos and axinos, Eur. Phys. J. C 59 (2009) 557 [arXiv:0811.3347] [INSPIRE].
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].
M. Fukugita and T. Yanagida, Baryogenesis without Grand Unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].
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].
S. Davidson, E. Nardi and Y. Nir, Leptogenesis, Phys. Rept. 466 (2008) 105 [arXiv:0802.2962] [INSPIRE].
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].
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].
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].
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].
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].
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].
A. Anisimov, W. Buchmüller, M. Drewes and S. Mendizabal, Quantum leptogenesis I, Annals Phys. 326 (2011) 1998 [arXiv:1012.5821] [INSPIRE].
C. Kiessig and M. Plümacher, Hard-thermal-loop corrections in leptogenesis I: CP-asymmetries, arXiv:1111.1231 [INSPIRE].
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].
S. Caron-Huot, Asymptotics of thermal spectral functions, Phys. Rev. D 79 (2009) 125009 [arXiv:0903.3958] [INSPIRE].
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].
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].
T. Asaka, M. Laine and M. Shaposhnikov, On the hadronic contribution to sterile neutrino production, JHEP 06 (2006) 053 [hep-ph/0605209] [INSPIRE].
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].
M. Le Bellac, Thermal field theory, Cambridge University Press, Cambridge U.K. (2000).
G. ’t Hooft and M.J.G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
P. Breitenlohner and D. Maison, Dimensional Renormalization and the Action Principle, Commun. Math. Phys. 52 (1977) 11 [INSPIRE].
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].
A.J. Buras and P.H. Weisz, QCD nonleading corrections to weak decays in dimensional regularization and ’t Hooft-Veltman schemes, Nucl. Phys. B 333 (1990) 66 [INSPIRE].
S.A. Larin, The renormalization of the axial anomaly in dimensional regularization, Phys. Lett. B 303 (1993) 113 [hep-ph/9302240] [INSPIRE].
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].
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].
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].
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].
J.I. Kapusta, Quantum chromodynamics at high temperature, Nucl. Phys. B 148 (1979) 461 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1112.1205
Rights and permissions
About this article
Cite this article
Laine, M., Schröder, Y. Thermal right-handed neutrino production rate in the non-relativistic regime. J. High Energ. Phys. 2012, 68 (2012). https://doi.org/10.1007/JHEP02(2012)068
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2012)068