Residual Symmetries for Neutrino Mixing with a Large ${\ensuremath{\theta}}_{13}$ and Nearly Maximal ${\ensuremath{\delta}}_{D}$

Residual Symmetries for Neutrino Mixing with a Large $θ_{13}$ and Nearly Maximal $δ_{D}$

Shao-Feng Ge, Duane A. Dicus, and Wayne W. Repko

Phys. Rev. Lett. 108, 041801 – Published 24 January 2012

Abstract

The residual $Z_{2}^{s} (k)$ and ${\bar{Z}}_{2}^{s} (k)$ symmetries induce a direct and unique phenomenological relation with $θ_{x} (\equiv θ_{13})$ expressed in terms of the other two mixing angles $θ_{s} (\equiv θ_{12})$ and $θ_{a} (\equiv θ_{23})$ and the Dirac $C P$ phase $δ_{D}$ . $Z_{2}^{s} (k)$ predicts a $θ_{x}$ probability distribution centered around 3°–6° with an uncertainty of 2°–4°, while those from ${\bar{Z}}_{2}^{s} (k)$ are approximately a factor of 2 larger. Either result fits the T2K, MINOS, and Double Chooz measurements. Alternately, a prediction for the Dirac $C P$ phase $δ_{D}$ results in a peak at $\pm 74 °$ ( $\pm 106 °$ ) for $Z_{2}^{s} (k)$ or $\pm 123 °$ ( $\pm 57 °$ ) for ${\bar{Z}}_{2}^{s} (k)$ which is consistent with the latest global fit. We also give a distribution for the leptonic Jarlskog invariant $J_{ν}$ which can provide further tests from measurements at T2K and $NO ν A$ .

Received 23 August 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.041801

Authors & Affiliations

Shao-Feng Ge^1,*, Duane A. Dicus^2,†, and Wayne W. Repko^3,‡

¹Institute of Modern Physics and Center for High Energy Physics, Tsinghua University, Beijing 100084, China
²Physics Department, University of Texas, Austin, Texas 78712, USA
³Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA