Exceptional Supersymmetric Standard Models with non-Abelian Discrete Family Symmetry

TL;DR

This paper integrates a non-Abelian discrete $ Delta_{27}$ family symmetry into Exceptional Supersymmetric Standard Models to address flavor issues, predict long-lived exotic states, and propose solutions to the $ Mu'$ problem, with implications for LHC phenomenology.

Contribution

It introduces a novel combination of $ Delta_{27}$ family symmetry with E$_6$SSM models, enhancing flavor structure and addressing proton decay and $ Mu'$ problems.

Findings

Suppressed proton decay due to symmetry constraints.

Prediction of long-lived TeV-scale color triplet states.

Potential signatures at the LHC from exotic particles.

Abstract

We introduce a non-Abelian discrete $\Delta_{27}$ family symmetry into the recently proposed classes of Exceptional Supersymmetric Standard Model ($E_6$SSM) based on a broken $E_6$ Grand Unified Theory (GUT) in order to solve the flavour problem in these models and in particular to account for tri-bimaximal neutrino mixing. We consider both the minimal version of the model (the ME$_6$SSM) with gauge coupling unification at the string scale and the E$_6$SSM broken via the Pati-Salam chain with gauge coupling unification at the conventional GUT scale. In both models there are low energy exotic colour triplets with couplings suppressed by the symmetries of the model, including the family symmetry. This leads to suppressed proton decay and long lived TeV mass colour triplet states with striking signatures at the LHC. We also present a dynamical solution to the $\mu'$ problem (where $\mu'$ is the mass of the additional pair of electroweak doublets in the E$_6$SSM).