Lepton flavor violation and the tau neutrino mass.

We point out that, in the left-right symmetric model of weak interactions, if ντ mass is in the keV to MeV range, there is a strong correlation between rare decays such as τ → 3μ, τ → 3e and the ντ mass. In particular, we point out that a large range of ντ masses are forbidden by the cosmological constraints on mντ in combination with the present upper limits on these processes. † Work supported by a grant from the National Science Foundation * Permanent address: Department of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel. 1 In the standard model of electroweak interactions, all lepton flavors Le, Lμ and Lτ are conserved. On the other hand, in most extensions of the standard model, lepton flavor conservation is not maintained; therefore, it is hoped that the nature of lepton flavor violation can help to narrow the possibilities of new physics. Crucial tests of lepton flavor violation are provided by the rare decays of μ and τ such as μ → 3e[1] and τ → lilj lk where li, j, k go over e and μ. The present stringent limits on μ → 3e already make it imperative that in all extensions of standard model, violation of Lμ + Le be very weak. On the other hand, the present upper limits on the branching ratios for rare τ decays[2] allow for possible violation of Lτ + Lμ or Lτ + Le at a much higher level. One class of models, where the possibility of a significant lepton violation exists, is the left-right symmetric model with see-saw mechanism for neutrino masses[3]. In this note, we investigate the rare τ decays and their implications for violation of Lτ + Lμ or Lτ + Le quantum numbers in these models. We show that there is a strong correlation between the tau neutrino mass and τ → 3μ and τ → 3e decays if mντ is in the keV to MeV range[4], as is allowed by existing laboratory upper limits[2]. First we derive lower limits on mντ for the case where B(τ → 3μ) = 0; Once the flavor violating decay τ → 3μ or τ → 3e is allowed we show that the present upper limits on their rates permit the lower bound on mντ to be somewhat relaxed. Improvement of the present experimental upper limits on mντ and the branching ratios for the above τ -decay modes can therefore throw light on the nature of lepton flavor violation in the left-right symmetric models. We consider the left-right symmetric model with a see-saw mechanism 2 for neutrino masses as described in ref.3. Let us display the leptonic and Higgs sector of the model. The three generations of lepton fields are Ψa ≡