# Solving the strong CP problem with non-conventional CP

## TL;DR

This paper introduces a simple model where all CP violation is spontaneous, solving the strong CP problem with minimal couplings and an unconventional CP symmetry, avoiding the need for extra symmetries.

## Contribution

It presents a novel model employing an order-4 CP symmetry with vector-like quarks and a scalar singlet, eliminating the need for additional symmetries in the Nelson-Barr mechanism.

## Key findings

- CKM phase generated unsuppressed
- Strong CP problem solved with two-loop corrections
- No extra symmetry needed for Nelson-Barr implementation

## Abstract

A very simple model is presented where all CP violation in Nature is spontaneous in origin. The CKM phase is generated unsuppressed and the strong CP problem is solved with only moderately small couplings between the SM and the CP violation sector or mediator sector because corrections to $\bar{\theta}$ arise only at two loops. The latter feature follows from an underlying unconventional CP symmetry of order 4 imposed in the sectors beyond the SM composed of only two vector-like quarks of charge $-1/3$ and one complex scalar singlet. No additional symmetry is necessary to implement the Nelson-Barr mechanism.