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

Abstract

Using the CLEO II detector at the Cornell Electron Storage Ring operated at $\sqrt{s}=10.6\mathrm{GeV},$ we have determined the Michel parameters \ensuremath{\rho}, \ensuremath{\xi}, and \ensuremath{\delta} in ${\ensuremath{\tau}}^{\ensuremath{\mp}}\ensuremath{\rightarrow}{l}^{\ensuremath{\mp}}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ decay as well as the \ensuremath{\tau} neutrino helicity parameter ${h}_{{\ensuremath{\nu}}_{\ensuremath{\tau}}}$ in ${\ensuremath{\tau}}^{\ensuremath{\mp}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{\mp}}{\ensuremath{\pi}}^{0}\ensuremath{\nu}$ decay. From a data sample of $3.02\ifmmode\times\else\texttimes\fi{}{10}^{6}$ produced \ensuremath{\tau} pairs we analyzed events of the topologies ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}{(l}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\nu}\overline{\ensuremath{\nu}})({\ensuremath{\pi}}^{\ensuremath{\mp}}{\ensuremath{\pi}}^{0}\ensuremath{\nu})$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{+}{\ensuremath{\tau}}^{\ensuremath{-}}\ensuremath{\rightarrow}({\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}{\ensuremath{\pi}}^{0}\overline{\ensuremath{\nu}})({\ensuremath{\pi}}^{\ensuremath{\mp}}{\ensuremath{\pi}}^{0}\ensuremath{\nu}).$ We obtain $\ensuremath{\rho}=0.747\ensuremath{\rho}=0.747\ifmmode\pm\else\textpm\fi{}0.010\ifmmode\pm\else\textpm\fi{}0.006,$ $\ensuremath{\xi}=1.007\ifmmode\pm\else\textpm\fi{}0.040\ifmmode\pm\else\textpm\fi{}0.015,$ $\ensuremath{\xi}\ensuremath{\delta}=0.745\ifmmode\pm\else\textpm\fi{}0.026\ifmmode\pm\else\textpm\fi{}0.009,$ and ${h}_{{\ensuremath{\nu}}_{\ensuremath{\tau}}}=\ensuremath{-}0.995\ifmmode\pm\else\textpm\fi{}0.010\ifmmode\pm\else\textpm\fi{}0.003,$ where we have used the previously determined sign of ${h}_{{\ensuremath{\nu}}_{\ensuremath{\tau}}}$ [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 $V\ensuremath{-}A$ interaction.