E6 inspired supersymmetric models

Abstract

This work investigates extensions to the Standard Model that are inspired by supersymmetric models with an E6 gauge group. The models are non-minimal supersymmetric theories which keep the Higgs mass stable against the quantum corrections from higher energy physics, but do not contain the mu-problem or little hierarchy problem of the Minimal Supersymmetric Standard Model (MSSM). Also, unlike conventional Grand Unified Theories, the E6 inspired models do not contain any doublet-triplet splitting and the Minimal E6 Supersymmetric Model (ME6SSM) only contains complete E6 multiplets at low energies. A particularly exciting feature of the ME6SSM is the prediction of gauge coupling unification at the Planck scale rather than the conventional GUT scale, hinting at a potential unification of the Standard Model forces with quantum gravity.

If extended with a discrete non-Abelian family symmetry, the E6 inspired models can explain the masses and mixings of the quarks and leptons that are observed in particle experiments. These are not understood in the Standard Model since they are free parameters, creating a flavour problem for the theory. Extending the Standard Model or MSSM with a family symmetry offers an attractive resolution to the flavour problem, and the recent discovery of neutrino oscillations, which indicate a high-level of symmetry in the lepton mixings, has led to a renewed interest in these models. However, explaining why the Higgs mass is small is essential in these models since it sets the scale for the quark and lepton masses. This motivates the synthesis of a family symmetry with the E6 inspired supersymmetric models, which resolves a number of problems facing the Standard Model including the hierarchy problem and the favour problem. A particular success of the resulting models is their ability to suppress proton decay and favour changing neutral currents, from supersymmetry and extended Higgs sectors, using the same family symmetry that is responsible for a tri-bi-maximal mixing of leptons.

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