Neutrino predictions from generalized CP symmetries of charged leptons

  • Peng Chen
  • Salvador Centelles Chuliá
  • Gui-Jun Ding
  • Rahul Srivastava
  • José W. F. Valle
Open Access
Regular Article - Theoretical Physics


We study the implications of generalized CP transformations acting on the mass matrices of charged leptons in a model-independent way. Generalized eμ, e − τ and μ−τ symmetries are considered in detail. In all cases the physical parameters of the lepton mixing matrix, three mixing angles and three CP phases can be expressed in terms of a restricted set of independent “theory parameters” that characterize a given choice of CP transformation. This leads to implications for neutrino oscillations as well as neutrinoless double beta decay experiments.


Neutrino Physics CP violation 


Open Access

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  1. [1]
    T. Kajita, Nobel Lecture: Discovery of atmospheric neutrino oscillations, Rev. Mod. Phys. 88 (2016)030501 [INSPIRE].
  2. [2]
    A.B. McDonald, Nobel Lecture: The Sudbury Neutrino Observatory: Observation of flavor change for solar neutrinos, Rev. Mod. Phys. 88 (2016) 030502 [INSPIRE].
  3. [3]
    P.F. de Salas, D.V. Forero, C.A. Ternes, M. Tortola and J.W.F. Valle, Status of neutrino oscillations 2018: 3σ hint for normal mass ordering and improved CP sensitivity, Phys. Lett. B 782 (2018) 633 [arXiv:1708.01186] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  4. [4]
    J. Schechter and J.W.F. Valle, Neutrino Masses in SU(2) × U(1) Theories, Phys. Rev. D 22 (1980)2227 [INSPIRE].
  5. [5]
    J. Schechter and J.W.F. Valle, Neutrino Oscillation Thought Experiment, Phys. Rev. D 23 (1981)1666 [INSPIRE].
  6. [6]
    T2K collaboration, K. Abe et al., Combined Analysis of Neutrino and Antineutrino Oscillations at T2K, Phys. Rev. Lett. 118 (2017) 151801 [arXiv:1701.00432] [INSPIRE].
  7. [7]
    NOvA collaboration, P. Adamson et al., Constraints on Oscillation Parameters from ν e Appearance and ν μ Disappearance in NOvA, Phys. Rev. Lett. 118 (2017) 231801 [arXiv:1703.03328] [INSPIRE].
  8. [8]
    K.S. Babu, E. Ma and J.W.F. Valle, Underlying A 4 symmetry for the neutrino mass matrix and the quark mixing matrix, Phys. Lett. B 552 (2003) 207 [hep-ph/0206292] [INSPIRE].
  9. [9]
    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
  10. [10]
    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].ADSCrossRefMATHGoogle Scholar
  11. [11]
    S. Morisi and J.W.F. Valle, Neutrino masses and mixing: a flavour symmetry roadmap, Fortsch. Phys. 61 (2013) 466 [arXiv:1206.6678] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  12. [12]
    S. Morisi, D.V. Forero, J.C. Romão and J.W.F. Valle, Neutrino mixing with revamped A 4 flavor symmetry, Phys. Rev. D 88 (2013) 016003 [arXiv:1305.6774] [INSPIRE].
  13. [13]
    S.F. King and C. Luhn, Neutrino Mass and Mixing with Discrete Symmetry, Rept. Prog. Phys. 76 (2013) 056201 [arXiv:1301.1340] [INSPIRE].
  14. [14]
    S.F. King, A. Merle, S. Morisi, Y. Shimizu and M. Tanimoto, Neutrino Mass and Mixing: from Theory to Experiment, New J. Phys. 16 (2014) 045018 [arXiv:1402.4271] [INSPIRE].
  15. [15]
    S.F. King, Models of Neutrino Mass, Mixing and CP-violation, J. Phys. G 42 (2015) 123001 [arXiv:1510.02091] [INSPIRE].
  16. [16]
    F. Feruglio, C. Hagedorn and R. Ziegler, Lepton Mixing Parameters from Discrete and CP Symmetries, JHEP 07 (2013) 027 [arXiv:1211.5560] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    M. Holthausen, M. Lindner and M.A. Schmidt, CP and Discrete Flavour Symmetries, JHEP 04 (2013) 122 [arXiv:1211.6953] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    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].
  19. [19]
    G.-J. Ding, S.F. King, C. Luhn and A.J. Stuart, Spontaneous CP-violation from vacuum alignment in S 4 models of leptons, JHEP 05 (2013) 084 [arXiv:1303.6180] [INSPIRE].
  20. [20]
    P. Chen, C.-C. Li and G.-J. Ding, Lepton Flavor Mixing and CP Symmetry, Phys. Rev. D 91 (2015)033003 [arXiv:1412.8352] [INSPIRE].
  21. [21]
    L.L. Everett, T. Garon and A.J. Stuart, A Bottom-Up Approach to Lepton Flavor and CP Symmetries, JHEP 04 (2015) 069 [arXiv:1501.04336] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    P. Chen, C.-Y. Yao and G.-J. Ding, Neutrino Mixing from CP Symmetry, Phys. Rev. D 92 (2015)073002 [arXiv:1507.03419] [INSPIRE].
  23. [23]
    P. Chen, G.-J. Ding, F. Gonzalez-Canales and J.W.F. Valle, Generalized μτ reflection symmetry and leptonic CP-violation, Phys. Lett. B 753 (2016) 644 [arXiv:1512.01551] [INSPIRE].
  24. [24]
    P. Chen, G.-J. Ding, F. Gonzalez-Canales and J.W.F. Valle, Classifying CP transformations according to their texture zeros: theory and implications, Phys. Rev. D 94 (2016) 033002 [arXiv:1604.03510] [INSPIRE].
  25. [25]
    G.-J. Ding, S.F. King and A.J. Stuart, Generalised CP and A 4 Family Symmetry, JHEP 12 (2013)006 [arXiv:1307.4212] [INSPIRE].
  26. [26]
    C. Hagedorn, A. Meroni and E. Molinaro, Lepton mixing from Δ(3n 2) and Δ(6n 2) and CP, Nucl. Phys. B 891 (2015) 499 [arXiv:1408.7118] [INSPIRE].
  27. [27]
    G.-J. Ding, S.F. King and T. Neder, Generalised CP and Δ(6n 2) family symmetry in semi-direct models of leptons, JHEP 12 (2014) 007 [arXiv:1409.8005] [INSPIRE].
  28. [28]
    C.-C. Li and G.-J. Ding, Lepton Mixing in A 5 Family Symmetry and Generalized CP, JHEP 05 (2015) 100 [arXiv:1503.03711] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    A. Di Iura, C. Hagedorn and D. Meloni, Lepton mixing from the interplay of the alternating group A 5 and CP, JHEP 08 (2015) 037 [arXiv:1503.04140] [INSPIRE].
  30. [30]
    P. Ballett, S. Pascoli and J. Turner, Mixing angle and phase correlations from A 5 with generalized CP and their prospects for discovery, Phys. Rev. D 92 (2015) 093008 [arXiv:1503.07543] [INSPIRE].
  31. [31]
    G.-J. Ding and S.F. King, Generalized CP and Δ(3n 2) Family Symmetry for Semi-Direct Predictions of the PMNS Matrix, Phys. Rev. D 93 (2016) 025013 [arXiv:1510.03188] [INSPIRE].
  32. [32]
    C.-C. Li, C.-Y. Yao and G.-J. Ding, Lepton Mixing Predictions from Infinite Group Series D 9 n,3 n(1) with Generalized CP, JHEP 05 (2016) 007 [arXiv:1601.06393] [INSPIRE].
  33. [33]
    C.-Y. Yao and G.-J. Ding, CP Symmetry and Lepton Mixing from a Scan of Finite Discrete Groups, Phys. Rev. D 94 (2016) 073006 [arXiv:1606.05610] [INSPIRE].
  34. [34]
    I.P. Ivanov, Radiative neutrino masses from order-4 CP symmetry, JHEP 02 (2018) 025 [arXiv:1712.02101] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    C.-C. Li, J.-N. Lu and G.-J. Ding, Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries, JHEP 02 (2018) 038 [arXiv:1706.04576] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    P. Ballett, S.F. King, C. Luhn, S. Pascoli and M.A. Schmidt, Testing atmospheric mixing sum rules at precision neutrino facilities, Phys. Rev. D 89 (2014) 016016 [arXiv:1308.4314] [INSPIRE].
  37. [37]
    S.T. Petcov, Predicting the values of the leptonic CP-violation phases in theories with discrete flavour symmetries, Nucl. Phys. B 892 (2015) 400 [arXiv:1405.6006] [INSPIRE].
  38. [38]
    I. Girardi, S.T. Petcov and A.V. Titov, Determining the Dirac CP-violation Phase in the Neutrino Mixing Matrix from Sum Rules, Nucl. Phys. B 894 (2015) 733 [arXiv:1410.8056] [INSPIRE].
  39. [39]
    P.F. Harrison and W.G. Scott, μτ reflection symmetry in lepton mixing and neutrino oscillations, Phys. Lett. B 547 (2002) 219 [hep-ph/0210197] [INSPIRE].
  40. [40]
    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].
  41. [41]
    P.F. Harrison and W.G. Scott, The simplest neutrino mass matrix, Phys. Lett. B 594 (2004) 324 [hep-ph/0403278] [INSPIRE].
  42. [42]
    W. Rodejohann and J.W.F. Valle, Symmetrical Parametrizations of the Lepton Mixing Matrix, Phys. Rev. D 84 (2011) 073011 [arXiv:1108.3484] [INSPIRE].
  43. [43]
    C. Jarlskog, Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal CP-violation, Phys. Rev. Lett. 55 (1985) 1039 [INSPIRE].ADSCrossRefGoogle Scholar
  44. [44]
    G.C. Branco, L. Lavoura and M.N. Rebelo, Majorana Neutrinos and CP Violation in the Leptonic Sector, Phys. Lett. B 180 (1986) 264 [INSPIRE].
  45. [45]
    E.E. Jenkins and A.V. Manohar, Rephasing Invariants of Quark and Lepton Mixing Matrices, Nucl. Phys. B 792 (2008) 187 [arXiv:0706.4313] [INSPIRE].
  46. [46]
    G.C. Branco, R.G. Felipe and F.R. Joaquim, Leptonic CP-violation, Rev. Mod. Phys. 84 (2012)515 [arXiv:1111.5332] [INSPIRE].
  47. [47]
    DUNE collaboration, R. Acciarri et al., Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE), arXiv:1601.02984 [INSPIRE].
  48. [48]
    DUNE collaboration, R. Acciarri et al., Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE), arXiv:1512.06148 [INSPIRE].
  49. [49]
    KamLAND-Zen collaboration, A. Gando et al., Search for Majorana Neutrinos near the Inverted Mass Hierarchy Region with KamLAND-Zen, Phys. Rev. Lett. 117 (2016) 082503 [Addendum ibid. 117 (2016) 109903] [arXiv:1605.02889] [INSPIRE].
  50. [50]
    EXO collaboration, J.B. Albert et al., Search for Neutrinoless Double-Beta Decay with the Upgraded EXO-200 Detector, Phys. Rev. Lett. 120 (2018) 072701 [arXiv:1707.08707] [INSPIRE].
  51. [51]
    Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.College of Information Science and Engineering, Ocean University of ChinaQingdaoChina
  2. 2.AHEP Group, Institut de Física CorpuscularCSIC/Universitat de ValènciaPaternaSpain
  3. 3.Interdisciplinary Center for Theoretical Study and Department of Modern PhysicsUniversity of Science and Technology of ChinaHefeiChina

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