Journal of High Energy Physics

, 2018:63 | Cite as

Signatures of the genuine and matter-induced components of the CP violation asymmetry in neutrino oscillations

  • José Bernabéu
  • Alejandro Segarra
Open Access
Regular Article - Theoretical Physics


CP asymmetries for neutrino oscillations in matter can be disentangled into the matter-induced CPT-odd (T-invariant) component and the genuine T-odd (CPT-invariant) component. For their understanding in terms of the relevant ingredients, we develop a new perturbative expansion in both Δm 21 2 , |a| ≪ |Δm 31 2 | without any assumptions between Δm 21 2 and a, and study the subtleties of the vacuum limit in the two terms of the CP asymmetry, moving from the CPT-invariant vacuum limit a → 0 to the T-invariant limit Δm 21 2  → 0. In the experimental region of terrestrial accelerator neutrinos, we calculate their approximate expressions from which we prove that, at medium baselines, the CPT-odd component is small and nearly δ-independent, so it can be subtracted from the experimental CP asymmetry as a theoretical background, provided the hierarchy is known. At long baselines, on the other hand, we find that (i) a Hierarchy-odd term in the CPT-odd component dominates the CP asymmetry for energies above the first oscillation node, and (ii) the CPT-odd term vanishes, independent of the CP phase δ, at E = 0.92 GeV (L/1300 km) near the second oscillation maximum, where the T-odd term is almost maximal and proportional to sin δ. A measurement of the CP asymmetry in these energy regions would thus provide separate information on (i) the neutrino mass ordering, and (ii) direct evidence of genuine CP violation in the lepton sector.


CP violation Discrete Symmetries Neutrino Physics 


Open Access

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  1. [1]
    M. Fukugita and T. Yanagida, Baryogenesis Without Grand Unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].
  2. [2]
    Hyper-Kamiokande proto-collaboration, K. Abe et al., Hyper-Kamiokande design report, KEK-Preprint-2016-21, ICRR-Report-701-2016-1 (2016).Google Scholar
  3. [3]
    DUNE collaboration, R. Acciarri et al., Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE), arXiv:1512.06148 [INSPIRE].
  4. [4]
    L. Wolfenstein, Neutrino Oscillations in Matter, Phys. Rev. D 17 (1978) 2369 [INSPIRE].
  5. [5]
    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
  6. [6]
    J. Bernabéu and A. Segarra, Disentangling genuine from matter-induced CP-violation in neutrino oscillations, arXiv:1806.07694 [INSPIRE].
  7. [7]
    V.D. Barger, K. Whisnant, S. Pakvasa and R.J.N. Phillips, Matter Effects on Three-Neutrino Oscillations, Phys. Rev. D 22 (1980) 2718 [INSPIRE].
  8. [8]
    T.-K. Kuo and J.T. Pantaleone, Neutrino Oscillations in Matter, Rev. Mod. Phys. 61 (1989) 937 [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    H.W. Zaglauer and K.H. Schwarzer, The mixing angles in matter for three generations of neutrinos and the MSW mechanism, Z. Phys. C 40 (1988) 273.Google Scholar
  10. [10]
    P.I. Krastev, Searching for the MSW effect with neutrino beams from next generation accelerators, Nuovo Cim. A 103 (1990) 361 [INSPIRE].
  11. [11]
    R.H. Bernstein and S.J. Parke, Terrestrial long baseline neutrino oscillation experiments, Phys. Rev. D 44 (1991) 2069 [INSPIRE].
  12. [12]
    S.T. Petcov and Y.-L. Zhou, On Neutrino Mixing in Matter and CP and T Violation Effects in Neutrino Oscillations, Phys. Lett. B 785 (2018) 95 [arXiv:1806.09112] [INSPIRE].
  13. [13]
    T. Ohlsson and S. Zhou, Extrinsic and Intrinsic CPT Asymmetries in Neutrino Oscillations, Nucl. Phys. B 893 (2015) 482 [arXiv:1408.4722] [INSPIRE].
  14. [14]
    Z.-z. Xing, New formulation of matter effects on neutrino mixing and CP-violation, Phys. Lett. B 487 (2000) 327 [hep-ph/0002246] [INSPIRE].
  15. [15]
    A. Cervera et al., Golden measurements at a neutrino factory, Nucl. Phys. B 579 (2000) 17 [Erratum ibid. B 593 (2001) 731] [hep-ph/0002108] [INSPIRE].
  16. [16]
    P.B. Denton, H. Minakata and S.J. Parke, Compact Perturbative Expressions For Neutrino Oscillations in Matter, JHEP 06 (2016) 051 [arXiv:1604.08167] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. [17]
    A. Ioannisian and S. Pokorski, Three Neutrino Oscillations in Matter, Phys. Lett. B 782 (2018) 641 [arXiv:1801.10488] [INSPIRE].
  18. [18]
    Z.-z. Xing and J.-y. Zhu, Analytical approximations for matter effects on CP-violation in the accelerator-based neutrino oscillations with E ≲ 1 GeV, JHEP 07 (2016) 011 [arXiv:1603.02002] [INSPIRE].
  19. [19]
    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].
  20. [20]
    M.C. Banuls, G. Barenboim and J. Bernabeu, Medium effects for terrestrial and atmospheric neutrino oscillations, Phys. Lett. B 513 (2001) 391 [hep-ph/0102184] [INSPIRE].
  21. [21]
    I. Mocioiu and R. Shrock, Matter effects on neutrino oscillations in long baseline experiments, Phys. Rev. D 62 (2000) 053017 [hep-ph/0002149] [INSPIRE].
  22. [22]
    J. Bernabeu, G.C. Branco and M. Gronau, CP Restrictions on Quark Mass Matrices, Phys. Lett. 169B (1986) 243 [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    P.F. Harrison and W.G. Scott, CP and T violation in neutrino oscillations and invariance of Jarlskog’s determinant to matter effects, Phys. Lett. B 476 (2000) 349 [hep-ph/9912435] [INSPIRE].
  24. [24]
    C. Jarlskog, A basis independent formulation of the connection between quark mass matrices, CP violation and experiment, Z. Phys. C 29 (1985) 491.Google Scholar
  25. [25]
    S.-F. Ge, K. Hagiwara and C. Rott, A Novel Approach to Study Atmospheric Neutrino Oscillation, JHEP 06 (2014) 150 [arXiv:1309.3176] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    K. Kimura, A. Takamura and H. Yokomakura, Exact formula of probability and CP-violation for neutrino oscillations in matter, Phys. Lett. B 537 (2002) 86 [hep-ph/0203099] [INSPIRE].
  27. [27]
    P.F. Harrison, W.G. Scott and T.J. Weiler,ss Exact matter covariant formulation of neutrino oscillation probabilities, Phys. Lett. B 565 (2003) 159 [hep-ph/0305175] [INSPIRE].
  28. [28]
    V. De Romeri, E. Fernandez-Martinez and M. Sorel, Neutrino oscillations at DUNE with improved energy reconstruction, JHEP 09 (2016) 030 [arXiv:1607.00293] [INSPIRE].CrossRefGoogle Scholar

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© The Author(s) 2018

Authors and Affiliations

  1. 1.Departament de Física Teòrica and IFICUniversitat de València - CSICValènciaSpain

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