Fermion texture and sterile neutrinos

Abstract

An explicit form of charged--lepton mass matrix, predicting $m_τ= 1776.80$ MeV from the experimental values of $m_e$ and $m_μ$ (in good agreement with the experimental figure $m_τ= 1777.05^{+0.29}_{-0.26}$ MeV), is applied to three neutrinos $ν_e, ν_μ, ν_τ$ 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 $ν_μ$ and $ν_τ$ is predicted in consistency with the observed deficit of atmospheric $ν_μ$'s. However, the predicted deficit of solar $ν_e$'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 $ν_e$ 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 $γ\simeq 70^\circ$ 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 $ν_e$ and $ν_μ$ oscillations. In Appendix, three conventional Majorana sterile neutrinos are discussed.