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: $<m>^2_e + < m>^2_\mu + < m>^2_\tau = m^2_1 + m^2_2 + m^2_3 < 0.5 ~ {\rm eV}^2$, or $<m>_\alpha < 0.71$ eV (for $\alpha = e, \mu, \tau$). When current neutrino oscillation data are taken into account, we obtain $<m>_e <0.24$ eV and $<m>_\mu \approx < m>_\tau < 0.24$ eV. Thus there is no hope to kinematically detect $<m>_\mu$ and $<m>_\tau$ in any realistic experiments.