Explicit lepton texture

Abstract

An explicit form of charged--lepton mass matrix, predicting $ m_\tau = 1776.80 $~MeV from the experimental values of $ m_e $ and $ m_\mu$ (in good agreement with the experimental figure $ m_\tau = 1777.05^{+0.29}_{-0.26}$ MeV), is applied to three neutrinos $\nu_e $, $\nu_\mu $, $\nu_\tau $ in order to correlate tentatively their masses and mixing parameters. While for charged leptons the off--diagonal mass--matrix elements turn out to be small {\it versus} its diagonal elements, it is suggested that for neutrinos the situation is inverse. Under such a conjecture, the neutrino masses, lepton \CKM matrix and neutrino oscillation probabilities are calculated in the corresponding lowest (and the next to lowest) perturbative order. Then, the nearly maximal mixing of $\nu_\mu $ and $\nu_\tau $ is predicted in consistency with the observed deficit of atmospheric $\nu_\mu $'s. However, the predicted deficit of solar $\nu_e $'s is much too small to explain the observed effect, what suggests the existence of (at least) one sort, $\nu_s $, of sterile neutrinos, whose mixing with $\nu_e$ would be responsible for the observed deficit. In the last Section, promising perspectives for applying the same form of mass matrix to quarks are outlined. Two independent predictions of $|V_{ub}|/|V_{cb}| = 0.0753 \pm 0.0032 $ and unitary angle $\gamma \simeq 70^\circ $ are deduced from the experimental values of $|V_{us}|$ and $|V_{cb}|$ (with the use of quark masses $ m_s $, $ m_c $ and $ m_b $).