Advertisement

Importance of generalized μτ symmetry and its CP extension on neutrino mixing and leptogenesis

  • Rome SamantaEmail author
  • Roopam Sinha
  • Ambar Ghosal
Open Access
Regular Article - Theoretical Physics
  • 25 Downloads

Abstract

Within the framework of residual symmetry, two 2 type associate μτ inter- change symmetries robustly constrain the Dirac CP phase δ in a model independent way. Both of them predict simultaneous maximality of δ and the atmospheric mixing angle θ23. We show how these well known correlations will be changed if we generalize the μτ in- terchange symmetry to a μτ mixing symmetry. In particular, we show that the stringent condition of simultaneous maximality could be relaxed even with a very small departure from the exact μτ interchange. In addition, the present neutrino data on δ and θ23 can be explained better by the mixing symmetry. After discussing the impact of the μτ mix- ing in some realistic neutrino mass models, we show how the proposed mixing could be realized with two simultaneous CP transformations which also lead to novel and testable correlations between δ and the mixing angles θij . Next we discuss in particular, the ‘three flavour regime’ of leptogenesis within the CP extended framework and show, unlike the ordinary CP extended μτ interchange symmetry, a resonant leptogenesis is possible due the generalization of μτ interchange to the μτ mixing and the resulting baryon asymmetry always requires a nonmaximal θ23 owing to the fact that the baryon to photon ratio ηB vanishes in the exact limit of θ23 = π/4. This is one of the robust predictions of this frame- work. The CP extended μτ mixing is also a novel example of a low energy effective model that provides an important insight to the off-diagonal terms of the flavour coupling matrix which have usually been neglected in literature to compute the final baryon asymmetry, in particular in the models with flavour symmetries.

Keywords

Cosmology of Theories beyond the SM CP violation Neutrino Physics 

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]
    H. Georgi and S.L. Glashow, Unity of all elementary particle forces, Phys. Rev. Lett.32 (1974) 438 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    H. Fritzsch and P. Minkowski, Unified interactions of leptons and hadrons, Annals Phys.93 (1975) 193 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    K.S. Babu and R.N. Mohapatra, Predictive neutrino spectrum in minimal SO(10) grand unification, Phys. Rev. Lett.70 (1993) 2845 [hep-ph/9209215] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    K.S. Babu and S. Khan, Minimal nonsupersymmetric SO(10) model: gauge coupling unification, proton decay and fermion masses, Phys. Rev.D 92 (2015) 075018 [arXiv:1507.06712] [INSPIRE].ADSGoogle Scholar
  5. [5]
    K.S. Babu, B. Bajc and S. Saad, Yukawa sector of minimal SO(10) unification, JHEP02 (2017) 136 [arXiv:1612.04329] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    A. Dueck and W. Rodejohann, Fits to SO(10) grand unified models, JHEP09 (2013) 024 [arXiv:1306.4468] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    A.S. Joshipura and K.M. Patel, Viability of the exact tri-bimaximal mixing at MGUT in SO(10), JHEP09 (2011) 137 [arXiv:1105.5943] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  8. [8]
    P. Di Bari and L. Marzola, SO(10)-inspired solution to the problem of the initial conditions in leptogenesis, Nucl. Phys.B 877 (2013) 719 [arXiv:1308.1107] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  9. [9]
    M.K. Parida, B.P. Nayak, R. Satpathy and R.L. Awasthi, Standard coupling unification in SO(10), hybrid seesaw neutrino mass and leptogenesis, dark matter and proton lifetime predictions, JHEP04 (2017) 075 [arXiv:1608.03956] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    B. Sahoo, M. Chakraborty and M.K. Parida, Neutrino mass, coupling unification, verifiable proton decay, vacuum stability and WIMP dark matter in SU(5), Adv. High Energy Phys.2018 (2018) 4078657 [arXiv:1804.01803] [INSPIRE].CrossRefGoogle Scholar
  11. [11]
    M. Fukugita and T. Yanagida, Baryogenesis without grand unification, Phys. Lett.B 174 (1986) 45 [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    A. Riotto and M. Trodden, Recent progress in baryogenesis, Ann. Rev. Nucl. Part. Sci.49 (1999) 35 [hep-ph/9901362] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    S. Davidson, E. Nardi and Y. Nir, Leptogenesis, Phys. Rept.466 (2008) 105 [arXiv:0802.2962] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    S. Davidson and A. Ibarra, A lower bound on the right-handed neutrino mass from leptogenesis, Phys. Lett.B 535 (2002) 25 [hep-ph/0202239] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    W. Buchmüller, P. Di Bari and M. Plümacher, Leptogenesis for pedestrians, Annals Phys.315 (2005) 305 [hep-ph/0401240] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  16. [16]
    K. Moffat, S. Pascoli, S.T. Petcov and J. Turner, Leptogenesis from low energy CP violation, JHEP03 (2019) 034 [arXiv:1809.08251] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    M.J. Dolan, T.P. Dutka and R.R. Volkas, Dirac-phase thermal leptogenesis in the extended type-I seesaw model, JCAP06 (2018) 012 [arXiv:1802.08373] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    T2K collaboration, Updated T2K measurements of muon neutrino and antineutrino disappearance using 1.5 × 1021protons on target, Phys. Rev.D 96 (2017) 011102 [arXiv:1704.06409] [INSPIRE].ADSGoogle Scholar
  19. [19]
    T2K collaboration, Combined analysis of neutrino and antineutrino oscillations at T2K, Phys. Rev. Lett.118 (2017) 151801 [arXiv:1701.00432] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    NOvA collaboration, Measurement of the neutrino mixing angle θ 23in NOvA, Phys. Rev. Lett.118 (2017) 151802 [arXiv:1701.05891] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    NOvA collaboration, Constraints on oscillation parameters from νe appearance and νμ disappearance in NOvA, Phys. Rev. Lett.118 (2017) 231801 [arXiv:1703.03328] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    A. Himmel, New neutrino oscillation results from NOvA, https://indico.cern.ch/event/696410/, (2018).
  23. [23]
    MINOS collaboration, Measurement of neutrino and antineutrino oscillations using beam and atmospheric data in MINOS, Phys. Rev. Lett.110 (2013) 251801 [arXiv:1304.6335] [INSPIRE].CrossRefGoogle Scholar
  24. [24]
    MINOS collaboration, Electron neutrino and antineutrino appearance in the full MINOS data sample, Phys. Rev. Lett.110 (2013) 171801 [arXiv:1301.4581] [INSPIRE].CrossRefGoogle Scholar
  25. [25]
    RENO collaboration, New results from RENO using 1500 days of data, in 15thInternational Conference on Topics in Astroparticle and Underground Physics (TAUP 2017), Sudbury, ON, Canada, 24–28 July 2017 [arXiv:1710.08204] [INSPIRE].
  26. [26]
    I. Esteban, M.C. Gonzalez-Garcia, A. Hernandez-Cabezudo, M. Maltoni and T. Schwetz, Global analysis of three-flavour neutrino oscillations: synergies and tensions in the determination of θ 23, δ CPand the mass ordering, JHEP01 (2019) 106 [arXiv:1811.05487] [INSPIRE].
  27. [27]
    I. Esteban, M.C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler and T. Schwetz, Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity, JHEP01 (2017) 087 [arXiv:1611.01514] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    P.F. Harrison and W.G. Scott, μ − τ reflection symmetry in lepton mixing and neutrino oscillations, Phys. Lett.B 547 (2002) 219 [hep-ph/0210197] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    W. Grimus and L. Lavoura, A nonstandard CP transformation leading to maximal atmospheric neutrino mixing, Phys. Lett.B 579 (2004) 113 [hep-ph/0305309] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    R.N. Mohapatra and C.C. Nishi, Implications of μ-τ flavored CP symmetry of leptons, JHEP08 (2015) 092 [arXiv:1506.06788] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    E. Ma, Neutrino mixing: A4 variations, Phys. Lett.B 752 (2016) 198 [arXiv:1510.02501] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    R. Samanta, P. Roy and A. Ghosal, Consequences of minimal seesaw with complex μ-τ antisymmetry of neutrinos, JHEP06 (2018) 085 [arXiv:1712.06555] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    G. Altarelli and F. Feruglio, Discrete flavor symmetries and models of neutrino mixing, Rev. Mod. Phys.82 (2010) 2701 [arXiv:1002.0211] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    H. Ishimori, T. Kobayashi, H. Ohki, Y. Shimizu, H. Okada and M. Tanimoto, Non-Abelian discrete symmetries in particle physics, Prog. Theor. Phys. Suppl.183 (2010) 1 [arXiv:1003.3552] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  35. [35]
    S.T. Petcov, Discrete flavour symmetries, neutrino mixing and leptonic CP-violation, Eur. Phys. J.C 78 (2018) 709 [arXiv:1711.10806] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    I. Girardi, S.T. Petcov and A.V. Titov, Predictions for the leptonic Dirac CP-violation phase: a systematic phenomenological analysis, Eur. Phys. J.C 75 (2015) 345 [arXiv:1504.00658] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    I. Girardi, S.T. Petcov, A.J. Stuart and A.V. Titov, Leptonic Dirac CP-violation predictions from residual discrete symmetries, Nucl. Phys.B 902 (2016) 1 [arXiv:1509.02502] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  38. [38]
    C.S. Lam, Symmetry of lepton mixing, Phys. Lett.B 656 (2007) 193 [arXiv:0708.3665] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    C.S. Lam, Determining horizontal symmetry from neutrino mixing, Phys. Rev. Lett.101 (2008) 121602 [arXiv:0804.2622] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    S.-F. Ge, D.A. Dicus and W.W. Repko, Z2 symmetry prediction for the leptonic Dirac CP phase, Phys. Lett.B 702 (2011) 220 [arXiv:1104.0602] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    S.-F. Ge, D.A. Dicus and W.W. Repko, Residual symmetries for neutrino mixing with a large θ13 and nearly maximal δD , Phys. Rev. Lett.108 (2012) 041801 [arXiv:1108.0964] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    S.-F. Ge, H.-J. He and F.-R. Yin, Common origin of soft μ-τ and CP breaking in neutrino seesaw and the origin of matter, JCAP05 (2010) 017 [arXiv:1001.0940] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    H.-J. He and F.-R. Yin, Common origin of μ-τ and CP breaking in neutrino seesaw, baryon asymmetry and hidden flavor symmetry, Phys. Rev.D 84 (2011) 033009 [arXiv:1104.2654] [INSPIRE].ADSGoogle Scholar
  44. [44]
    Particle Data Group collaboration, Review of particle physics, Chin. PhysC 38 (2014) 090001 [INSPIRE].
  45. [45]
    R.N. Mohapatra and S. Nussinov, Bimaximal neutrino mixing and neutrino mass matrix, Phys. Rev.D 60 (1999) 013002 [hep-ph/9809415] [INSPIRE].ADSGoogle Scholar
  46. [46]
    T. Fukuyama and H. Nishiura, Mass matrix of Majorana neutrinos, hep-ph/9702253 [INSPIRE].
  47. [47]
    Daya Bay collaboration, New measurement of antineutrino oscillation with the full detector configuration at Daya Bay, Phys. Rev. Lett.115 (2015) 111802 [arXiv:1505.03456] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    W. Grimus, A.S. Joshipura, S. Kaneko, L. Lavoura and M. Tanimoto, Lepton mixing angle θ 13 = 0 with a horizontal symmetry D4, JHEP07 (2004) 078 [hep-ph/0407112] [INSPIRE].ADSCrossRefGoogle Scholar
  49. [49]
    W. Grimus, A.S. Joshipura, S. Kaneko, L. Lavoura, H. Sawanaka and M. Tanimoto, Non-vanishing U e3and cos 2θ 23from a broken Z2 symmetry, Nucl. Phys.B 713 (2005) 151 [hep-ph/0408123] [INSPIRE].ADSCrossRefGoogle Scholar
  50. [50]
    R.N. Mohapatra and W. Rodejohann, Scaling in the neutrino mass matrix, Phys. Lett.B 644 (2007) 59 [hep-ph/0608111] [INSPIRE].ADSCrossRefGoogle Scholar
  51. [51]
    A.S. Joshipura and W. Rodejohann, Scaling in the neutrino mass matrix, μ-τ symmetry and the see-saw mechanism, Phys. Lett.B 678 (2009) 276 [arXiv:0905.2126] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    R. Samanta, P. Roy and A. Ghosal, Extended scaling and residual flavor symmetry in the neutrino Majorana mass matrix, Eur. Phys. J.C 76 (2016) 662 [arXiv:1604.06731] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    R. Samanta, P. Roy and A. Ghosal, Complex scaling in neutrino mass matrix, Acta Phys. Polon. Supp.9 (2016) 807 [arXiv:1604.01206] [INSPIRE].CrossRefGoogle Scholar
  54. [54]
    R. Samanta, M. Chakraborty, P. Roy and A. Ghosal, Baryon asymmetry via leptogenesis in a neutrino mass model with complex scaling, JCAP03 (2017) 025 [arXiv:1610.10081] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    R. Sinha, R. Samanta and A. Ghosal, Generalized Z2 × Z2 in scaling neutrino Majorana mass matrix and baryogenesis via flavored leptogenesis, JHEP12 (2017) 030 [arXiv:1706.00946] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    A. Ghosal and R. Samanta, Probing texture zeros with scaling ansatz in inverse seesaw, JHEP05 (2015) 077 [arXiv:1501.00916] [INSPIRE].ADSCrossRefGoogle Scholar
  57. [57]
    R. Samanta, M. Chakraborty and A. Ghosal, Evaluation of the Majorana phases of a general Majorana neutrino mass matrix: testability of hierarchical flavour models, Nucl. Phys.B 904 (2016) 86 [arXiv:1502.06508] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  58. [58]
    G.C. Branco, D. Emmanuel-Costa, M.N. Rebelo and P. Roy, Four zero neutrino Yukawa textures in the minimal seesaw framework, Phys. Rev.D 77 (2008) 053011 [arXiv:0712.0774] [INSPIRE].ADSGoogle Scholar
  59. [59]
    J. Liao, D. Marfatia and K. Whisnant, Seesaw mechanism with four texture zeros in the neutrino Yukawa matrix, Phys. Rev.D 87 (2013) 073013 [arXiv:1302.2372] [INSPIRE].ADSGoogle Scholar
  60. [60]
    G. Ecker, W. Grimus and H. Neufeld, A standard form for generalized CP transformations, J. Phys.A 20 (1987) L807 [INSPIRE].ADSGoogle Scholar
  61. [61]
    H. Neufeld, W. Grimus and G. Ecker, Generalized CP invariance, neutral flavor conservation and the structure of the mixing matrix, Int. J. Mod. Phys.A 3 (1988) 603 [INSPIRE].ADSCrossRefGoogle Scholar
  62. [62]
    W. Grimus and M.N. Rebelo, Automorphisms in gauge theories and the definition of CP and P, Phys. Rept.281 (1997) 239 [hep-ph/9506272] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  63. [63]
    R.N. Mohapatra and C.C. Nishi, S4 flavored CP symmetry for neutrinos, Phys. Rev.D 86 (2012) 073007 [arXiv:1208.2875] [INSPIRE].ADSGoogle Scholar
  64. [64]
    S. Gupta, A.S. Joshipura and K.M. Patel, Minimal extension of tri-bimaximal mixing and generalized Z2 × Z2 symmetries, Phys. Rev.D 85 (2012) 031903 [arXiv:1112.6113] [INSPIRE].ADSGoogle Scholar
  65. [65]
    F. Feruglio, C. Hagedorn and R. Ziegler, Lepton mixing parameters from discrete and CP symmetries, JHEP07 (2013) 027 [arXiv:1211.5560] [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    M. Holthausen, M. Lindner and M.A. Schmidt, CP and discrete flavour symmetries, JHEP04 (2013) 122 [arXiv:1211.6953] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  67. [67]
    M.-C. Chen, M. Fallbacher, K.T. Mahanthappa, M. Ratz and A. Trautner, CP violation from finite groups, Nucl. Phys.B 883 (2014) 267 [arXiv:1402.0507] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  68. [68]
    G.-J. Ding, S.F. King, C. Luhn and A.J. Stuart, Spontaneous CP-violation from vacuum alignment in S4 models of leptons, JHEP05 (2013) 084 [arXiv:1303.6180] [INSPIRE].ADSCrossRefGoogle Scholar
  69. [69]
    G.-J. Ding, S.F. King and A.J. Stuart, Generalised CP and A4 family symmetry, JHEP12 (2013) 006 [arXiv:1307.4212] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    F. Feruglio, C. Hagedorn and R. Ziegler, A realistic pattern of lepton mixing and masses from S4 and CP, Eur. Phys. J.C 74 (2014) 2753 [arXiv:1303.7178] [INSPIRE].ADSCrossRefGoogle Scholar
  71. [71]
    P. Chen, C.-Y. Yao and G.-J. Ding, Neutrino mixing from CP symmetry, Phys. Rev.D 92 (2015) 073002 [arXiv:1507.03419] [INSPIRE].ADSGoogle Scholar
  72. [72]
    C.C. Nishi, New and trivial CP symmetry for extended A4 flavor, Phys. Rev.D 93 (2016) 093009 [arXiv:1601.00977] [INSPIRE].ADSGoogle Scholar
  73. [73]
    C.C. Nishi and B.L. Sánchez-Vega, μ-τ reflection symmetry with a texture-zero, JHEP01 (2017) 068 [arXiv:1611.08282] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  74. [74]
    W. Rodejohann and X.-J. Xu, Trimaximal μ-τ reflection symmetry, Phys. Rev.D 96 (2017) 055039 [arXiv:1705.02027] [INSPIRE].ADSGoogle Scholar
  75. [75]
    R. Samanta and A. Ghosal, Probing maximal zero textures with broken cyclic symmetry in inverse seesaw, Nucl. Phys.B 911 (2016) 846 [arXiv:1507.02582] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  76. [76]
    J.T. Penedo, S.T. Petcov and A.V. Titov, Neutrino mixing and leptonic CP-violation from S4 flavour and generalised CP symmetries, JHEP12 (2017) 022 [arXiv:1705.00309] [INSPIRE].ADSCrossRefGoogle Scholar
  77. [77]
    S.F. King, Unified models of neutrinos, flavour and CP-violation, Prog. Part. Nucl. Phys.94 (2017) 217 [arXiv:1701.04413] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    A. Abada, S. Davidson, A. Ibarra, F.-X. Josse-Michaux, M. Losada and A. Riotto, Flavour matters in leptogenesis, JHEP09 (2006) 010 [hep-ph/0605281] [INSPIRE].ADSCrossRefGoogle Scholar
  79. [79]
    S. Blanchet and P. Di Bari, Flavor effects on leptogenesis predictions, JCAP03 (2007) 018 [hep-ph/0607330] [INSPIRE].ADSCrossRefGoogle Scholar
  80. [80]
    P.S.B. Dev, P. Di Bari, B. Garbrecht, S. Lavignac, P. Millington and D. Teresi, Flavor effects in leptogenesis, Int. J. Mod. Phys.A 33 (2018) 1842001 [arXiv:1711.02861] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  81. [81]
    A. Pilaftsis and T.E.J. Underwood, Resonant leptogenesis, Nucl. Phys.B 692 (2004) 303 [hep-ph/0309342] [INSPIRE].
  82. [82]
    E. Nardi, Y. Nir, E. Roulet and J. Racker, The importance of flavor in leptogenesis, JHEP01 (2006) 164 [hep-ph/0601084] [INSPIRE].
  83. [83]
    R. Barbieri, P. Creminelli, A. Strumia and N. Tetradis, Baryogenesis through leptogenesis, Nucl. Phys.B 575 (2000) 61 [hep-ph/9911315] [INSPIRE].ADSCrossRefGoogle Scholar
  84. [84]
    S. Antusch, P. Di Bari, D.A. Jones and S.F. King, A fuller flavour treatment of N2 -dominated leptogenesis, Nucl. Phys.B 856 (2012) 180 [arXiv:1003.5132] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  85. [85]
    P. Di Bari and S.F. King, Successful N2 leptogenesis with flavour coupling effects in realistic unified models, JCAP10 (2015) 008 [arXiv:1507.06431] [INSPIRE].CrossRefGoogle Scholar
  86. [86]
    M. Hirsch, S. Morisi, E. Peinado and J.W.F. Valle, Discrete dark matter, Phys. Rev.D 82 (2010) 116003 [arXiv:1007.0871] [INSPIRE].ADSGoogle Scholar
  87. [87]
    Y. Hamada, T. Kobayashi, A. Ogasahara, Y. Omura, F. Takayama and D. Yasuhara, Revisiting discrete dark matter model: θ 13 ≠ 0 and νR dark matter, JHEP10 (2014) 183 [arXiv:1405.3592] [INSPIRE].ADSCrossRefGoogle Scholar
  88. [88]
    W. Grimus and L. Lavoura, Softly broken lepton number L e − L μ − L τwith non-maximal solar neutrino mixing, J. Phys.G 31 (2005) 683 [hep-ph/0410279] [INSPIRE].ADSCrossRefGoogle Scholar
  89. [89]
    P.H. Frampton and R.N. Mohapatra, Possible gauge theoretic origin for quark-lepton complementarity, JHEP01 (2005) 025 [hep-ph/0407139] [INSPIRE].ADSCrossRefGoogle Scholar
  90. [90]
    K.S. Babu and R.N. Mohapatra, Predictive schemes for bimaximal neutrino mixings, Phys. Lett.B 532 (2002) 77 [hep-ph/0201176] [INSPIRE].ADSCrossRefGoogle Scholar
  91. [91]
    M.S. Berger and M. Dawid, A Froggatt-Nielsen flavor model for neutrino physics, Int. J. Mod. Phys.A 34 (2019) 1950102 [arXiv:1901.10504] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  92. [92]
    P. Chen, G.-J. Ding, F. Gonzalez-Canales and J.W.F. Valle, Generalized μ-τ reflection symmetry and leptonic CP-violation, Phys. Lett.B 753 (2016) 644 [arXiv:1512.01551] [INSPIRE].ADSCrossRefGoogle Scholar
  93. [93]
    R. Sinha, P. Roy and A. Ghosal, CP transformed mixed μ-τ antisymmetry for neutrinos and its consequences, Phys. Rev.D 99 (2019) 033009 [arXiv:1809.06615] [INSPIRE].ADSGoogle Scholar
  94. [94]
    P. Chen, G.-J. Ding and S.F. King, Leptogenesis and residual CP symmetry, JHEP03 (2016) 206 [arXiv:1602.03873] [INSPIRE].ADSCrossRefGoogle Scholar
  95. [95]
    E.W. Kolb and M.S. Turner, The early universe, Front. Phys.69 (1990) 1 [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  96. [96]
    B. Adhikary, M. Chakraborty and A. Ghosal, Flavored leptogenesis with quasidegenerate neutrinos in a broken cyclic symmetric model, Phys. Rev.D 93 (2016) 113001 [arXiv:1407.6173] [INSPIRE].
  97. [97]
    Planck collaboration, Planck 2018 results. VI. Cosmological parameters, arXiv:1807.06209 [INSPIRE].
  98. [98]
    S. Blanchet, P. Di Bari, D.A. Jones and L. Marzola, Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations, JCAP01 (2013) 041 [arXiv:1112.4528] [INSPIRE].ADSCrossRefGoogle Scholar
  99. [99]
    K. Moffat, S. Pascoli, S.T. Petcov, H. Schulz and J. Turner, Three-flavored nonresonant leptogenesis at intermediate scales, Phys. Rev.D 98 (2018) 015036 [arXiv:1804.05066] [INSPIRE].ADSGoogle Scholar
  100. [100]
    G. Engelhard, Y. Grossman, E. Nardi and Y. Nir, The importance of N 2leptogenesis, Phys. Rev. Lett.99 (2007) 081802 [hep-ph/0612187] [INSPIRE].ADSCrossRefGoogle Scholar
  101. [101]
    D.M. Barreiros, R.G. Felipe and F.R. Joaquim, Combining texture zeros with a remnant CP symmetry in the minimal type-I seesaw, JHEP01 (2019) 223 [arXiv:1810.05454] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  102. [102]
    R. Samanta and M. Chakraborty, A study on a minimally broken residual TBM-Klein symmetry with its implications on flavoured leptogenesis and ultra high energy neutrino flux ratios, JCAP02 (2019) 003 [arXiv:1802.04751] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  103. [103]
    P.S. Bhupal Dev, R. Franceschini and R.N. Mohapatra, Bounds on TeV seesaw models from LHC Higgs data, Phys. Rev.D 86 (2012) 093010 [arXiv:1207.2756] [INSPIRE].ADSGoogle Scholar
  104. [104]
    P.S. Bhupal Dev, P. Millington, A. Pilaftsis and D. Teresi, Flavour covariant transport equations: an application to resonant leptogenesis, Nucl. Phys. B 886 (2014) 569 [arXiv:1404.1003] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  105. [105]
    M. Drewes, B. Garbrecht, D. Gueter and J. Klaric, Testing the low scale seesaw and leptogenesis, JHEP08 (2017) 018 [arXiv:1609.09069] [INSPIRE].ADSCrossRefGoogle Scholar
  106. [106]
    B. Garbrecht, Why is there more matter than antimatter? Calculational methods for leptogenesis and electroweak baryogenesis, arXiv:1812.02651 [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Physics and AstronomyUniversity of SouthamptonSouthamptonU.K.
  2. 2.Saha Institute of Nuclear Physics, HBNIKolkataIndia

Personalised recommendations