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$\Delta m_{LSND}^{2} = 0.5 - 2.0 eV^2$\mathrm{.}Thentheselightneutrinoscanaccountfor$\sim (2.4-4.8)% (6.2-12.4 %)$ofthedarkmatterfor$h = 0.8 (0.5)$. Our model predicts the ${\nu }_{\mu }\to {\nu }_{\tau }$ oscillation probability in the range sensitive to the future experiments such as CHORUS and NOMAD.