Journal of High Energy Physics

, 2018:196 | Cite as

Modular A4 invariance and neutrino mixing

  • Tatsuo Kobayashi
  • Naoya Omoto
  • Yusuke Shimizu
  • Kenta TakagiEmail author
  • Morimitsu Tanimoto
  • Takuya H. Tatsuishi
Open Access
Regular Article - Theoretical Physics


We study the phenomenological implications of the modular symmetry Γ(3) ≃ A4 of lepton flavors facing recent experimental data of neutrino oscillations. The mass matrices of neutrinos and charged leptons are essentially given by fixing the expectation value of modulus τ, which is the only source of modular invariance breaking. We introduce no flavons in contrast with the conventional flavor models with A4 symmetry. We classify our neutrino models along with the type I seesaw model, the Weinberg operator model and the Dirac neutrino model. In the normal hierarchy of neutrino masses, the seesaw model is available by taking account of recent experimental data of neutrino oscillations and the cosmological bound of sum of neutrino masses. The predicted sin2θ23 is restricted to be larger than 0.54 and δCP = ±(50°-180°). Since the correlation of sin2θ23 and δCP is sharp, the prediction is testable in the future. It is remarkable that the effective mass mee of the neutrinoless double beta decay is around 22 meV while the sum of neutrino masses is predicted to be 145 meV. On the other hand, for the inverted hierarchy of neutrino masses, only the Dirac neutrino model is consistent with the experimental data.


Discrete Symmetries Neutrino Physics Solar and Atmospheric Neutrinos Compactification and String Models 


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.


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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Tatsuo Kobayashi
    • 1
  • Naoya Omoto
    • 1
  • Yusuke Shimizu
    • 2
  • Kenta Takagi
    • 2
    Email author
  • Morimitsu Tanimoto
    • 3
  • Takuya H. Tatsuishi
    • 1
  1. 1.Depertment of PhysicsHokkaido UniversitySapporoJapan
  2. 2.Graduate School of ScienceHiroshima UniversityHigashi-HiroshimaJapan
  3. 3.Depertment of PhysicsNiigata UniversityNiigataJapan

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