Determination of the Michel parameters and the τ neutrino helicity in τ decay

Using the CLEO II detector at the Cornell Electron Storage Ring operated at $\sqrt{s}=10.6\mathrm{}\mathrm{GeV},$ we have determined the Michel parameters ρ, ξ, and δ in ${\tau }^{\mp }\to l^{\mp }\nu \overline{\nu }$ decay as well as the τ neutrino helicity parameter $h_{{\nu }_{\tau }}$ in ${\tau }^{\mp }\to {\pi }^{\mp }{\pi }^0\nu$ decay. From a data sample of $3.02\times {10}^6$ produced τ pairs we analyzed events of the topologies $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}\to {(l}^{\pm }\nu \overline{\nu }\left)\right({\pi }^{\mp }{\pi }^0\nu )$ and $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}\to \left({\pi }^{\pm }{\pi }^0\overline{\nu }\right)\left({\pi }^{\mp }{\pi }^0\nu \right).\mathrm{}$ We obtain $\rho =0.747\mathrm{}\rho =0.747\mathrm{}\pm 0.010\pm 0.006,$ $\xi =1.007\mathrm{}\pm 0.040\pm 0.015,$ $\xi \delta =0.745\mathrm{}\pm 0.026\pm 0.009,$ and $h_{{\nu }_{\tau }}=-0.995\pm 0.010\pm 0.003,$ where we have used the previously determined sign of $h_{{\nu }_{\tau }}$ [ARGUS Collaboration, H. Albrecht et al., Z. Phys. C 58, 61 (1993); Phys. Lett. B 349, 576 (1995)]. We also present the Michel parameters as determined from the electron and muon samples separately. All results are in agreement with the standard model $V-A$ interaction.