Journal of High Energy Physics

, 2019:15 | Cite as

Non-unitary evolution of neutrinos in matter and the leptonic unitarity test

  • Chee Sheng FongEmail author
  • Hisakazu Minakata
  • Hiroshi Nunokawa
Open Access
Regular Article - Theoretical Physics


We present a comprehensive study of the three-active plus N sterile neutrino model as a framework for constraining leptonic unitarity violation induced at energy scales much lower than the electroweak scale. We formulate a perturbation theory with expansion in small unitarity violating matrix element W while keeping (non-W suppressed) matter effect to all orders. We show that under the same condition of sterile state masses 0.1 eV2m J 2 ≲ (1–10) GeV2 as in vacuum, assuming typical accelerator based long-baseline neutrino oscillation experiment, one can derive a very simple form of the oscillation probability which consists only of zeroth-order terms with the unique exception of probability leaking term \( \mathcal{C} \)αβ of \( \mathcal{O} \)(W4). We argue, based on our explicit computation to fourth-order in W, that all the other terms are negligibly small after taking into account the suppression due to the mass condition for sterile states, rendering the oscillation probability sterile-sector model independent. Then, we identify a limited energy region in which this suppression is evaded and the effects of order W2 corrections may be observable. Its detection would provide another way, in addition to detecting \( \mathcal{C} \)αβ, to distinguish between low-scale and high-scale unitarity violation. We also solve analytically the zeroth-order system in matter with uniform density to provide a basis for numerical evaluation of non-unitary neutrino evolution.


Beyond Standard Model Neutrino Physics 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade de São PauloSão PauloBrazil
  2. 2.Instituto Física Teórica, UAM/CSICMadridSpain
  3. 3.Research Center for Cosmic Neutrinos, Institute for Cosmic Ray ResearchUniversity of TokyoKashiwaJapan
  4. 4.Departamento de FísicaPontifícia Universidade Católica do Rio de JaneiroRio de JaneiroBrazil
  5. 5.Centro de Ciências Naturais e HumanasUniversidade Federal do ABCSanto AndréBrazil

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