Solving the Flavour Problem in Supersymmetric Standard Models with Three Higgs Families

TL;DR

This paper introduces a model using the Delta(27) family symmetry to address the flavour problem in supersymmetric models with three Higgs families, predicting specific particle properties and phenomena testable at the LHC.

Contribution

It demonstrates how Delta(27) symmetry can unify family and Higgs sectors, solving flavour issues and providing testable phenomenological predictions.

Findings

Predicts tri-bi-maximal lepton mixing

Forecasts two nearly degenerate LSPs and D-fermion families

Suggests PGBs below the TeV scale

Abstract

We show how a non-Abelian family symmetry Delta(27) can be used to solve the flavour problem of supersymmetric standard models containing three Higgs families such as the Exceptional Supersymmetric Standard Model (E(6)SSM). The three 27 dimensional families of the E(6)SSM, including the three families of Higgs fields, transform in a triplet representation of the Delta(27) family symmetry, allowing the family symmetry to commute with a possible high energy E(6) symmetry. The Delta(27) family symmetry here provides a high energy understanding of the Z(2)H symmetry of the E(6)SSM, which solves the flavour changing neutral current problem of the three families of Higgs fields. The main phenomenological predictions of the model are tri-bi-maximal mixing for leptons, two almost degenerate LSPs and two almost degenerate families of colour triplet D-fermions, providing a clear prediction for the LHC. In addition the model predicts PGBs with masses below the TeV scale, and possibly much lighter, which appears to be a quite general and robust prediction of all models based on the D-term vacuum alignment mechanism.