A 3-3-1 model with right-handed neutrinos based on the $$\varDelta \left( 27\right) $$ Δ 27 family symmetry

A. E. Cárcamo Hernández,V. V. Vien,H. N. Long

doi:10.1140/epjc/s10052-016-4074-0

Abstract

We present the first multiscalar singlet extension of the 3-3-1 model with right-handed neutrinos, based on the $\Delta \left( 27\right) $ family symmetry, supplemented by the $Z_{4}\otimes Z_{8}\otimes Z_{14}$ flavor group, consistent with current low energy fermion flavor data. In the model under consideration, the light active neutrino masses are generated from a double seesaw mechanism and the observed pattern of charged fermion masses and quark mixing angles is caused by the breaking of the $\Delta \left( 27\right) \otimes Z_{4}\otimes Z_{8}\otimes Z_{14}$ discrete group at very high energy. Our model has only 14 effective free parameters, which are fitted to reproduce the experimental values of the 18 physical observables in the quark and lepton sectors. The obtained physical observables for the quark sector agree with their experimental values, whereas those ones for the lepton sector also do, only for the inverted neutrino mass hierarchy. The normal neutrino mass hierarchy scenario of the model is disfavored by the neutrino oscillation experimental data. We find an effective Majorana neutrino mass parameter of neutrinoless double beta decay of $m_{\beta \beta }=$ 22 meV, a leptonic Dirac CP violating phase of $34^{\circ }$ and a Jarlskog invariant of about $10^{-2}$ for the inverted neutrino mass spectrum.

Highlights

The unexplained Standard Model (SM) fermion mass and mixing pattern motivates us to consider models with extended symmetry and larger scalar and/or fermion content, addressed to explain the fermion mass and mixing pattern
We constructed the first multiscalar singlet extension of the original 3-3-1 model with right-handed neutrinos, based on the Δ (27) family symmetry supplemented by the Z4 ⊗ Z8 ⊗ Z14 discrete group
The Δ (27), Z4, and Z8 symmetries allow one to reduce the number of parameters in the Yukawa terms, increasing the predictivity power of the model, whereas the Z14 symmetry causes the charged fermion mass and quark mixing pattern

Summary

Introduction

The unexplained SM fermion mass and mixing pattern motivates us to consider models with extended symmetry and larger scalar and/or fermion content, addressed to explain the fermion mass and mixing pattern. [130], in our current 3-3-1 model, the charged fermion mass and quark mixing pattern can successfully be accounted for, by having all Yukawa couplings of order unity, and arises from the breaking of the Δ (27) ⊗ Z4 ⊗ Z8 ⊗ Z14 discrete group at very high energy, triggered by SU (3)L scalar singlets acquiring vacuum expectation values much larger than the TeV scale. Our current 3-3-1 model with Δ(27) family symmetry, does not include the U(1)L new lepton global symmetry presented in our previous Δ(27) flavor 3-31 model, but it has instead a Z4⊗ Z8⊗ Z14 discrete symmetry, whose breaking at very high energy gives rise to the observed pattern of charged fermion masses and quark mixing angles. Appendix B includes a discussion of the scalar potential for two Δ(27) scalar triplets and its minimization equations

The model

Lepton masses and mixings

Quark masses and mixings

Conclusions

A Appendices