# Predictive Pati-Salam theory of fermion masses and mixing

## TL;DR

This paper introduces a Pati-Salam extension with a flavor symmetry that predicts specific neutrino oscillation patterns, CP violation, and links to potential collider signals, advancing the understanding of fermion masses.

## Contribution

It develops a novel Pati-Salam model with a $ riangle(27)$ flavor symmetry that provides predictive neutrino oscillation patterns and connects low-scale seesaw mechanisms to collider phenomenology.

## Key findings

- Normal hierarchy predicts higher octant atmospheric angle and CP violation.
- Inverted hierarchy favors lower octant and possible CP conservation.
- Lower bound on neutrinoless double beta decay rate.

## Abstract

We propose a Pati-Salam extension of the standard model incorporating a flavor symmetry based on the $\Delta \left( 27\right)$ group. The theory realizes a realistic Froggatt-Nielsen picture of quark mixing and a predictive pattern of neutrino oscillations. We find that, for normal neutrino mass ordering, the atmospheric angle must lie in the higher octant, CP must be violated in oscillations, and there is a lower bound for the $0\nu\beta\beta$ decay rate. For the case of inverted mass ordering, we find that the lower atmospheric octant is preferred, and that CP can be conserved in oscillations. Neutrino masses arise from a low-scale seesaw mechanism, whose messengers can be produced by a $Z^{\prime }$ portal at the LHC.