The CKM Phase and $\bar\theta$ in Nelson-Barr Models

Understand

We analyze the Nelson-Barr approach to the Strong CP Problem.

• We derive the necessary conditions in order to simultaneously reproduce the CKM phase and the quark masses.
• Then we quantify the irreducible contributions to the QCD topological angle, namely the corrections arising from loops of the colored fermion mediators that characterize these models.
• Corrections analytic in the couplings first arise at 3-loop order and are safely below current bounds; non-analytic effects are 2-loop order and decouple as the mediators exceed a few TeV.