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
θˉ 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.Comment: Comments added, comply with published versio