Recently, two SUSY GUTs of flavour have been proposed, based on SU(5) and SO(10) with non-Abelian flavour symmetry. They are reasonably complete, resolving many outstanding problems in GUT model building; as a result, they are rather involved. I am currently working on constructing the minimal and most predictive viable SO(10) model within this framework, with a focus on producing the correct masses and mixings for quarks and leptons. This may be combined with a Peccei-Quinn (PQ) symmetry to resolve the strong CP problem, giving a “flavoured PQ” GUT model. Within this framework, one might explore SUSY and/or axion phenomenology.
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