The framework for a common origin of $$\delta _{\mathrm{CKM}}$$ δ CKM and $$\delta _{\mathrm{PMNS}}$$ δ PMNS

We analyse a possible connection between CP violations in the quark and lepton sectors, parametrised by the CKM and PMNS phases. If one assumes that CP breaking arises from complex Yukawa couplings, both in the quark and lepton sectors, the above connection is not possible in general, since Yukawa couplings in the two sectors have independent flavour structures. We show that both the CKM and PMNS phases can instead be generated by a vacuum phase in a class of two Higgs doublet models, and in this case a connection may be established. This scenario requires the presence of scalar FCNC at tree level, both in the quark and lepton sectors. The appearance of these FCNC is an obstacle and a blessing. An obstacle since one has to analyse which models are able to conform to the strict experimental limits on FCNC, both in the quark and lepton sectors. A blessing, because this class of models is falsifiable since FCNC arise at a level which can be probed experimentally in the near future, specially in the processes $$\mathrm{h}\rightarrow e^\pm \tau ^\mp $$ and $$t\rightarrow \mathrm{h}c$$ . The connection between CP violations in CKM and PMNS is explicitely illustrated in models with Minimal Flavour Violation.