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Leptogenesis from low energy CP violation

  • K. MoffatEmail author
  • S. Pascoli
  • S. T. Petcov
  • J. Turner
Open Access
Regular Article - Theoretical Physics

Abstract

We revisit the possibility of producing the observed baryon asymmetry of the Universe via thermal leptogenesis, where CP violation comes exclusively from the low-energy phases of the neutrino mixing matrix. We demonstrate the viability of thermal flavoured leptogenesis across seven orders of magnitude (106< T (GeV) < 1013), using modern numerical machinery, where the lower bound can be reached only if flavour effects are taken into account and its value depends on the allowed degree of cancellation between the tree-level and radiative contributions to the light neutrino masses. At very high scales (T ≫1012 GeV), we clarify that thermal leptogenesis is sensitive to the low-energy phases, in contradiction with what is usually claimed in the literature. In particular we demonstrate that Majorana-phase leptogenesis is in general viable while Dirac-phase leptogenesis requires some level of fine-tuning.

Keywords

CP violation Neutrino Physics Beyond Standard Model 

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.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
  2. [2]
    Super-Kamiokande collaboration, Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 81 (1998) 1562 [hep-ex/9807003] [INSPIRE].
  3. [3]
    V.A. Kuzmin, V.A. Rubakov and M.E. Shaposhnikov, On the anomalous electroweak baryon number nonconservation in the early universe, Phys. Lett. B 155 (1985) 36.Google Scholar
  4. [4]
    S.Yu. Khlebnikov and M.E. Shaposhnikov, The statistical theory of anomalous fermion number nonconservation, Nucl. Phys. B 308 (1988) 885 [INSPIRE].
  5. [5]
    P. Minkowski, μeγ at a rate of one out of 109 muon decays?, Phys. Lett. 67B (1977) 421 [INSPIRE].
  6. [6]
    T. Yanagida, Horizontal gauge symmetry and masses of neutrinos, Conf. Proc. C 7902131 (1979) 95 [INSPIRE].
  7. [7]
    M. Gell-Mann, P. Ramond and R. Slansky, Complex spinors and unified theories, Conf. Proc. C 790927 (1979) 315 [arXiv:1306.4669] [INSPIRE].
  8. [8]
    R.N. Mohapatra and G. Senjanović, Neutrino mass and spontaneous parity nonconservation, Phys. Rev. Lett. 44 (1980) 912 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  9. [9]
    M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].
  10. [10]
    W. Buchmüller and M. Plümacher, Baryon asymmetry and neutrino mixing, Phys. Lett. B 389 (1996) 73 [hep-ph/9608308] [INSPIRE].
  11. [11]
    W. Buchmüller, P. Di Bari and M. Plümacher, Leptogenesis for pedestrians, Annals Phys. 315 (2005) 305 [hep-ph/0401240] [INSPIRE].
  12. [12]
    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].
  13. [13]
    A. Pilaftsis, CP violation and baryogenesis due to heavy Majorana neutrinos, Phys. Rev. D 56 (1997) 5431 [hep-ph/9707235] [INSPIRE].
  14. [14]
    Particle Data Group collaboration, Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
  15. [15]
    G.C. Branco, T. Morozumi, B.M. Nobre and M.N. Rebelo, A bridge between CP-violation at low-energies and leptogenesis, Nucl. Phys. B 617 (2001) 475 [hep-ph/0107164] [INSPIRE].
  16. [16]
    G.C. Branco et al., Minimal scenarios for leptogenesis and CP-violation, Phys. Rev. D 67 (2003) 073025 [hep-ph/0211001] [INSPIRE].
  17. [17]
    T. Endoh et al., CP violation in neutrino oscillation and leptogenesis, Phys. Rev. Lett. 89 (2002) 231601 [hep-ph/0209020] [INSPIRE].
  18. [18]
    P.H. Frampton, S.L. Glashow and T. Yanagida, Cosmological sign of neutrino CP-violation, Phys. Lett. B 548 (2002) 119 [hep-ph/0208157] [INSPIRE].
  19. [19]
    Y. Shimizu, K. Takagi and M. Tanimoto, Neutrino CP-violation and sign of baryon asymmetry in the minimal seesaw model, Phys. Lett. B 778 (2018) 6 [arXiv:1711.03863] [INSPIRE].
  20. [20]
    E. Nardi, Y. Nir, J. Racker and E. Roulet, On Higgs and sphaleron effects during the leptogenesis era, JHEP 01 (2006) 068 [hep-ph/0512052] [INSPIRE].
  21. [21]
    A. Abada et al., Flavour matters in leptogenesis, JHEP 09 (2006) 010 [hep-ph/0605281] [INSPIRE].
  22. [22]
    A. Abada et al., Flavor issues in leptogenesis, JCAP 04 (2006) 004 [hep-ph/0601083] [INSPIRE].
  23. [23]
    R. Barbieri, P. Creminelli, A. Strumia and N. Tetradis, Baryogenesis through leptogenesis, Nucl. Phys. B 575 (2000) 61 [hep-ph/9911315] [INSPIRE].
  24. [24]
    H.B. Nielsen and Y. Takanishi, Baryogenesis via lepton number violation and family replicated gauge group, Nucl. Phys. B 636 (2002) 305 [hep-ph/0204027] [INSPIRE].
  25. [25]
    S. Pascoli, S.T. Petcov and A. Riotto, Connecting low energy leptonic CP-violation to leptogenesis, Phys. Rev. D 75 (2007) 083511 [hep-ph/0609125] [INSPIRE].
  26. [26]
    S. Pascoli, S.T. Petcov and A. Riotto, Leptogenesis and low energy CP-violation in neutrino physics, Nucl. Phys. B 774 (2007) 1 [hep-ph/0611338] [INSPIRE].
  27. [27]
    S. Blanchet and P. Di Bari, Flavor effects on leptogenesis predictions, JCAP 03 (2007) 018 [hep-ph/0607330] [INSPIRE].
  28. [28]
    G.C. Branco, R. Gonzalez Felipe and F.R. Joaquim, A new bridge between leptonic CP-violation and leptogenesis, Phys. Lett. B 645 (2007) 432 [hep-ph/0609297] [INSPIRE].
  29. [29]
    A. Anisimov, S. Blanchet and P. Di Bari, Viability of Dirac phase leptogenesis, JCAP 04 (2008) 033 [arXiv:0707.3024] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    E. Molinaro and S.T. Petcov, The interplay between the ‘low’ and ‘high’ energy CP-violation in leptogenesis, Eur. Phys. J. C 61 (2009) 93 [arXiv:0803.4120] [INSPIRE].
  31. [31]
    E. Molinaro and S.T. Petcov, A case of subdominant/suppressed ‘high energy’ contribution to the baryon asymmetry of the universe in flavoured leptogenesis, Phys. Lett. B 671 (2009) 60 [arXiv:0808.3534] [INSPIRE].
  32. [32]
    M.J. Dolan, T.P. Dutka and R.R. Volkas, Dirac-phase thermal leptogenesis in the extended Type-I seesaw model, JCAP 06 (2018) 012 [arXiv:1802.08373] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    C. Hagedorn et al., CP violation in the lepton sector and implications for leptogenesis, Int. J. Mod. Phys. A 33 (2018) 1842006 [arXiv:1711.02866] [INSPIRE].
  34. [34]
    G.C. Branco et al., Another look at minimal lepton flavour violation, l il , leptogenesis and the ratio M ν /ΛLF V , JHEP 09 (2007) 004 [hep-ph/0609067] [INSPIRE].
  35. [35]
    L. Merlo and S. Rosauro-Alcaraz, Predictive leptogenesis from minimal lepton flavour violation, JHEP 07 (2018) 036 [arXiv:1801.03937] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    C.C. Nishi, B.L. Sánchez-Vega and G. Souza Silva, μτ reflection symmetry with a high scale texture-zero, JHEP 09 (2018) 042 [arXiv:1806.07412] [INSPIRE].
  37. [37]
    A. Meroni, E. Molinaro and S.T. Petcov, Revisiting leptogenesis in a SUSY SU(5) × T model of flavour, Phys. Lett. B 710 (2012) 435 [arXiv:1203.4435] [INSPIRE].
  38. [38]
    R.N. Mohapatra and C.C. Nishi, Implications of μ-τ flavored CP symmetry of leptons, JHEP 08 (2015) 092 [arXiv:1506.06788] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    C. Hagedorn and E. Molinaro, Flavor and CP symmetries for leptogenesis and 0νββ decay, Nucl. Phys. B 919 (2017) 404 [arXiv:1602.04206] [INSPIRE].
  40. [40]
    P. Chen, G.-J. Ding and S.F. King, Leptogenesis and residual CP symmetry, JHEP 03 (2016) 206 [arXiv:1602.03873] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    C.-C. Li and G.-J. Ding, Implications of residual CP symmetry for leptogenesis in a model with two right-handed neutrinos, Phys. Rev. D 96 (2017) 075005 [arXiv:1701.08508] [INSPIRE].
  42. [42]
    L. Covi, J.E. Kim, B. Kyae and S. Nam, Leptogenesis with high-scale electroweak symmetry breaking and an extended Higgs sector, Phys. Rev. D 94 (2016) 065004 [arXiv:1601.00411] [INSPIRE].
  43. [43]
    S.M. Bilenky, J. Hosek and S.T. Petcov, On oscillations of neutrinos with Dirac and Majorana masses, Phys. Lett. B 94 (1980) 495.Google Scholar
  44. [44]
    I. Esteban et al., Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity, JHEP 01 (2017) 087 [arXiv:1611.01514] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    A. Pilaftsis, Radiatively induced neutrino masses and large Higgs neutrino couplings in the standard model with Majorana fields, Z. Phys. C 55 (1992) 275 [hep-ph/9901206] [INSPIRE].
  46. [46]
    D. Aristizabal Sierra and C.E. Yaguna, On the importance of the 1-loop finite corrections to seesaw neutrino masses, JHEP 08 (2011) 013 [arXiv:1106.3587] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  47. [47]
    J. Lopez-Pavon, S. Pascoli and C.-f. Wong, Can heavy neutrinos dominate neutrinoless double beta decay?, Phys. Rev. D 87 (2013) 093007 [arXiv:1209.5342] [INSPIRE].
  48. [48]
    W. Grimus and L. Lavoura, One-loop corrections to the seesaw mechanism in the multi-Higgs-doublet standard model, Phys. Lett. B 546 (2002) 86 [hep-ph/0207229] [INSPIRE].
  49. [49]
    J.A. Casas and A. Ibarra, Oscillating neutrinos and μe, γ, Nucl. Phys. B 618 (2001) 171 [hep-ph/0103065] [INSPIRE].
  50. [50]
    J. Lopez-Pavon, E. Molinaro and S.T. Petcov, Radiative corrections to light neutrino masses in low scale Type I seesaw scenarios and neutrinoless double beta decay, JHEP 11 (2015) 030 [arXiv:1506.05296] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    S.M. Bilenky and S.T. Petcov, Massive neutrinos and neutrino oscillations, Rev. Mod. Phys. 59 (1987) 671 [Erratum ibid. 61 (1989) 169] [INSPIRE].
  52. [52]
    T2K collaboration, The T2K experiment, Nucl. Instrum. Meth. A 659 (2011) 106 [arXiv:1106.1238] [INSPIRE].
  53. [53]
    NOvA collaboration, NOvA: proposal to build a 30 kiloton off-axis detector to study ν μν e oscillations in the NuMI beamline, hep-ex/0503053 [INSPIRE].
  54. [54]
    Daya Bay collaboration, Observation of electron-antineutrino disappearance at Daya Bay, Phys. Rev. Lett. 108 (2012) 171803 [arXiv:1203.1669] [INSPIRE].
  55. [55]
    RENO collaboration, Observation of reactor electron antineutrino disappearance in the RENO experiment, Phys. Rev. Lett. 108 (2012) 191802 [arXiv:1204.0626] [INSPIRE].
  56. [56]
    Double CHOOZ collaboration, Double CHOOZ: a search for the neutrino mixing angle theta(13), hep-ex/0606025 [INSPIRE].
  57. [57]
    N. Cabibbo, Time reversal violation in neutrino oscillation, Phys. Lett. B 72 (1978) 333.Google Scholar
  58. [58]
    S. Bilenky, J. Hošek and S. Petcov, On the oscillations of neutrinos with dirac and majorana masses, Phys. Lett. B 94 (1980) 495.Google Scholar
  59. [59]
    V.D. Barger, K. Whisnant and R.J.N. Phillips, CP violation in three neutrino oscillations, Phys. Rev. Lett. 45 (1980) 2084 [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    P.I. Krastev and S.T. Petcov, Resonance amplification and t violation effects in three neutrino oscillations in the Earth, Phys. Lett. B 205 (1988) 84 [INSPIRE].
  61. [61]
    DUNE collaboration, Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE), arXiv:1512.06148 [INSPIRE].
  62. [62]
    Hyper-Kamiokande Proto-Collaboration collaboration, Physics potential of a long-baseline neutrino oscillation experiment using a J-PARC neutrino beam and Hyper-Kamiokande, PTEP 2015 (2015) 053C02 [arXiv:1502.05199] [INSPIRE].
  63. [63]
    S.M. Bilenky, S. Pascoli and S.T. Petcov, Majorana neutrinos, neutrino mass spectrum, CP-violation and neutrinoless double beta decay. 1. The Three neutrino mixing case, Phys. Rev. D 64 (2001) 053010 [hep-ph/0102265] [INSPIRE].
  64. [64]
    S. Pascoli, S.T. Petcov and L. Wolfenstein, Searching for the CP-violation associated with Majorana neutrinos, Phys. Lett. B 524 (2002) 319 [hep-ph/0110287] [INSPIRE].
  65. [65]
    S. Pascoli, S.T. Petcov and T. Schwetz, The absolute neutrino mass scale, neutrino mass spectrum, Majorana CP-violation and neutrinoless double-beta decay, Nucl. Phys. B 734 (2006) 24 [hep-ph/0505226] [INSPIRE].
  66. [66]
    V. Barger, S.L. Glashow, P. Langacker and D. Marfatia, No go for detecting CP-violation via neutrinoless double beta decay, Phys. Lett. B 540 (2002) 247 [hep-ph/0205290] [INSPIRE].
  67. [67]
    S. Pascoli and S.T. Petcov, The SNO solar neutrino data, neutrinoless double beta decay and neutrino mass spectrum, Phys. Lett. B 544 (2002) 239 [hep-ph/0205022] [INSPIRE].
  68. [68]
    M. Blennow, E. Fernandez-Martinez, J. Lopez-Pavon and J. Menendez, Neutrinoless double beta decay in seesaw models, JHEP 07 (2010) 096 [arXiv:1005.3240] [INSPIRE].
  69. [69]
    J.D. Vergados, H. Ejiri and F. Šimkovic, Neutrinoless double beta decay and neutrino mass, Int. J. Mod. Phys. E 25 (2016) 1630007 [arXiv:1612.02924] [INSPIRE].
  70. [70]
    M. Doi et al., CP violation in Majorana neutrinos, Phys. Lett. B 102 (1981) 323.Google Scholar
  71. [71]
    L. Wolfenstein, CP properties of Majorana neutrinos and double beta decay, Phys. Lett. B 107 (1981) 7.Google Scholar
  72. [72]
    S.M. Bilenky, N.P. Nedelcheva and S.T. Petcov, Some implications of the CP invariance for mixing of Majorana neutrinos, Nucl. Phys. B 247 (1984) 61 [INSPIRE].
  73. [73]
    B. Kayser, CPT, CP and c phases and their effects in Majorana particle processes, Phys. Rev. D 30 (1984) 1023 [INSPIRE].
  74. [74]
    KamLAND-Zen collaboration, Search for Majorana neutrinos near the inverted mass hierarchy region with KamLAND-Zen, Phys. Rev. Lett. 117 (2016) 082503 [arXiv:1605.02889] [INSPIRE].
  75. [75]
    S. Dell’Oro, S. Marcocci, M. Viel and F. Vissani, Neutrinoless double beta decay: 2015 review, Adv. High Energy Phys. 2016 (2016) 2162659 [arXiv:1601.07512] [INSPIRE].Google Scholar
  76. [76]
    S. Blanchet and P. Di Bari, New aspects of leptogenesis bounds, Nucl. Phys. B 807 (2009) 155 [arXiv:0807.0743] [INSPIRE].
  77. [77]
    S. Antusch, S. Blanchet, M. Blennow and E. Fernandez-Martinez, Non-unitary Leptonic Mixing and Leptogenesis, JHEP 01 (2010) 017 [arXiv:0910.5957] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  78. [78]
    K. Moffat et al., Three-flavored nonresonant leptogenesis at intermediate scales, Phys. Rev. D 98 (2018) 015036 [arXiv:1804.05066] [INSPIRE].
  79. [79]
    Particle Data Group collaboration, Review of particle physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
  80. [80]
    Planck collaboration, Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].
  81. [81]
    A. De Simone and A. Riotto, On the impact of flavour oscillations in leptogenesis, JCAP 02 (2007) 005 [hep-ph/0611357] [INSPIRE].
  82. [82]
    S. Blanchet, P. Di Bari and G.G. Raffelt, Quantum Zeno effect and the impact of flavor in leptogenesis, JCAP 03 (2007) 012 [hep-ph/0611337] [INSPIRE].
  83. [83]
    S. Biondini et al., Status of rates and rate equations for thermal leptogenesis, Int. J. Mod. Phys. A 33 (2018) 1842004 [arXiv:1711.02864].
  84. [84]
    S. Biondini et al., 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].
  85. [85]
    S. Biondini, N. Brambilla and A. Vario, CP asymmetry in heavy Majorana neutrino decays at finite temperature: the hierarchical case, JHEP 09 (2016) 126 [arXiv:1608.01979].ADSCrossRefGoogle Scholar
  86. [86]
    S. Blanchet, P. Di Bari, D.A. Jones and L. Marzola, Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations, JCAP 01 (2013) 041 [arXiv:1112.4528] [INSPIRE].
  87. [87]
    L. Covi, E. Roulet and F. Vissani, CP violating decays in leptogenesis scenarios, Phys. Lett. B 384 (1996) 169 [hep-ph/9605319] [INSPIRE].
  88. [88]
    A. Fowlie and M.H. Bardsley, Superplot: a graphical interface for plotting and analysing MultiNest output, Eur. Phys. J. Plus 131 (2016) 391 [arXiv:1603.00555] [INSPIRE].CrossRefGoogle Scholar
  89. [89]
    A. Pilaftsis and T.E.J. Underwood, Resonant leptogenesis, Nucl. Phys. B 692 (2004) 303 [hep-ph/0309342] [INSPIRE].
  90. [90]
    L. Covi and E. Roulet, Baryogenesis from mixed particle decays, Phys. Lett. B 399 (1997) 113 [hep-ph/9611425] [INSPIRE].
  91. [91]
    W. Buchmüller and M. Plümacher, CP asymmetry in Majorana neutrino decays, Phys. Lett. B 431 (1998) 354 [hep-ph/9710460] [INSPIRE].
  92. [92]
    C. Weinheimer, Direct neutrino mass experiments: Present and future, Nucl. Phys. Proc. Suppl. 118 (2003) 279 [INSPIRE].ADSCrossRefGoogle Scholar
  93. [93]
    C. Kraus et al., Final results from phase II of the Mainz neutrino mass search in tritium beta decay, Eur. Phys. J. C 40 (2005) 447 [hep-ex/0412056] [INSPIRE].
  94. [94]
    V.M. Lobashev et al., Direct search for neutrino mass and anomaly in the tritium beta-spectrum: status of ‘Troitsk neutrino mass’ experiment, Nucl. Phys. Proc. Suppl. 91 (2001) 280 [INSPIRE].ADSCrossRefGoogle Scholar
  95. [95]
    W. Buchmüller and M. Plümacher, Spectator processes and baryogenesis, Phys. Lett. B 511 (2001) 74 [hep-ph/0104189] [INSPIRE].
  96. [96]
    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].
  97. [97]
    G.F. Giudice et al., Towards a complete theory of thermal leptogenesis in the SM and MSSM, Nucl. Phys. B 685 (2004) 89 [hep-ph/0310123] [INSPIRE].
  98. [98]
    A. De Simone and A. Riotto, Quantum Boltzmann equations and leptogenesis, JCAP 08 (2007) 002 [hep-ph/0703175] [INSPIRE].
  99. [99]
    M. Beneke et al., Flavoured leptogenesis in the CTP formalism, Nucl. Phys. B 843 (2011) 177 [arXiv:1007.4783] [INSPIRE].
  100. [100]
    A. Anisimov, W. Buchmüller, M. Drewes and S. Mendizabal, Quantum leptogenesis I, Annals Phys. 326 (2011) 1998 [Erratum ibid. 338 (2011) 376] [arXiv:1012.5821] [INSPIRE].
  101. [101]
    M. Beneke, B. Garbrecht, M. Herranen and P. Schwaller, Finite number density corrections to leptogenesis, Nucl. Phys. B 838 (2010) 1 [arXiv:1002.1326] [INSPIRE].
  102. [102]
    T. Frossard, A. Kartavtsev and D. Mitrouskas, Systematic approach to ΔL = 1 processes in thermal leptogenesis, Phys. Rev. D 87 (2013) 125006 [arXiv:1304.1719] [INSPIRE].
  103. [103]
    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
  104. [104]
    B. Garbrecht and P. Schwaller, Spectator Effects during Leptogenesis in the Strong Washout Regime, JCAP 10 (2014) 012 [arXiv:1404.2915] [INSPIRE].ADSCrossRefGoogle Scholar
  105. [105]
    W. Weckesser, odeintw: complex and matrix differential equations (2014).Google Scholar
  106. [106]
    A.C. Hindmarsh, ODEPACK, a systematized collection of ODE solvers, in Scientific computing, R.S. Stepleman et al. eds., North-Holland, Amsterdam, Netherlands (1983).Google Scholar
  107. [107]
    E. Jone et al., SciPy: open source scientific tools for Python (2001).Google Scholar
  108. [108]
    F. Feroz, M. P. Hobson and M. Bridges, MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics, Mon. Not. Roy. Astron. Soc. 398 (2009) 1601 [arXiv:0809.3437].
  109. [109]
    F. Feroz and M. P. Hobson, Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis, Mon. Not. Roy. Astron. Soc. 384 (2008) 449 [arXiv:0704.3704].ADSCrossRefGoogle Scholar
  110. [110]
    F. Feroz, M.P. Hobson, E. Cameron and A.N. Pettitt, Importance nested sampling and the MultiNest algorithm, arXiv:1306.2144 [INSPIRE].
  111. [111]
    J. Buchner et al., X-ray spectral modelling of the agn obscuring region in the cdfs: Bayesian model selection and catalogue, Astron. Astrophys. 564 (2014) A125.CrossRefGoogle Scholar
  112. [112]
    C.S. Fong, E. Nardi and A. Riotto, Leptogenesis in the Universe, Adv. High Energy Phys. 2012 (2012) 158303 [arXiv:1301.3062] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  113. [113]
    A. Ibarra and G.G. Ross, Neutrino phenomenology: the case of two right-handed neutrinos, Phys. Lett. B 591 (2004) 285 [hep-ph/0312138] [INSPIRE].
  114. [114]
    S. Antusch, P. Di Bari, D.A. Jones and S.F. King, Leptogenesis in the two right-handed neutrino model revisited, Phys. Rev. D 86 (2012) 023516 [arXiv:1107.6002] [INSPIRE].
  115. [115]
    S. Blanchet, Dirac phase leptogenesis, J. Phys. Conf. Ser. 120 (2008) 022007 [arXiv:0710.0570] [INSPIRE].
  116. [116]
    S. Lavignac, I. Masina and C.A. Savoy, Large solar angle and seesaw mechanism: a bottom up perspective, Nucl. Phys. B 633 (2002) 139 [hep-ph/0202086] [INSPIRE].

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Institute for Particle Physics Phenomenology, Department of PhysicsDurham UniversityDurhamU.K.
  2. 2.SISSA/INFNTriesteItaly
  3. 3.Kavli IPMU (WPI)University of TokyoKashiwaJapan
  4. 4.Theoretical Physics DepartmentFermi National Accelerator LaboratoryBataviaU.S.A.

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