Tau Decays to Five and Seven Charged Particles and the Tau Neutrino Mass.

The production of tau-lepton pairs in e^+e^- collisions at 29 GeV has been used to study the inclusive tau decay into five and seven charged particles. The results obtained in this analysis are based on a data sample corresponding to a total integrated luminosity of 300 pb^{-1}. Thirteen events are observed in which the tau decays to five charged particles giving a branching ratio of B(tau to 5pi^+/-nu_tau + ngamma) = (10.2 +/- 2.9) times 10 ^{-4}. Six of these events contain neutral energy consistent with a single pi ^{o}. With this interpretation the exclusive branching ratios are measured to be B( tau to 5pi ^+/-nu_tau) = (5.1 +/- 2.0) times 10^{-4} and B( tau to 5pi ^+/-pi^{o}nu_ tau) = (5.1 +/- 2.2) times 10^{-4 }. No tau decays to seven charged particles were observed giving an upper limit on the branching ratio of B(tau to 7pi^+/- nu_tau + ngamma ) < 1.9 times 10^{-4} at the 90% confidence level. This data was used to look for tau to K^{o }3pi^+/-nu _tau + ngamma. No K^{o}'s were found in the sample of 13 events, yielding an upper limit on the branching ratio of B(tau to K^{o}3 pi^+/-nu_tau + ngamma) < 2.1 times 10^{ -3} at the 90% confidence level. The 5 pi^+/-pi^{o} events were also used to place limits on tau decays involving one or two eta's. The 90% confidence level upper limits are found to be B( tau to eta 3pi^+/-n pi^{o}nu_tau) < 0.005 and B(tau to etaetapi ^+/-npi^{o }nu_tau) < 0.007 (n >= 0). The hadronic mass spectrum of the five-prong tau events was used to place an upper limit on the mass of the tau neutrino. At the 95% confidence level the upper limit is M_nu_tau < 76MeV/c^2.