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: $<m{>}_e^2+<m{>}_{\mu }^2+<m{>}_{\tau }^2=m_1^2+m_2^2+m_3^2<0.5{\mathrm{eV}}^2$, 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.

Comments: RevTex 9 pages (2 PS figures)