Future limits on theντmass

In this paper we show that the current limit on the $\tau$-neutrino mass can be improved by more than one order of magnitude in an experiment running at a new type of low-energy, high-luminosity collider recently proposed, the so-called Tau-Charm Factory. The design of the machine allows a luminosity of ${10}^{33}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\mathrm{s}}^{-1\mathrm{}}$, at a center-of-mass energy in the range 3-4.2 GeV, thus allowing high-precision, high-statistics studies of the $\tau$ lepton with typical production rates of the order of ${10}^7$ $\tau$ pairs per year. One of the main goals of this factory would be the improvement of the current limits on the $\tau$-neutrino mass $m_{{\nu }_{\tau }}$. The most promising technique to do so is the study of the behavior of the hadronic mass spectrum in the decay ${\tau }^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}{\nu }_{\tau }$. To achieve a good upper limit on $m_{{\nu }_{\tau }}$ from this decay, one needs not only a very high luminosity, but also an excellent detector, providing good particle identification and momentum resolution. In this paper we attempt to quantify these detector requirements as well as to estimate the limit that can be achieved on $m_{{\nu }_{\tau }}$. We show that the ${\nu }_{\tau }$ mass limit can be reduced to about 3.5-5 MeV by this experiment.