Solving the strong CP problem with horizontal gauge symmetry

Understand

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).