Effective Mass Matrix for Light Neutrinos Consistent with Solar and Atmospheric Neutrino Experiments

We propose an effective mass matrix for light neutrinos which is consistent with the mixing pattern indicated by solar and atmospheric neutrino experiments. Two scenarios for the mass eigenvalues are discussed and the connection with double beta decay is noted. 96.60.Kx,14.60.Pq Typeset using REVTEX 1 There are significant hints for neutrino mass coming from solar [1] and atmospheric [2] neutrino experiments and they present an interesting theoretical challenge. Solar neutrino experiments suggest that electron neutrinos oscillate into other lepton flavors with a small mixing angle [3], sin 2θ ≈ 7×10, and a small mass-squared difference, ∆m ≈ 5×10 eV. Atmospheric neutrino experiments, on the other hand, suggest that muon neutrinos oscillate into tau neutrinos with maximal mixing [4], sin 2θ = 1, and a much larger mass-squared difference, ∆m ≈ 2 × 10 eV. How can we accommodated these very different sets of oscillation parameters within one neutrino mass matrix? Here we wish to propose an effective mass matrix, M, of the form: ν̄Mν ≡ ( ν̄e, ν̄μ, ν̄τ ) 