An upper limit for the $\tau$ –neutrino mass from $\tau\rightarrow 5\pi^{\pm}\nu_{\tau}$ decays

An upper limit for the \(\tau\)–neutrino mass has been determined from the decay \(\tau\rightarrow 5\pi^{\pm}\nu_{\tau}\) using data collected with the OPAL detector from 1991 to 1995 in \(\rm e^{+}e^{-}\) collisions at \(\sqrt{s}\approx M_\mathrm{Z}\). A limit of 43.2 MeV at 95% CL is obtained using a two–dimensional method in the \(5\pi\) invariant mass and energy distribution from 22 selected events. Combining this result with OPAL's previously published measurement using \(\rm \tau^{+}\tau^{-}\rightarrow 3h^{\pm}\bar{\nu}_{\tau}+3h^{\mp}\nu_{\tau}\) decays, a new combined limit of \(m_{\nu_{\tau}}