Strong and weak CP violation

We study the renormalization of the QCD vacuum parameter θ which arises from CP violation in the weak interactions. In the Kobayashi-Maskawa extension of the Weinberg-Salam model to include six quarks, the first renormalization of θ occurs in O( α²) and is apparently O(10 ^-16). If we assume that θ = 0 at some unknown "relaxation" scale μ₀, this renormalization makes a contribution to the neutron electric dipole moment which is probably O(10 ^-31 to 10 ^-32)cm and smaller that the purely perturbative contribution. Infinite renormalization of θ may first occur in O( α⁷), and we isolate a topological class of diagrams of this order which do indeed require infinite renormalization of θ. For any reasonable choice of the relaxation scale μ₀, the residual finiteθ renormalization is much smaller than the first finite O( α²) contribution. We finish with some remarks about θ renormalization in other weak interaction models of CP violation.