The Nelson-Barr mechanism to solve the strong CP problem requires vector-like quarks (VLQs) to transmit the spontaneous CP breaking to the SM. Even in the scenario where the spontaneous CP breaking sector is inaccessible, these VLQs can be at the TeV scale in reach at present colliders. In this talk I will show how these VLQs of Nelson-Barr type differ from generic VLQs and find from parameter counting that one less parameter is needed. In particular, for one VLQ of Nelson-Barr type, there is only one CP odd quantity that is responsible for all CP violation in the quark sector. In this case, I will show that the model is largely flavor safe. A global fit on the relevant flavor observables is also performed, and a comparison is made to the case of one generic VLQ. We find that the allowed parameter space for the VLQ Yukawa couplings and the mixing to the SM are confined to a region much smaller than in the generic case, making the NB case falsifiable in principle. I conclude presenting some recent analyses for the case in which two VLQs (either of down or up-type) are considered at the same time.
With support from FCT through project UIDB/00777/2020