Unifying CP violations of quark and lepton sectors

Abstract

A preliminary determination of the Dirac phase in the PMNS matrix is $\dell\approx -\frac{\pi}{2}$. A rather accurately determined Jarlskog invariant $J$ in the CKM matrix is close to the maximum. Since the phases in the CKM and PMNS matrices will be accurately determined in the future, it is an interesting problem to relate these two phases. This can be achieved in a families-unified grand unification if the weak CP violation is introduced spontaneously {\it \`a la} Froggatt and Nielsen at a high energy scale, where only one meaningful Dirac CP phase appears.