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

Abstract

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: $<m>^2_e + < m>^2_μ+ < m>^2_τ= m^2_1 + m^2_2 + m^2_3 < 0.5 ~ {\rm eV}^2$, 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 $<m>_μ\approx < m>_τ< 0.24$ eV. Thus there is no hope to kinematically detect $<m>_μ$ and $<m>_τ$ in any realistic experiments.