A neutrino mass matrix with seesaw mechanism and two-loop mass splitting

Abstract

We propose a model which uses the seesaw mechanism and the lepton number $\bar{L}=L_e-L_{\mu }-L_{\tau }$ 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 this way, we accommodate atmospheric neutrino oscillations. A small mass splitting $m_1>m_2$ is generated by breaking $\bar{L}$ spontaneously and using Babu's two-loop mechanism. This allows us to incorporate ``just so'' solar-neutrino oscillations with maximal mixing into the model. The resulting mass matrix has three parameters only, since $\bar{L}$ breaking leads exclusively to a non-zero $ee$ matrix element.

8 pages, Latex

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