No Hope to Kinematically Detect the Effective Masses of Muon and Tau Neutrinos

We show that the recent WMAP data can impose a generous upper bound on the effective masses of electron, muon and tau neutrinos defined in the kinematic measurements: 〈m〉e + 〈m〉μ+ 〈m〉τ = m21 +m22 +m23 < 0.5 eV, or 〈m〉α < 0.71 eV (for α = e, μ, τ). When current neutrino oscillation data are taken into account, we obtain 〈m〉e < 0.24 eV and 〈m〉μ ≈ 〈m〉τ < 0.24 eV. Thus there is no hope to kinematically detect 〈m〉μ and 〈m〉τ in any realistic experiments. PACS number(s): 14.60.Pq, 13.10.+q, 25.30.Pt Typeset using REVTEX 1 Thanks to the recent Super-Kamiokande [1], K2K [2], SNO [3] and KamLAND [4] experiments, we are now convinced that the deficit of atmospheric νμ neutrinos and the deficit of solar νe neutrinos are both due to neutrino oscillations, a quantum phenomenon which can naturally happen if neutrinos are massive and lepton flavors are mixed. Furthermore, current experimental data indicate that solar and atmospheric neutrino oscillations are dominated respectively by νe → νμ and νμ → ντ transitions. The neutrino mass-squared differences associated with solar and atmospheric neutrino oscillations are thus defined as ∆m2sun ≡ ∣