Lepton flavor violation and theτneutrino mass

We point out that, in the left-right symmetric model of weak interactions, if the ${\nu }_{\tau }$ mass is in the keV to MeV range, there is a correlation between rare decays such as $\tau \to 3\mu$, $\tau \to \mu \mathrm{ee}$, and the allowed values of the ${\nu }_{\tau }$ mass. In particular, we point out that a large range of ${\nu }_{\tau }$ masses are forbidden by the cosmological constraints on $m_{{\nu }_{\tau }}$ and this forbidden range will increase further, as the upper limits on these processes become lower.