Softly broken lepton number L_e - L_\mu - L_\tau with non-maximal solar neutrino mixing

Abstract

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 $\bar{L}=L_e-L_{\mu }-L_{\tau }$ and on the seesaw mechanism. This model needs only one Higgs doublet and has only two right-handed neutrino singlets. Soft $\bar{L}$ breaking is accomplished by the Majorana mass terms of the right-handed neutrinos; if the $\bar{L}$-conserving and $\bar{L}$-breaking mass terms are of the same order of magnitude, then it is possible to obtain a consistent $\bar{L}$ model with a solar mixing angle significantly smaller than $45^{\circ }$. 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.

Comments: 11 pages, plain LaTeX, no figures