Fermion masses and mixings in the 3-3-1 model with right-handed neutrinos based on the $$S_3$$ S 3 flavor symmetry

A E Cárcamo Hernández,F Ochoa,R Martinez

doi:10.1140/epjc/s10052-016-4480-3

Abstract

We propose a 3-3-1 model where the $${SU}(3)_{C}\otimes {SU}(3)_{L}\otimes U(1)_{X}$$ symmetry is extended by $$S_{3}\otimes Z_{3}\otimes Z_{3}^{\prime }\otimes Z_{8}\otimes Z_{16}$$ and the scalar spectrum is enlarged by extra $$ {SU}(3)_{L}$$ singlet scalar fields. The model successfully describes the observed SM fermion mass and mixing pattern. In this framework, the light active neutrino masses arise via an inverse seesaw mechanism and the observed charged fermion mass and quark mixing hierarchy is a consequence of the $$Z_{3}\otimes Z_{3}^{\prime }\otimes Z_{8}\otimes Z_{16}$$ symmetry breaking at very high energy. The obtained physical observables for both quark and lepton sectors are compatible with their experimental values. The model predicts the effective Majorana neutrino mass parameter of neutrinoless double beta decay to be $$m_{\beta \beta }=$$ 4 and 48 meV for the normal and the inverted neutrino spectra, respectively. Furthermore, we found a leptonic Dirac CP-violating phase close to $$\frac{\pi }{2}$$ and a Jarlskog invariant close to about $$3\times 10^{-2}$$ for both normal and inverted neutrino mass hierarchy.

Highlights

The aforementioned flavor puzzle, not understood in the context of the SM, motivates extensions of the Standard Model that explain the fermion mass and mixing patterns
A very promising approach is the use of discrete flavor groups, which have been considered in several models to explain the fermion masses and mixing
It is interesting to find an alternative and better explanation for the SM fermion mass and mixing hierarchy than the ones considered in Refs. [69,78]. To this end we propose a multiscalar singlet extension of the SU (3)C × SU (3)L × U (1)X model with right-handed neutrinos, where β = − √1 and an extra S3 ⊗ Z3 ⊗ Z3 ⊗ Z8 ⊗ Z16 discrete group, that extends the symmetry of the model and 15 very heavy SU (3)L singlet scalar fields are added with the aim to generate viable textures for the fermion sector, which successfully describe the observed SM fermion mass and mixing pattern

Summary

Introduction

The aforementioned flavor puzzle, not understood in the context of the SM, motivates extensions of the Standard Model that explain the fermion mass and mixing patterns. [69], 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 Z3 ⊗ Z3 ⊗ Z8 ⊗ Z16 discrete group at very high energy, triggered by SU (3)L scalar singlets acquiring vacuum expectation values much larger than the TeV scale. The model we are building with the aforementioned discrete symmetries, preserves the content of particles of the 3-3-1 model with β = − √1 , but we add 15 additional very heavy SU (3)L singlet scalar fields, with quantum numbers that allow to build Yukawa terms invariant under the local and discrete groups This generates the right textures that successfully account for SM fermion masses and mixings. In the appendices we present several technical details: Appendix A gives a brief description of the S3 group; Appendix B shows a discussion of the stability conditions of the low energy scalar potential

Particle content

Low energy scalar potential

Lepton masses and mixings

Quark masses and mixing

Conclusions