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We show how a non-Abelian family symmetry Delta(27) can be used to solve theflavour problem of supersymmetric standard models containing three Higgsfamilies such as the Exceptional Supersymmetric Standard Model (E(6)SSM). Thethree 27 dimensional families of the E(6)SSM, including the three families ofHiggs fields, transform in a triplet representation of the Delta(27) familysymmetry, allowing the family symmetry to commute with a possible high energyE(6) symmetry. The Delta(27) family symmetry here provides a high energyunderstanding of the Z(2)H symmetry of the E(6)SSM, which solves the flavourchanging neutral current problem of the three families of Higgs fields. Themain phenomenological predictions of the model are tri-bi-maximal mixing forleptons, two almost degenerate LSPs and two almost degenerate families ofcolour triplet D-fermions, providing a clear prediction for the LHC. Inaddition the model predicts PGBs with masses below the TeV scale, and possiblymuch lighter, which appears to be a quite general and robust prediction of allmodels based on the D-term vacuum alignment mechanism.

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