Explicit parametrization of more than one vectorlike quark of Nelson-Barr type

Nelson-Barr models solve the strong CP problem based on spontaneous CP violation and generically require vectorlike quarks (VLQs) mixing with standard quarks to transmit the CP violation. We devise an explicit parametrization for the case of two VLQs of either down or up type and quantitatively study several aspects including the hierarchy of the VLQ Yukawas and their irreducible contribution to & theta; over bar . In particular, with the use of the parametrization, we show that a big portion of the parameter space for two up-type VLQs at the TeV scale is still allowed by the constraint on & theta; over bar , although this case had been previously shown to be very restricted based on estimates.