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Journal of High Energy Physics

, 2019:42 | Cite as

Unitarity and CP violation in leptogenesis at NLO: general considerations and top Yukawa contributions

  • J. RackerEmail author
Open Access
Regular Article - Theoretical Physics
  • 58 Downloads

Abstract

With an emphasis on unitarity and CPT requirements, we study the inclusion of CP-violating processes in baryogenesis at next-to-leading order, particularly those involving the top Yukawa interaction in leptogenesis. We show that there are more contributions than previously considered, but also important cancellations. Some of these involve the interference of connected with disconnected diagrams. We also discuss on the application of the Kinoshita-Lee-Nauenberg theorem to treat the infrared divergences that are common at next-to-leading order. Finally, we calculate the CP asymmetry in the three-body decay of a sterile neutrino into a lepton and top quarks.

Keywords

Cosmology of Theories beyond the SM Beyond Standard Model CP violation 

Notes

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.

References

  1. [1]
    A. Pilaftsis and T.E.J. Underwood, Resonant leptogenesis, Nucl. Phys. B 692 (2004) 303 [hep-ph/0309342] [INSPIRE].
  2. [2]
    A. Pilaftsis and T.E.J. Underwood, Electroweak-scale resonant leptogenesis, Phys. Rev. D 72 (2005) 113001 [hep-ph/0506107] [INSPIRE].
  3. [3]
    A. Abada, S. Davidson, A. Ibarra, F.X. Josse-Michaux, M. Losada and A. Riotto, Flavour Matters in Leptogenesis, JHEP 09 (2006) 010 [hep-ph/0605281] [INSPIRE].
  4. [4]
    E. Nardi, J. Racker and E. Roulet, CP violation in scatterings, three body processes and the Boltzmann equations for leptogenesis, JHEP 09 (2007) 090 [arXiv:0707.0378] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    C.S. Fong, M.C. Gonzalez-Garcia and J. Racker, CP Violation from Scatterings with Gauge Bosons in Leptogenesis, Phys. Lett. B 697 (2011) 463 [arXiv:1010.2209] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    I. Baldes, N.F. Bell, A. Millar, K. Petraki and R.R. Volkas, The role of CP-violating scatterings in baryogenesis — case study of the neutron portal, JCAP 11 (2014) 041 [arXiv:1410.0108] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    I. Baldes, N.F. Bell, K. Petraki and R.R. Volkas, Particle-antiparticle asymmetries from annihilations, Phys. Rev. Lett. 113 (2014) 181601 [arXiv:1407.4566] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    I. Baldes, N.F. Bell, A.J. Millar and R.R. Volkas, Asymmetric Dark Matter and CP-violating Scatterings in a UV Complete Model, JCAP 10 (2015) 048 [arXiv:1506.07521] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    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
  10. [10]
    S. Biondini, N. Brambilla, M.A. Escobedo and A. Vairo, CP asymmetry in heavy Majorana neutrino decays at finite temperature: the nearly degenerate case, JHEP 03 (2016) 191 [Erratum ibid. 08 (2016) 072] [arXiv:1511.02803] [INSPIRE].
  11. [11]
    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
  12. [12]
    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].ADSCrossRefzbMATHGoogle Scholar
  13. [13]
    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
  14. [14]
    M. Laine and Y. Schröder, Thermal right-handed neutrino production rate in the non-relativistic regime, JHEP 02 (2012) 068 [arXiv:1112.1205] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  15. [15]
    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
  16. [16]
    B. Garbrecht, F. Glowna and M. Herranen, Right-Handed Neutrino Production at Finite Temperature: Radiative Corrections, Soft and Collinear Divergences, JHEP 04 (2013) 099 [arXiv:1302.0743] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    M. Laine, Thermal right-handed neutrino production rate in the relativistic regime, JHEP 08 (2013) 138 [arXiv:1307.4909] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    S. Biondini, N. Brambilla, M.A. Escobedo and A. Vairo, An effective field theory for non-relativistic Majorana neutrinos, JHEP 12 (2013) 028 [arXiv:1307.7680] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    D. Bödeker and M. Laine, Kubo relations and radiative corrections for lepton number washout, JCAP 05 (2014) 041 [arXiv:1403.2755] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  20. [20]
    I. Ghisoiu and M. Laine, Right-handed neutrino production rate at T > 160 GeV, JCAP 12 (2014) 032 [arXiv:1411.1765] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    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
  22. [22]
    S. Biondini et al., Status of rates and rate equations for thermal leptogenesis, Int. J. Mod. Phys. A 33 (2018) 1842004 [arXiv:1711.02864] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    T. Kinoshita, Mass singularities of Feynman amplitudes, J. Math. Phys. 3 (1962) 650 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  24. [24]
    T.D. Lee and M. Nauenberg, Degenerate Systems and Mass Singularities, Phys. Rev. 133 (1964) B1549 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    M. Beneke, F. Dighera and A. Hryczuk, Relic density computations at NLO: infrared finiteness and thermal correction, JHEP 10 (2014) 45 [Erratum ibid. 07 (2016) 106] [arXiv:1409.3049] [INSPIRE].
  26. [26]
    S. Weinberg, Cosmological Production of Baryons, Phys. Rev. Lett. 42 (1979) 850 [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    E.W. Kolb and S. Wolfram, Baryon Number Generation in the Early Universe, Nucl. Phys. B 172 (1980) 224 [Erratum ibid. B 195 (1982) 542] [INSPIRE].
  28. [28]
    A.D. Sakharov, Violation of CP Invariance, C asymmetry and baryon asymmetry of the universe, Pisma Zh. Eksp. Teor. Fiz. 5 (1967) 32 [INSPIRE].Google Scholar
  29. [29]
    D. Aristizabal Sierra, L.A. Muñoz and E. Nardi, Purely Flavored Leptogenesis, Phys. Rev. D 80 (2009) 016007 [arXiv:0904.3043] [INSPIRE].ADSGoogle Scholar
  30. [30]
    R.E. Cutkosky, Singularities and discontinuities of Feynman amplitudes, J. Math. Phys. 1 (1960) 429 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    M.J.G. Veltman, Diagrammatica: The Path to Feynman rules, Cambridge Lect. Notes Phys. 4 (1994) 1 [INSPIRE].Google Scholar
  32. [32]
    E. Roulet, L. Covi and F. Vissani, On the CP asymmetries in Majorana neutrino decays, Phys. Lett. B 424 (1998) 101 [hep-ph/9712468] [INSPIRE].
  33. [33]
    A. Hook, Unitarity constraints on asymmetric freeze-in, Phys. Rev. D 84 (2011) 055003 [arXiv:1105.3728] [INSPIRE].ADSGoogle Scholar
  34. [34]
    D. Binosi and L. Theussl, JaxoDraw: A Graphical user interface for drawing Feynman diagrams, Comput. Phys. Commun. 161 (2004) 76 [hep-ph/0309015] [INSPIRE].
  35. [35]
    M. Lavelle and D. McMullan, Collinearity, convergence and cancelling infrared divergences, JHEP 03 (2006) 026 [hep-ph/0511314] [INSPIRE].
  36. [36]
    M. Lavelle, D. McMullan and T. Steele, Soft Collinear Degeneracies in an Asymptotically Free Theory, Adv. High Energy Phys. 2012 (2012) 379736 [arXiv:1008.3949] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  37. [37]
    C. Frye, H. Hannesdottir, N. Paul, M.D. Schwartz and K. Yan, Infrared Finiteness and Forward Scattering, arXiv:1810.10022 [INSPIRE].
  38. [38]
    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].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Instituto de Astronomía Teórica y Experimental (IATE), Universidad Nacional de Córdoba (UNC) — Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)CórdobaArgentina
  2. 2.Observatorio Astronómico de Córdoba (OAC)Universidad Nacional de Córdoba (UNC)CórdobaArgentina

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