Advertisement

Journal of High Energy Physics

, 2015:16 | Cite as

On the determination of the leptonic CP phase

  • Jessica ElevantEmail author
  • Thomas Schwetz
Open Access
Regular Article - Theoretical Physics

Abstract

The combination of data from long-baseline and reactor oscillation experiments leads to a preference of the leptonic CP phase δ CP in the range between π and 2π. We study the statistical significance of this hint by performing a Monte Carlo simulation of the relevant data. We find that the distribution of the standard test statistic used to derive confidence intervals for δ CP is highly non-Gaussian and depends on the unknown true values of θ 23 and the neutrino mass ordering. Values of δ CP around π/2 are disfavored at between 2σ and 3σ, depending on the unknown true values of θ 23 and the mass ordering. Typically the standard χ 2 approximation leads to over-coverage of the confidence intervals for δ CP. For the 2-dimensional confidence region in the (δ CP, θ 23) plane the usual χ 2 approximation is better justified. The 2-dimensional region does not include the value δ CP = π/2 up to the 86.3% (89.2%) CL assuming a true normal (inverted) mass ordering. Furthermore, we study the sensitivity to δ CP and θ 23 of an increased exposure of the T2K experiment, roughly a factor 12 larger than the current exposure and including also anti-neutrino data. Also in this case deviations from Gaussianity may be significant, especially if the mass ordering is unknown.

Keywords

Neutrino Physics 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]
    Super-Kamiokande collaboration, Y. Fukuda et al., Evidence for oscillation of atmospheric neutrinos, Phys. Rev. Lett. 81 (1998) 1562 [hep-ex/9807003] [INSPIRE].
  2. [2]
    Super-Kamiokande collaboration, R. Wendell et al., Atmospheric neutrino oscillation analysis with sub-leading effects in Super-Kamiokande I, II and III, Phys. Rev. D 81 (2010) 092004 [arXiv:1002.3471] [INSPIRE].
  3. [3]
    SNO collaboration, Q.R. Ahmad et al., Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory, Phys. Rev. Lett. 89 (2002) 011301 [nucl-ex/0204008] [INSPIRE].
  4. [4]
    KamLAND collaboration, T. Araki et al., Measurement of neutrino oscillation with KamLAND: Evidence of spectral distortion, Phys. Rev. Lett. 94 (2005) 081801 [hep-ex/0406035] [INSPIRE].
  5. [5]
    MINOS collaboration, P. Adamson et al., Measurement of Neutrino Oscillations with the MINOS Detectors in the NuMI Beam, Phys. Rev. Lett. 101 (2008) 131802 [arXiv:0806.2237] [INSPIRE].
  6. [6]
    MINOS collaboration, P. Adamson et al., Electron neutrino and antineutrino appearance in the full MINOS data sample, Phys. Rev. Lett. 110 (2013) 171801 [arXiv:1301.4581] [INSPIRE].
  7. [7]
    MINOS collaboration, P. Adamson et al., Measurement of Neutrino and Antineutrino Oscillations Using Beam and Atmospheric Data in MINOS, Phys. Rev. Lett. 110 (2013) 251801 [arXiv:1304.6335] [INSPIRE].
  8. [8]
    Double CHOOZ collaboration, Y. Abe et al., Reactor electron antineutrino disappearance in the Double CHOOZ experiment, Phys. Rev. D 86 (2012) 052008 [arXiv:1207.6632] [INSPIRE].
  9. [9]
    Double CHOOZ collaboration, Y. Abe et al., Improved measurements of the neutrino mixing angle θ 13 with the Double CHOOZ detector, JHEP 10 (2014) 086 [Erratum ibid. 1502 (2015) 074] [arXiv:1406.7763] [INSPIRE].
  10. [10]
    RENO collaboration, J.K. Ahn et al., Observation of Reactor Electron Antineutrino Disappearance in the RENO Experiment, Phys. Rev. Lett. 108 (2012) 191802 [arXiv:1204.0626] [INSPIRE].
  11. [11]
    Daya Bay collaboration, F.P. An et al., Observation of electron-antineutrino disappearance at Daya Bay, Phys. Rev. Lett. 108 (2012) 171803 [arXiv:1203.1669] [INSPIRE].
  12. [12]
    Daya Bay collaboration, F.P. An et al., Spectral measurement of electron antineutrino oscillation amplitude and frequency at Daya Bay, Phys. Rev. Lett. 112 (2014) 061801 [arXiv:1310.6732] [INSPIRE].
  13. [13]
    T2K collaboration, K. Abe et al., Observation of Electron Neutrino Appearance in a Muon Neutrino Beam, Phys. Rev. Lett. 112 (2014) 061802 [arXiv:1311.4750] [INSPIRE].
  14. [14]
    T2K collaboration, K. Abe et al., Precise Measurement of the Neutrino Mixing Parameter θ 23 from Muon Neutrino Disappearance in an Off-Axis Beam, Phys. Rev. Lett. 112 (2014) 181801 [arXiv:1403.1532] [INSPIRE].
  15. [15]
    T2K collaboration, K. Abe et al., Measurements of neutrino oscillation in appearance and disappearance channels by the T2K experiment with 6.6 × 1020 protons on target, Phys. Rev. D 91 (2015) 072010 [arXiv:1502.01550] [INSPIRE].
  16. [16]
    Particle Data Group, K. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
  17. [17]
    M.C. Gonzalez-Garcia, M. Maltoni and T. Schwetz, Updated fit to three neutrino mixing: status of leptonic CP-violation, JHEP 11 (2014) 052 [arXiv:1409.5439] [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    F. Capozzi, G.L. Fogli, E. Lisi, A. Marrone, D. Montanino and A. Palazzo, Status of three-neutrino oscillation parameters, circa 2013, Phys. Rev. D 89 (2014) 093018 [arXiv:1312.2878] [INSPIRE].ADSGoogle Scholar
  19. [19]
    D.V. Forero, M. Tortola and J.W.F. Valle, Neutrino oscillations refitted, Phys. Rev. D 90 (2014) 093006 [arXiv:1405.7540] [INSPIRE].ADSGoogle Scholar
  20. [20]
    N. Cabibbo, Time Reversal Violation in Neutrino Oscillation, Phys. Lett. B 72 (1978) 333 [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    S.M. Bilenky, J. Hosek and S.T. Petcov, On Oscillations of Neutrinos with Dirac and Majorana Masses, Phys. Lett. B 94 (1980) 495 [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    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
  23. [23]
    H. Nunokawa, S.J. Parke and J.W.F. Valle, CP Violation and Neutrino Oscillations, Prog. Part. Nucl. Phys. 60 (2008) 338 [arXiv:0710.0554] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    G.C. Branco, R.G. Felipe and F.R. Joaquim, Leptonic CP-violation, Rev. Mod. Phys. 84 (2012) 515 [arXiv:1111.5332] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    P. Huber, M. Lindner, T. Schwetz and W. Winter, First hint for CP-violation in neutrino oscillations from upcoming superbeam and reactor experiments, JHEP 11 (2009) 044 [arXiv:0907.1896] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    S. Prakash, S.K. Raut and S.U. Sankar, Getting the Best Out of T2K and NOvA, Phys. Rev. D 86 (2012) 033012 [arXiv:1201.6485] [INSPIRE].ADSGoogle Scholar
  27. [27]
    S.K. Agarwalla, S. Prakash, S.K. Raut and S.U. Sankar, Potential of optimized NOvA for large θ 13 & combined performance with a LArTPC & T2K, JHEP 12 (2012) 075 [arXiv:1208.3644] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    P.A.N. Machado, H. Minakata, H. Nunokawa and R. Zukanovich Funchal, What can we learn about the lepton CP phase in the next 10 years?, JHEP 05 (2014) 109 [arXiv:1307.3248] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    M. Ghosh, P. Ghoshal, S. Goswami, N. Nath and S.K. Raut, Identifying and resolving the degeneracies in neutrino oscillation parameters in current experiments, arXiv:1504.06283 [INSPIRE].
  30. [30]
    S. Wilks, The large-sample distribution of the likelihood ratio for testing composite hypotheses, Annals Math. Statist. 9 (1938) 60.CrossRefzbMATHGoogle Scholar
  31. [31]
    T. Schwetz, What is the probability that theta(13) and CP-violation will be discovered in future neutrino oscillation experiments?, Phys. Lett. B 648 (2007) 54 [hep-ph/0612223] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    M. Blennow, P. Coloma and E. Fernandez-Martinez, Reassessing the sensitivity to leptonic CP-violation, JHEP 03 (2015) 005 [arXiv:1407.3274] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    G.J. Feldman and R.D. Cousins, A Unified approach to the classical statistical analysis of small signals, Phys. Rev. D 57 (1998) 3873 [physics/9711021] [INSPIRE].ADSGoogle Scholar
  34. [34]
    M. Ravonel, Antineutrino oscillations with T2K, talk at EPS HEP 2015, 22-29 July 2015, Vienna, Austria.Google Scholar
  35. [35]
    A. Cervera, A. Donini, M.B. Gavela, J.J. Gomez Cadenas, P. Hernández, O. Mena et al., Golden measurements at a neutrino factory, Nucl. Phys. B 579 (2000) 17 [Erratum ibid. B 593 (2001) 731] [hep-ph/0002108] [INSPIRE].
  36. [36]
    M. Freund, Analytic approximations for three neutrino oscillation parameters and probabilities in matter, Phys. Rev. D 64 (2001) 053003 [hep-ph/0103300] [INSPIRE].ADSGoogle Scholar
  37. [37]
    G.L. Fogli and E. Lisi, Tests of three flavor mixing in long baseline neutrino oscillation experiments, Phys. Rev. D 54 (1996) 3667 [hep-ph/9604415] [INSPIRE].ADSGoogle Scholar
  38. [38]
    H. Minakata and H. Nunokawa, Exploring neutrino mixing with low-energy superbeams, JHEP 10 (2001) 001 [hep-ph/0108085] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    H. Minakata and S.J. Parke, Correlated, precision measurements of θ 23 and δ using only the electron neutrino appearance experiments, Phys. Rev. D 87 (2013) 113005 [arXiv:1303.6178] [INSPIRE].ADSGoogle Scholar
  40. [40]
    P. Coloma, H. Minakata and S.J. Parke, Interplay between appearance and disappearance channels for precision measurements of θ 23 and δ, Phys. Rev. D 90 (2014) 093003 [arXiv:1406.2551] [INSPIRE].ADSGoogle Scholar
  41. [41]
    M. Blennow, P. Coloma, P. Huber and T. Schwetz, Quantifying the sensitivity of oscillation experiments to the neutrino mass ordering, JHEP 03 (2014) 028 [arXiv:1311.1822] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    T2K collaboration, K. Abe et al., Neutrino oscillation physics potential of the T2K experiment, PTEP 2015 (2015) 043C01 [arXiv:1409.7469] [INSPIRE].
  43. [43]
    NOvA collaboration, D.S. Ayres et al., NOvA: Proposal to build a 30 kiloton off-axis detector to study ν μν e oscillations in the NuMI beamline, hep-ex/0503053 [INSPIRE].
  44. [44]
    NOvA collaboration, R.B. Patterson, The NOvA Experiment: Status and Outlook, arXiv:1209.0716 [INSPIRE].

Copyright information

© The Author(s) 2015

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Oskar Klein Centre for Cosmoparticle Physics, Department of PhysicsStockholm UniversityStockholmSweden
  2. 2.Institut für Kernphysik, Karlsruhe Institute of Technology (KIT)KarlsruheGermany

Personalised recommendations