Prediction on Neutrino Dirac and Majorana Phases and Absolute Mass Scale from the CKM Matrix

Abstract

In Type-I seesaw model, the lepton flavor mixing matrix (PMNS matrix) and the quark flavor mixing matrix (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 $Y_D\propto \mathrm{diag}(y_d,y_s,y_b)V_{CKM}^T$ or $Y_D\propto \mathrm{diag}(y_u,y_c,y_t)V_{CKM}^{\ast }$ without contradicting the current experimental data on quarks and neutrino oscillations. We search for sets of values of the neutrino Dirac CP phase ${\delta }_{CP}$, Majorana phases ${\alpha }_2,{\alpha }_3$, and the lightest active neutrino mass that satisfy either of the above relations, with the normal or inverted hierarchy of neutrino mass. 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 $Y_D\propto \mathrm{diag}(y_d,y_s,y_b)V_{CKM}^T$ with the normal neutrino mass hierarchy holds, based on which we make a prediction for ${\delta }_{CP},{\alpha }_2,{\alpha }_3$ and the lightest active neutrino mass.

22 pages, 7 figures. Effectively the same as the version to appear in Physical Review D

References in corpus (11)

• CMB-S4 Science Book, First Edition
• Current status of the Standard Model CKM fit and constraints on $\Delta F=2$ New Physics
• Quark mass relations to four-loop order
• Lattice QCD at the physical point: light quark masses
• Measurement of neutrino and antineutrino oscillations by the T2K experiment including a new additional sample of ${\nu }_e$ interactions at the far detector
• Anomalous dimensions of gauge fields and gauge coupling beta-functions in the Standard Model at three loops
• Three-loop SM beta-functions for matrix Yukawa couplings
• Two-loop electroweak threshold corrections in the Standard Model
• mr: a C++ library for the matching and running of the Standard Model parameters
• Staggered chiral perturbation theory in the two-flavor case and SU(2) analysis of the MILC data
• Present status of neutrinoless double beta decay searches