A sample of $\tau$-lepton decays to ${5\pi }^{\pm }{\nu }_{\tau }$ and ${5\pi }^{\pm }{\pi }^0{\nu }_{\tau }$ observed in the high-resolution spectrometer at the SLAC$e^{+}{e}^{-}$ storage ring PEP, has been used to place an upper limit on the mass of the tau neutrino of 84 MeV/${\mathit{c}}^2$ at the 95% confidence level.

• Received 10 December 1985

DOI:https://doi.org/10.1103/PhysRevLett.56.1039