Leptonic CP phase determined by an equation involving PMNS matrix elements

Abstract

Several approximate equalities among the matrix elements of the Cabibbo–Kobayashi–Maskawa (CKM) and Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrices imply that hidden symmetries may exist and be common for both quark and neutrino sectors. The charge parity (CP) phase of the CKM matrix () is involved in these equalities and can be investigated when these equalities turn into several equations. As we substitute those experimentally measured values of the three mixing angles into the equations for quarks, it is noted that one of the equations which holds exactly has a solution . That value accords with determined from available data. Generalizing the scenario to the lepton sector, the same equality determines the leptonic CP phase to be . Thus we predict the value of from the equation. So far there is no direct measurement on , but a recent analysis based on the neutrino oscillation data prefers a phase close to 270°.