Strong CP and Flavor in Multi-Higgs Theories

Abstract: We introduce a class of multi-Higgs doublet extensions of the Standard Model that solves the strong CP problem with profound consequences for the flavor sector. The Yukawa matrices are constrained to have many zero entries by a "Higgs-Flavor" symmetry, $G_{\rm HF}$, that acts on Higgs and quark fields. The violation of both CP and $G_{\rm HF}$ occurs in the Higgs mass matrix so that, for certain choices of $G_{\rm HF}$ charges, the strong CP parameter $\bar{\theta}$ is zero at tree-level. Radiative corrections to $\bar{\theta}$ are computed in this class of theories. They vanish in realistic two-Higgs doublet models with $G_{\rm HF} = \mathbb{Z}3$. We also construct realistic three-Higgs models with $G{\rm HF} = \rm U(1)$, where the one-loop results for $\bar{\theta}$ are model-dependent. Requiring $\bar{\theta}< 10^{-10}$ has important implications for the flavor problem by constraining the Yukawa coupling and Higgs mass matrices. Contributions to $\bar{\theta}$ from higher-dimension operators are computed at 1-loop and can also be sufficiently small, although the hierarchy problem of this class of theories is worse than in the Standard Model.