Mass and CKM Matrices of Quarks and Leptons, the Leptonic CP-phase in neutrino oscillations

TL;DR

This paper develops a unified approach to constructing quark and lepton mass matrices, incorporating the leptonic CP-phase, and analyzes its implications for neutrino oscillation probabilities and CP-violation effects.

Contribution

It introduces a hierarchical mass matrix model for quarks and leptons that naturally includes the leptonic CP-phase, based on a rotation of generation numbers and the see-saw mechanism.

Findings

Hierarchical mass matrices explain quark and lepton mixing angles.

The leptonic CP-phase significantly affects neutrino oscillation probabilities.

Time reversal effects are small, but CP-phase impacts transition probabilities substantially.

Abstract

A general approach for construction of quark and lepton mass matrices is formulated. The hierarchy of quarks and charged leptons ("electrons") is large, it leads using the experimental values of mixing angles to the hierarchical mass matrix slightly deviating from one's suggested earlier by Stech and including naturally the CP-phase. The same method based on the rotation of generation numbers in the diagonal mass matrix is used in the electron-neutrino sector of theory, where neutrino mass matrix is determined by the Majorano see-saw approach. The hierarchy of neutrino masses, much smaller than for quarks, was used including all existing (even preliminary) experimental data on neutrinos mixing. The leptonic mass matrix found in this way includes not known value of the leptonic CP-phase. It leads to a large $\nu_\mu \nu_\tau$ oscillations and suppresses the $\nu_e\nu_\tau$ and also $\nu_e \nu_\mu$ oscillations. The explicit expressions for the probabilities of neutrino oscillation were obtained in order to specify the role of leptonic CP-phase. The value of time reversal effect (proportional to $\sin\delta'$) was found to be small $\sim 1%$. However, a dependence of the values of $\nu_e \nu_\mu, \nu_e \nu_\tau$ transition probabilities, averaged over oscillations, on the leptonic CP-phase has found to be not small - of order of tens percent.