Pseudo-Dirac Solar Neutrinos

Three of the four viable solutions of the solar neutrino problem are consistent with close to maximal leptonic mixing: $\sin^2\theta_{12}=(1/2)(1-\epsilon)$ with $|\epsilon|\ll1$. Theoretical models can naturally explain such a situation if approximate horizontal symmetries force a pseudo-Dirac structure on the neutrino mass matrix. An experimental determination of $|\epsilon|$ and sign($\epsilon$) will constrain the structure of the neutrino mass matrix and consequently provide stringent tests of such flavor models. If both $|\epsilon|$ and $\Delta m^2_{12}$ are known, it will be possible to estimate the mass scale of the pseudo-Dirac neutrinos. Various subtleties related to the diagonalization of the charged lepton mass matrix, to mixing with the third generation, to radiative corrections, and to the kinetic terms are clarified.