Softly broken lepton numbers and maximal neutrino mixing

We consider lepton mixing in an extension of the Standard Model with three right-handed neutrino singlets. We require that the three lepton numbers L- e, L-mu, and L-tau be separately conserved in the Yukawa couplings, and we assume that they are softly broken only by the Majorana mass matrix M-R of the neutrino singlets. In this framework, where lepton-number breaking occu rs at a scale much higher than the electroweak scale, deviations from famil y-lepton-number conservation are calculable and finite, and lepton mixing s tems exclusively from M-R. We then show that a discrete symmetry exists suc h that, in the lepton mixing matrix U, maximal atmospheric neutrino mixing together with U-e3 = 0 can be obtained naturally. Alternatively, if one ass umes that there are two different scales in M-R and that the lepton number (L) over barL = L-e L-mu - L-tau is conserved in between them, then maximal solar neutrino mixing follows naturally. If both the discrete symmetry and intermediate (L) over bar conservation are introduced, bimaximal mixing is achieved.