Solving the strong CP problem with horizontal gauge symmetry

TL;DR

This paper proposes a novel solution to the strong CP problem using horizontal gauge symmetry and CP invariance, explaining quark-Higgs Yukawa hierarchy and satisfying experimental constraints.

Contribution

It introduces a Nelson-Barr type model with sequential breaking of horizontal $SU(3)_f$ symmetry, naturally small scalar coupling, and compatibility with thermal leptogenesis.

Findings

Explains the quark-Higgs Yukawa hierarchy via sequential symmetry breaking.

Achieves $ar{ heta} o 10^{-10}$ with high scalar VEVs and small quartic coupling.

More compatible with thermal leptogenesis than previous models.

Abstract

We present a solution to the strong CP problem, which relies on the horizontal gauge symmetry and CP invariance in a full theory. Similar to other Nelson-Barr type solutions, CP violation in both the strong and weak sectors in the Standard model (SM) is attributed to the condensation of complex scalars $\Phi$ in the model. The model is differentiated by others in that it explains the hierarchy in quark-Higgs Yukawa coupling in the SM based on a series of sequential breaking of the horizontal $SU(3)_{f}$ gauge symmetry. The experimental constraint $\overline{\theta}\lesssim10^{-10}$ requires $<\!\!\Phi\!\!>\,\lesssim\,10^{13}-10^{14}{\rm GeV}$ (vacuum expectation value of complex scalars) and $\lambda\,\lesssim\,10^{-6}$ (scalar quartic coupling). We show that this small coupling is natural in the sense of 'tHooft naturalness. Compared to other models of Nelson-Barr type with CP breaking scale $\Lambda_{CP}\lesssim10^{8}{\rm GeV}$, our model is more advantageous in terms of consistency with the thermal leptogenesis.