Automatic Nelson-Barr solutions to the strong CP puzzle

Abstract: We discuss a simple model, based on the gauge group ${\rm SU}(3)_C\otimes {\rm SU}(2)_L \otimes \text{U}(1)_Y\otimes \text{U}(1)_R$, where the Nelson-Barr solution to the strong CP problem is implemented. This model automatically provides a high quality solution to the strong CP puzzle. Weak CP violation in the lepton sector arises in the same fashion as in the quark sector. We derive explicit expressions for the flavor changing couplings of the electroweak and Higgs bosons. These expressions are more general than the particular model considered. Constraints from finite naturalness are briefly discussed. We briefly also discuss related models based on the gauge group B-L.