S_4 x Z_2 Flavor Symmetry in Supersymmetric Extra U(1) Model

TL;DR

This paper introduces a supersymmetric model inspired by E_6 with an S_4 x Z_2 flavor symmetry, addressing flavor puzzles, proton stability, and the mu-problem through exotic fields and discrete symmetries.

Contribution

It presents a novel E_6 inspired SUSY model incorporating S_4 x Z_2 symmetry, providing predictive frameworks for quark and lepton sectors.

Findings

Proton decay is suppressed due to S_4 triplet embedding of exotic quarks.

Yukawa couplings are significantly reduced by the discrete symmetry.

Two predictive models for quark and lepton sectors are demonstrated.

Abstract

We propose a E_6 inspired supersymmetric model with a non-Abelian discrete flavor symmetry (S_4 group); that is, SU(3)_c x SU(2)_W x U(1)_Y x U(1)_X x S_4 x Z_2. In our scenario, the additional abelian gauge symmetry; U(1)_X, not only solves the mu-problem in the minimal Supersymmetric Standard Model(MSSM), but also requires new exotic fields which play an important role in solving flavor puzzles. If our exotic quarks can be embedded into a S_4 triplet, which corresponds to the number of the generation, one finds that dangerous proton decay can be well-suppressed. Hence, it might be expected that the generation structure for lepton and quark in the SM(Standard Model) can be understood as a new system in order to stabilize the proton in a supersymemtric standard model (SUSY). Moreover, due to the nature of the discrete non-Abelian symmetry itself, Yukawa coupling constants of our model are drastically reduced. In our paper, we show two predictive examples of the models for quark sector and lepton sector, respectively.