Abstract
We discuss the mass matrices with texture zeros for the quarks and leptons. The flavor mixing angles for the quarks are functions of the quark masses and can be calculated. The results agree with the experimental data. The texture zero mass matrices for the leptons and the see-saw mechanism are used to derive relations between the matrix elements of the lepton mixing matrix and the ratios of the neutrino masses. Using the measured neutrino mass differences, the neutrino masses can be calculated. The neutrinoless double beta decay is discussed. The effective Majorana neutrino mass, describing the neutrinoless double beta decay, can be calculated—it is about 4.6 meV. The present experimental limit is at least twenty times larger.
Highlights
We discuss the mass matrices with texture zeros for the quarks and leptons
There are several ways to describe the CKM-matrix in terms of three angles and one phase parameter
If we take the central values of the three neutrino masses, we find θ13 = 8.3◦, in agreement with relation (12)
Summary
We discuss the mass matrices with texture zeros for the quarks and leptons. The flavor mixing angles for the quarks are functions of the quark masses and can be calculated. Using these masses for the quarks, we find for the mixing angles: θd ' (12.9 ± 0.4)◦ , θu ' (3.2 ± 0.7)◦ . If the neutrinos have a small mass and if they are superpositions of mass eigenstates, there would be a flavor mixing of the leptons. By comparing the interaction rates for the neutral and for the charged current interactions, one has observed the oscillations of the solar neutrinos.
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