The strong CP problem and Nelson-Barr models
The CP symmetry is violated in the Standard Model (SM) by the phase of the CKM matrix in the electroweak sector and, in addition, the presence of the theta term in the strong sector would violate CP as well. The strong CP problem consists on explaining why this last violation is not experimentally observed and the value of theta should be so small. Nelson-Barr models are models with spontaneous CP violation that are capable of explaining simultaneously the value of the CKM phase and the theta term. Models of this kind require the presence of vector-like quarks that transmit the CP violation to the SM.
In this work, we study two models of Nelson-Barr type: the first is the minimal extension of the SM with the usual CP symmetry and the second with the non-conventional CP symmetry, CP4. We also discuss the phenomenological consequences and experimental limits from the electroweak sector and flavor physics for Nelson-Barr models with different contents of vector-like quarks.