New "square root" model of lepton family cyclic symmetry

Abstract

Following the newly formulated notion of form invariance of the neutrino mass matrix, a complete model of leptons is constructed. It is based on a specific unitary 3×3 matrix U in family space, such that U² is the simple discrete symmetry ν_e→ν_e, ν_μ↔ν_t. Thus U also generates the cyclic group Z₄. The charged-lepton mass matrix is nearly diagonal while the neutrino mass matrix is of a form suitable for explaining maximal (large) mixing in atmospheric (solar) neutrino oscillations in the context of three nearly degenerate neutrino masses. Observable lepton flavor violation is predicted. Quarks may be treated in the same way as charged leptons.