Closing the Windows on Mev Tau Neutrinos

Abstract

In this note, we analyze various constraints on the ``visible'' decay modes of a massive $τ$ neutrino, $ν_τ\rightarrowν^\prime\,γ$ and $ν_τ\rightarrowν^\prime\, e^+ e^-$, where $ν^\prime$ is a light neutrino. The BEBC beam dump experiment provides model-independent constraints on these modes. The lifetime for the $ν^\prime\, e^+e^-$ mode is constrained to be $τ_{ν^\prime\, e^+e^-} \ge 0.18~(m_{ν_τ}/MeV)~sec.$ We point out that the same experiment implies a similar constraint on the $ν^\prime\,γ$ mode. This results in a new upper limit on the transition magnetic moment of $ν_τ$, $μ_{\rm tran} \le 1.1 \times 10^{-9} (MeV/m_{ν_τ})^2 μ_B $. Furthermore, a limit on the electric charge of $ν_τ$ may be obtained, $Q_{ν_τ} \le 4 \times 10^{-4}e$. Combining these constraints with those arising from supernova observations and primordial nucleosynthesis calculations, we show that these ``visible'' decays cannot be the dominant decay modes of the $τ$ neutrino.