Flavour symmetries in a renormalizable SO(10) model

TL;DR

This paper explores how imposing flavor symmetries in a supersymmetric SO(10) GUT can reduce Yukawa parameters, identifying 14 symmetry cases, with only two fitting fermion data well.

Contribution

It systematically classifies flavor symmetry implementations in a renormalizable SO(10) model and identifies the few cases compatible with experimental fermion data.

Findings

14 inequivalent Yukawa coupling cases identified

13 cases generated by Z_n symmetries, 1 by Z_2 x Z_2

Only two cases fit fermion masses and mixings well

Abstract

In the context of a renormalizable supersymmetric SO(10) Grand Unified Theory, we consider the fermion mass matrices generated by the Yukawa couplings to a $\mathbf{10} \oplus \mathbf{120} \oplus \bar{\mathbf{126}}$ representation of scalars. We perform a complete investigation of the possibilities of imposing flavour symmetries in this scenario; the purpose is to reduce the number of Yukawa coupling constants in order to identify potentially predictive models. We have found that there are only 14 inequivalent cases of Yukawa coupling matrices, out of which 13 cases are generated by $Z_n$ symmetries, with suitable $n$, and one case is generated by a $Z_2 \times Z_2$ symmetry. A numerical analysis of the 14 cases reveals that only two of them---dubbed A and B in the present paper---allow good fits to the experimentally known fermion masses and mixings.