English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The 3-3-1 model proposed in 2011 based on discrete symmetry $S_4$ responsiblefor the neutrino and quark masses is updated, in which the non-zero$\theta_{13}$ is focused. Neutrino masses and mixings are consistent with themost recent data on neutrino oscillations without perturbation. The new featureis adding a new $SU(3)_L$ anti-sextet lying in doublet under $S_4$ which canresult the non-zero $\theta_{13}$ without perturbation, and consequently, thenumber of Higgs multiplets required is less than those of other models based onnon-Abelian discrete symmetries and the 3-3-1 models. The exact tribimaximalform obtained with the breaking $S_4 \rightarrow Z_3$ in charged lepton sectorand $S_4 \rightarrow \mathcal{K}$ in neutrino sector. If both breakings$S_4\rightarrow \mathcal{K}$ and $\mathcal{K} \rightarrow Z_2$ are taken placein neutrino sector, the realistic neutrino spectrum is obtained withoutperturbation. The upper bound on neutrino mass and the effective mass governingneutrinoless double beta decay at the tree level are presented. The modelpredicts the Dirac CP violation phase $\delta=292.45^\circ$ in the normalspectrum (with $\theta_{23}\neq \frac{\pi}{4}$) and $\delta=303.14^\circ$ inthe inverted spectrum.

Neutrino Mixing with Non-Zero $\theta_{13}$ and CP Violation in the 3-3-1 Model Based on $S_4$ Flavor Symmetry