Fermion texture and sterile neutrinos

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. It is suggested that for neutrinos the diagonal elements of the mass matrix are small versus its off-diagonal elements. Under such a conjecture, the neutrino masses, lepton \CKM matrix and neutrino oscillation probabilities are calculated in the corresponding 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, $\enu$, of sterile neutrinos, whose mixing with $\nu_e$ would be responsible for the observed deficit. Perspectives for applying the same form of mass matrix to quarks are also 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). In the last three Sections, the option of two sorts, $\enu$ and $\mnu$, of sterile neutrinos is considered. They may dominate neutrino mixing, and even cause that two extra neutrino mass states (arising then) are agents of some tiny neutrino instability and related damping of $\nu_e$ and $\nu_\mu$ oscillations. In Appendix, three conventional Majorana sterile neutrinos are discussed.