Softly broken lepton number Le-Lμ-Lτ with non-maximal solar neutrino mixing

We consider the most general neutrino mass matrix which leads to theta(13) = 0, and present the formulae needed for obtaining the neutrino masses and mixing parameters in that case. We apply this formalism to a model based on the lepton number L = L-e - L-mu - L-tau and on the seesaw mechanism. This model needs only one Higgs doublet and has only two right-handed neutrino singlets. Soft L breaking is accomplished by the Majorana mass terms of the right-handed neutrinos; if the L-conserving and L-breaking mass terms are of the same order of magnitude, then it is possible to obtain a consistent L model with a solar mixing angle significantly smaller than 45. degrees We show that the predictions of this model, m(3) = 0 and theta(13) = 0, are invariant under the renormalization-group running of the neutrino mass matrix.