Flavor Symmetries in the Yukawa Sector of Non-Supersymmetric SO(10): Numerical Fits Using Renormalization Group Running

TL;DR

This paper evaluates SO(10) grand unified models with flavor symmetries by numerically fitting fermion masses and mixings through renormalization group equations, identifying two viable models consistent with current data.

Contribution

It introduces a comprehensive numerical fitting approach for SO(10) models with flavor symmetries, incorporating RG running and seesaw mechanisms, and identifies two models that fit fermion data well.

Findings

Only two out of 14 models fit the data well.

The successful models involve $ ext{Z}_2$ flavor symmetries.

Predictions are consistent with current neutrino mass bounds.

Abstract

We consider a class of $\text{SO}(10)$ models with flavor symmetries in the Yukawa sector and investigate their viability by performing numerical fits to the fermion masses and mixing parameters. The fitting procedure involves a top-down approach in which we solve the renormalization group equations from the scale of grand unification down to the electroweak scale. This allows the intermediate scale right-handed neutrinos and scalar triplet, involved in the type I and II seesaw mechanisms, to be integrated out at their corresponding mass scales, leading to a correct renormalization group running. The result is that, of the 14 models considered, only two are able to fit the known data well. Both these two models correspond to $\mathbb{Z}_2$ symmetries. In addition to being able to fit the fermion masses and mixing parameters, they provide predictions for the sum of light neutrino masses and the effective neutrinoless double beta decay mass parameter, which are both within current observational bounds.