# A Grand Unified Parity Solution to Strong CP Problem

## TL;DR

This paper presents a supersymmetric SO(10) grand unified model that naturally solves the strong CP problem via parity symmetry, predicts a small but testable neutron electric dipole moment, and unifies quark and lepton masses.

## Contribution

It embeds a parity-based solution to the strong CP problem into a supersymmetric SO(10) GUT with specific discrete symmetries, ensuring vanishing theta at tree and loop levels.

## Key findings

- The model achieves hermitian quark mass matrices due to parity symmetry.
- Three-loop effects induce a theta near current experimental bounds.
- The model is testable through neutron electric dipole moment experiments.

## Abstract

A beyond the standard model theory that respects parity symmetry at short distances is known to provide a solution to the strong CP problem without the need for an axion, while keeping the CKM phase unconstrained. In this paper we present a supersymmetric SO(10) grand unified embedding of this idea with Yukawa couplings generated by {\bf 10}, ${\bf \overline{126}}$ and {\bf 120} Higgs fields. This model is known to provide a unified description of masses and mixings of quarks and leptons. When CP symmetry is imposed on this model, the discrete gauge subgroup C of SO(10) combines with it to generate an effective parity symmetry, leading to hermitian quark mass matrices. Imposing an additional discrete symmetry, $G$, we show that there are no other tree level sources of $\theta$ in the model; $G$ also guarantees that the one- and two-loop contributions to $\theta$ vanish. We then show that the leading three-loop effects and the effect of higher-dimensional operators invariant under $G$ give rise to $\theta$ near the current experimental bound, making the model testable in the current searches for neutron electric dipole moment.