SO(10) models with flavour symmetries: Classification and examples

Renormalizable SO(10) grand unified theory (GUT) models equipped with flavour symmetries are a popular framework for addressing the flavour puzzle. Usually, the flavour symmetry group has been an ad hoc choice, and no general arguments limiting this choice were known. In this paper, we establish the full list of flavour symmetry groups which may be enforced, without producing any further accidental symmetry, on the Yukawa-coupling matrices of an SO(10) GUT with arbitrary numbers of scalar multiplets in the ${\bf{10}}$, $\bar{{\bf{126}}}$, and ${\bf{120}}$ representations of SO(10). For each of the possible discrete non-Abelian symmetry groups, we present examples of minimal models which do not run into obvious contradiction with the phenomenological fermion masses and mixings.