Prediction on neutrino Dirac and Majorana phases and absolute mass scale from the CKM matrix

Abstract

In the type-I seesaw model, the lepton-flavor-mixing matrix (Pontecorvo-Maki-Nakagawa-Sakata matrix) and the quark-flavor-mixing matrix [Cabibbo-Kobayashi-Maskawa (CKM) matrix] may be connected implicitly through a relation between the neutrino Dirac Yukawa coupling ${Y}_{D}$ and the quark Yukawa couplings. In this paper, we study whether ${Y}_{D}$ can satisfy---in the flavor basis where the charged lepton Yukawa and right-handed neutrino Majorana mass matrices are diagonal---the relation ${Y}_{D}\ensuremath{\propto}\mathrm{diag}({y}_{d},{y}_{s},{y}_{b}){V}_{\mathrm{CKM}}^{T}$ or ${Y}_{D}\ensuremath{\propto}\mathrm{diag}({y}_{u},{y}_{c},{y}_{t}){V}_{\mathrm{CKM}}^{*}$ without contradicting the current experimental data on quarks and neutrino oscillations. We search for sets of values of the neutrino Dirac $CP$ phase ${\ensuremath{\delta}}_{CP}$, Majorana phases ${\ensuremath{\alpha}}_{2}$, ${\ensuremath{\alpha}}_{3}$, and the lightest active neutrino mass that satisfy either of the above relations, with the normal or inverted hierarchy of neutrino masses. In performing the search, we consider renormalization group evolutions of the quark masses and CKM matrix and the propagation of their experimental errors along the evolutions. We find that only the former relation ${Y}_{D}\ensuremath{\propto}\mathrm{diag}({y}_{d},{y}_{s},{y}_{b}){V}_{\mathrm{CKM}}^{T}$ with the normal neutrino mass hierarchy holds, based on which we make predictions for ${\ensuremath{\delta}}_{CP}$, ${\ensuremath{\alpha}}_{2}$, ${\ensuremath{\alpha}}_{3}$, and the lightest active neutrino mass.