Neutrino mass matrix with the seesaw mechanism and two-loop mass splitting- art. no. 093012

We propose a model which uses the seesaw mechanism and the lepton number (L ) over bar =L-e-L-mu-L-tau to achieve the neutrino mass spectrum m(1) = m(2 ) and m(3) = 0, together with a lepton mixing matrix U with U-e3 = 0. In th is way, we accommodate atmospheric neutrino oscillations. A small mass spli tting m(1)>m(2) is generated by breaking (L) over bar spontaneously and usi ng Babu's two-loop mechanism. This allows us to incorporate either the "jus t so" or the LOW solution of the solar-neutrino problem, with maximal mixin g, into the model. The resulting mass matrix has three parameters only, sin ce (L) over bar breaking leads exclusively to a non-zero ee matrix element.