A simple modification of the maximal mixing scenario for three light neutrinos

We suggest a simple modification of the maximal mixing scenario (with $S_3$ permutation symmetry) for three light neutrinos. Our neutrino mass matrix has smaller permutation symmetry $S_{2}$ ($\nu_{\mu} \leftrightarrow \nu_{e}$), and is consistent with all neutrino experiments except the $^{37}$Cl experiment. The resulting mass eigenvalues for three neutrinos are $m_{1} \approx (2.55-1.27) \times 10^{-3} eV, m_{2,3} \approx (0.71-1.43) eV$ for $\Delta m_{LSND}^{2} = 0.5 - 2.0 eV^2$. Then these light neutrinos can account for $\sim (2.4-4.8)$ of the dark matter for $h = 0.8 (0.5)$. Our model predicts the $\nu_{\mu} \rightarrow \nu_{\tau}$ oscillation probability in the range sensitive to the future experiments such as CHORUS and NOMAD.