On the determination of leptonic CP violation and neutrino mass ordering in presence of non-standard interactions: present status

  • Ivan Esteban
  • M. C. Gonzalez-Garcia
  • Michele MaltoniEmail author
Open Access
Regular Article - Theoretical Physics


We perform a global analysis of neutrino data in the framework of three massive neutrinos with non-standard neutrino interactions which affect their evolution in the matter background. We focus on the effect of NSI in the present observables sensitive to leptonic CP violation and to the mass ordering. We consider complex neutral current neutrino interactions with quarks whose lepton-flavor structure is independent of the quark type. We quantify the status of the “hints” for CP violation, the mass-ordering and non-maximality of θ23 in these scenarios. We also present a parametrization-invariant formalism for leptonic CP violation in presence of a generalized matter potential induced by NSI.


Neutrino Physics Solar and Atmospheric Neutrinos 


Open Access

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  1. [1]
    B. Pontecorvo, Neutrino Experiments and the Problem of Conservation of Leptonic Charge, Sov. Phys. JETP 26 (1968) 984 [INSPIRE].Google Scholar
  2. [2]
    R. Bojoi, E. Levi, F. Farina, A. Tenconi and F. Profumo, Dual three-phase induction motor drive with digital current control in the stationary reference frame, IEE Proc. Elec. Power Appl. 153 (2006) 129.Google Scholar
  3. [3]
    V.N. Gribov and B. Pontecorvo, Neutrino astronomy and lepton charge, Phys. Lett. 28B (1969) 493 [INSPIRE].CrossRefGoogle Scholar
  4. [4]
    M.C. Gonzalez-Garcia and M. Maltoni, Phenomenology with Massive Neutrinos, Phys. Rept. 460 (2008) 1 [arXiv:0704.1800] [INSPIRE].CrossRefGoogle Scholar
  5. [5]
    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 C P and the mass ordering, JHEP 01 (2019) 106 [arXiv:1811.05487] [INSPIRE].
  6. [6]
    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].
  7. [7]
    F. Capozzi, E. Lisi, A. Marrone and A. Palazzo, Current unknowns in the three neutrino framework, Prog. Part. Nucl. Phys. 102 (2018) 48 [arXiv:1804.09678] [INSPIRE].CrossRefGoogle Scholar
  8. [8]
    T2K collaboration, Measurement of neutrino and antineutrino oscillations by the T2K experiment including a new additional sample of ν e interactions at the far detector, Phys. Rev. D 96 (2017) 092006 [Erratum ibid. D 98 (2018) 019902] [arXiv:1707.01048] [INSPIRE].
  9. [9]
    T2K collaboration, Search for CP-violation in Neutrino and Antineutrino Oscillations by the T2K Experiment with 2.2 × 1021 Protons on Target, Phys. Rev. Lett. 121 (2018) 171802 [arXiv:1807.07891] [INSPIRE].
  10. [10]
    NOvA collaboration, Constraints on Oscillation Parameters from ν e Appearance and ν μ Disappearance in NOvA, Phys. Rev. Lett. 118 (2017) 231801 [arXiv:1703.03328] [INSPIRE].
  11. [11]
    NOvA collaboration, New constraints on oscillation parameters from ν e appearance and ν μ disappearance in the NOvA experiment, Phys. Rev. D 98 (2018) 032012 [arXiv:1806.00096] [INSPIRE].
  12. [12]
    DUNE collaboration, Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE), arXiv:1601.02984 [INSPIRE].
  13. [13]
    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].
  14. [14]
    S. Weinberg, Baryon and Lepton Nonconserving Processes, Phys. Rev. Lett. 43 (1979) 1566 [INSPIRE].CrossRefGoogle Scholar
  15. [15]
    L. Wolfenstein, Neutrino Oscillations in Matter, Phys. Rev. D 17 (1978) 2369 [INSPIRE].
  16. [16]
    J.W.F. Valle, Resonant Oscillations of Massless Neutrinos in Matter, Phys. Lett. B 199 (1987) 432 [INSPIRE].
  17. [17]
    M.M. Guzzo, A. Masiero and S.T. Petcov, On the MSW effect with massless neutrinos and no mixing in the vacuum, Phys. Lett. B 260 (1991) 154 [INSPIRE].
  18. [18]
    Y. Farzan and M. Tortola, Neutrino oscillations and Non-Standard Interactions, Front. in Phys. 6 (2018) 10 [arXiv:1710.09360] [INSPIRE].CrossRefGoogle Scholar
  19. [19]
    S.P. Mikheyev and A. Yu. Smirnov, Resonance Amplification of Oscillations in Matter and Spectroscopy of Solar Neutrinos, Sov. J. Nucl. Phys. 42 (1985) 913 [INSPIRE].Google Scholar
  20. [20]
    M.C. Gonzalez-Garcia, M. Maltoni and J. Salvado, Testing matter effects in propagation of atmospheric and long-baseline neutrinos, JHEP 05 (2011) 075 [arXiv:1103.4365] [INSPIRE].CrossRefzbMATHGoogle Scholar
  21. [21]
    M.C. Gonzalez-Garcia and M. Maltoni, Determination of matter potential from global analysis of neutrino oscillation data, JHEP 09 (2013) 152 [arXiv:1307.3092] [INSPIRE].CrossRefGoogle Scholar
  22. [22]
    I. Esteban, M.C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler and J. Salvado, Updated Constraints on Non-Standard Interactions from Global Analysis of Oscillation Data, JHEP 08 (2018) 180 [arXiv:1805.04530] [INSPIRE].CrossRefGoogle Scholar
  23. [23]
    M.C. Gonzalez-Garcia, Y. Grossman, A. Gusso and Y. Nir, New CP-violation in neutrino oscillations, Phys. Rev. D 64 (2001) 096006 [hep-ph/0105159] [INSPIRE].
  24. [24]
    P. Bakhti and Y. Farzan, Shedding light on LMA-Dark solar neutrino solution by medium baseline reactor experiments: JUNO and RENO-50, JHEP 07 (2014) 064 [arXiv:1403.0744] [INSPIRE].CrossRefGoogle Scholar
  25. [25]
    P. Coloma and T. Schwetz, Generalized mass ordering degeneracy in neutrino oscillation experiments, Phys. Rev. D 94 (2016) 055005 [Erratum ibid. D 95 (2017) 079903] [arXiv:1604.05772] [INSPIRE].
  26. [26]
    ISS Physics Working Group collaboration, Physics at a future Neutrino Factory and super-beam facility, Rept. Prog. Phys. 72 (2009) 106201 [arXiv:0710.4947] [INSPIRE].
  27. [27]
    A.M. Gago, H. Minakata, H. Nunokawa, S. Uchinami and R. Zukanovich Funchal, Resolving CP-violation by Standard and Nonstandard Interactions and Parameter Degeneracy in Neutrino Oscillations, JHEP 01 (2010) 049 [arXiv:0904.3360] [INSPIRE].
  28. [28]
    P. Coloma, A. Donini, J. Lopez-Pavon and H. Minakata, Non-Standard Interactions at a Neutrino Factory: Correlations and CP-violation, JHEP 08 (2011) 036 [arXiv:1105.5936] [INSPIRE].CrossRefGoogle Scholar
  29. [29]
    P. Coloma, Non-Standard Interactions in propagation at the Deep Underground Neutrino Experiment, JHEP 03 (2016) 016 [arXiv:1511.06357] [INSPIRE].CrossRefGoogle Scholar
  30. [30]
    M. Masud, A. Chatterjee and P. Mehta, Probing CP-violation signal at DUNE in presence of non-standard neutrino interactions, J. Phys. G 43 (2016) 095005 [arXiv:1510.08261] [INSPIRE].
  31. [31]
    A. de Gouvêa and K.J. Kelly, Non-standard Neutrino Interactions at DUNE, Nucl. Phys. B 908 (2016) 318 [arXiv:1511.05562] [INSPIRE].
  32. [32]
    J. Liao, D. Marfatia and K. Whisnant, Degeneracies in long-baseline neutrino experiments from nonstandard interactions, Phys. Rev. D 93 (2016) 093016 [arXiv:1601.00927] [INSPIRE].
  33. [33]
    K. Huitu, T.J. Kärkkäinen, J. Maalampi and S. Vihonen, Constraining the nonstandard interaction parameters in long baseline neutrino experiments, Phys. Rev. D 93 (2016) 053016 [arXiv:1601.07730] [INSPIRE].
  34. [34]
    P. Bakhti and Y. Farzan, CP-Violation and Non-Standard Interactions at the MOMENT, JHEP 07 (2016) 109 [arXiv:1602.07099] [INSPIRE].CrossRefGoogle Scholar
  35. [35]
    M. Masud and P. Mehta, Nonstandard interactions spoiling the CP-violation sensitivity at DUNE and other long baseline experiments, Phys. Rev. D 94 (2016) 013014 [arXiv:1603.01380] [INSPIRE].
  36. [36]
    S. C and R. Mohanta, Impact of lepton flavor universality violation on CP-violation sensitivity of long-baseline neutrino oscillation experiments, Eur. Phys. J. C 77 (2017) 32 [arXiv:1701.00327] [INSPIRE].
  37. [37]
    A. Rashed and A. Datta, Determination of mass hierarchy with ν μν τ appearance and the effect of nonstandard interactions, Int. J. Mod. Phys. A 32 (2017) 1750060 [arXiv:1603.09031] [INSPIRE].
  38. [38]
    M. Masud and P. Mehta, Nonstandard interactions and resolving the ordering of neutrino masses at DUNE and other long baseline experiments, Phys. Rev. D 94 (2016) 053007 [arXiv:1606.05662] [INSPIRE].
  39. [39]
    M. Blennow, S. Choubey, T. Ohlsson, D. Pramanik and S.K. Raut, A combined study of source, detector and matter non-standard neutrino interactions at DUNE, JHEP 08 (2016) 090 [arXiv:1606.08851] [INSPIRE].CrossRefGoogle Scholar
  40. [40]
    S.-F. Ge and A. Yu. Smirnov, Non-standard interactions and the CP phase measurements in neutrino oscillations at low energies, JHEP 10 (2016) 138 [arXiv:1607.08513] [INSPIRE].CrossRefGoogle Scholar
  41. [41]
    D.V. Forero and W.-C. Huang, Sizable NSI from the SU(2)L scalar doublet-singlet mixing and the implications in DUNE, JHEP 03 (2017) 018 [arXiv:1608.04719] [INSPIRE].
  42. [42]
    M. Blennow, P. Coloma, E. Fernandez-Martinez, J. Hernandez-Garcia and J. Lopez-Pavon, Non-Unitarity, sterile neutrinos and Non-Standard neutrino Interactions, JHEP 04 (2017) 153 [arXiv:1609.08637] [INSPIRE].CrossRefGoogle Scholar
  43. [43]
    S. Fukasawa, M. Ghosh and O. Yasuda, Sensitivity of the T2HKK experiment to nonstandard interactions, Phys. Rev. D 95 (2017) 055005 [arXiv:1611.06141] [INSPIRE].
  44. [44]
    J. Liao, D. Marfatia and K. Whisnant, Nonstandard neutrino interactions at DUNE, T2HK and T2HKK, JHEP 01 (2017) 071 [arXiv:1612.01443] [INSPIRE].CrossRefGoogle Scholar
  45. [45]
    K.N. Deepthi, S. Goswami and N. Nath, Can nonstandard interactions jeopardize the hierarchy sensitivity of DUNE?, Phys. Rev. D 96 (2017) 075023 [arXiv:1612.00784] [INSPIRE].
  46. [46]
    K.N. Deepthi, S. Goswami and N. Nath, Challenges posed by non-standard neutrino interactions in the determination of δCP at DUNE, Nucl. Phys. B 936 (2018) 91 [arXiv:1711.04840] [INSPIRE].
  47. [47]
    D. Meloni, On the systematic uncertainties in DUNE and their role in New Physics studies, JHEP 08 (2018) 028 [arXiv:1805.01747] [INSPIRE].CrossRefGoogle Scholar
  48. [48]
    L.J. Flores, E.A. Garcés and O.G. Miranda, Exploring NSI degeneracies in long-baseline experiments, Phys. Rev. D 98 (2018) 035030 [arXiv:1806.07951] [INSPIRE].
  49. [49]
    S. Verma and S. Bhardwaj, Non-standard interactions and parameter degeneracies in DUNE and T2HKK, arXiv:1808.04263 [INSPIRE].
  50. [50]
    A. Chatterjee, F. Kamiya, C.A. Moura and J. Yu, Impact of Matter Density Profile Shape on Non-Standard Interactions at DUNE, arXiv:1809.09313 [INSPIRE].
  51. [51]
    M. Masud, S. Roy and P. Mehta, Correlations and degeneracies among the NSI parameters with tunable beams at DUNE, arXiv:1812.10290 [INSPIRE].
  52. [52]
    D.V. Forero and P. Huber, Hints for leptonic CP-violation or New Physics?, Phys. Rev. Lett. 117 (2016) 031801 [arXiv:1601.03736] [INSPIRE].
  53. [53]
    J. Liao, D. Marfatia and K. Whisnant, Nonmaximal neutrino mixing at NOνA from nonstandard interactions, Phys. Lett. B 767 (2017) 350 [arXiv:1609.01786] [INSPIRE].
  54. [54]
    Z. Maki, M. Nakagawa and S. Sakata, Remarks on the unified model of elementary particles, Prog. Theor. Phys. 28 (1962) 870 [INSPIRE].CrossRefzbMATHGoogle Scholar
  55. [55]
    M. Kobayashi and T. Maskawa, CP Violation in the Renormalizable Theory of Weak Interaction, Prog. Theor. Phys. 49 (1973) 652 [INSPIRE].CrossRefGoogle Scholar
  56. [56]
    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, JHEP 01 (2017) 087 [arXiv:1611.01514] [INSPIRE].CrossRefGoogle Scholar
  57. [57]
    A. Dziewonski and D. Anderson, Preliminary reference earth model, Phys. Earth Planet. Interiors 25 (1981) 297.CrossRefGoogle Scholar
  58. [58]
    B.T. Cleveland et al., Measurement of the solar electron neutrino flux with the Homestake chlorine detector, Astrophys. J. 496 (1998) 505 [INSPIRE].
  59. [59]
    F. Kaether, W. Hampel, G. Heusser, J. Kiko and T. Kirsten, Reanalysis of the GALLEX solar neutrino flux and source experiments, Phys. Lett. B 685 (2010) 47 [arXiv:1001.2731] [INSPIRE].
  60. [60]
    SAGE collaboration, Measurement of the solar neutrino capture rate with gallium metal. III: Results for the 2002-2007 data-taking period, Phys. Rev. C 80 (2009) 015807 [arXiv:0901.2200] [INSPIRE].
  61. [61]
    Super-Kamiokande collaboration, Solar neutrino measurements in Super-Kamiokande-I, Phys. Rev. D 73 (2006) 112001 [hep-ex/0508053] [INSPIRE].
  62. [62]
    Super-Kamiokande collaboration, Solar neutrino measurements in Super-Kamiokande-II, Phys. Rev. D 78 (2008) 032002 [arXiv:0803.4312] [INSPIRE].
  63. [63]
    Super-Kamiokande collaboration, Solar neutrino results in Super-Kamiokande-III, Phys. Rev. D 83 (2011) 052010 [arXiv:1010.0118] [INSPIRE].
  64. [64]
    Y. Nakano, 8 B solar neutrino spectrum measurement using Super-Kamiokande IV, Ph.D. Thesis, Tokyo University, (2016).Google Scholar
  65. [65]
    SNO collaboration, Combined Analysis of all Three Phases of Solar Neutrino Data from the Sudbury Neutrino Observatory, Phys. Rev. C 88 (2013) 025501 [arXiv:1109.0763] [INSPIRE].
  66. [66]
    G. Bellini et al., Precision measurement of the 7Be solar neutrino interaction rate in Borexino, Phys. Rev. Lett. 107 (2011) 141302 [arXiv:1104.1816] [INSPIRE].CrossRefGoogle Scholar
  67. [67]
    Borexino collaboration, Measurement of the solar 8B neutrino rate with a liquid scintillator target and 3 MeV energy threshold in the Borexino detector, Phys. Rev. D 82 (2010) 033006 [arXiv:0808.2868] [INSPIRE].
  68. [68]
    BOREXINO collaboration, Neutrinos from the primary proton-proton fusion process in the Sun, Nature 512 (2014) 383 [INSPIRE].
  69. [69]
    KamLAND collaboration, Reactor On-Off Antineutrino Measurement with KamLAND, Phys. Rev. D 88 (2013) 033001 [arXiv:1303.4667] [INSPIRE].
  70. [70]
    A. Cabrera Serra, Double Chooz Improved Multi-Detector Measurements, Talk given at the CERN EP colloquium, CERN, Switzerland, September 20, 2016.Google Scholar
  71. [71]
    Daya Bay collaboration, Measurement of electron antineutrino oscillation based on 1230 days of operation of the Daya Bay experiment, Phys. Rev. D 95 (2017) 072006 [arXiv:1610.04802] [INSPIRE].
  72. [72]
    H. Seo, New Results from RENO, Talk given at the EPS Conference on High Energy Physics, Venice, Italy, July 5-12, 2017.Google Scholar
  73. [73]
    IceCube collaboration, Searches for Sterile Neutrinos with the IceCube Detector, Phys. Rev. Lett. 117 (2016) 071801 [arXiv:1605.01990] [INSPIRE].
  74. [74]
    IceCube collaboration, Determining neutrino oscillation parameters from atmospheric muon neutrino disappearance with three years of IceCube DeepCore data, Phys. Rev. D 91 (2015) 072004 [arXiv:1410.7227] [INSPIRE].
  75. [75]
    Super-Kamiokande collaboration, Atmospheric Results from Super-Kamiokande, AIP Conf. Proc. 1666 (2015) 100001 [arXiv:1412.5234] [INSPIRE].
  76. [76]
    Super-Kamiokande collaboration, Atmospheric neutrino oscillation analysis with external constraints in Super-Kamiokande I-IV, Phys. Rev. D 97 (2018) 072001 [arXiv:1710.09126] [INSPIRE].
  77. [77]
    COHERENT collaboration, Observation of Coherent Elastic Neutrino-Nucleus Scattering, Science 357 (2017) 1123 [arXiv:1708.01294] [INSPIRE].
  78. [78]
    O.G. Miranda, M.A. Tortola and J.W.F. Valle, Are solar neutrino oscillations robust?, JHEP 10 (2006) 008 [hep-ph/0406280] [INSPIRE].
  79. [79]
    J. Bernabeu, G.C. Branco and M. Gronau, CP Restrictions on Quark Mass Matrices, Phys. Lett. 169B (1986) 243 [INSPIRE].CrossRefGoogle Scholar
  80. [80]
    M. Gronau, A. Kfir and R. Loewy, Basis Independent Tests of CP Violation in Fermion Mass Matrices, Phys. Rev. Lett. 56 (1986) 1538 [INSPIRE].CrossRefGoogle Scholar
  81. [81]
    C. Jarlskog, A Basis Independent Formulation of the Connection Between Quark Mass Matrices, CP-violation and Experiment, Z. Phys. C 29 (1985) 491 [INSPIRE].
  82. [82]
    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].CrossRefGoogle Scholar
  83. [83]
    C. Jarlskog, Flavor Projection Operators and Applications to CP Violation With Any Number of Families, Phys. Rev. D 36 (1987) 2128 [INSPIRE].
  84. [84]
    C. Jarlskog, Matrix Representation of Symmetries in Flavor Space, Invariant Functions of Mass Matrices and Applications, Phys. Rev. D 35 (1987) 1685 [INSPIRE].

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Departament de Fisíca Quàntica i Astrofísica and Institut de Ciencies del CosmosUniversitat de BarcelonaBarcelonaSpain
  2. 2.C.N. Yang Institute for Theoretical PhysicsState University of New York at Stony BrookStony BrookU.S.A.
  3. 3.Institució Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain
  4. 4.Instituto de Física Teórica UAM/CSICUniversidad Autónoma de MadridMadridSpain

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