Measurement of the Michel parameters in leptonic tau decays

Abstract.

The Michel parameters of the leptonic $\tau$ decays are measured using the OPAL detector at LEP. The parameters $\rho_\ell$, $\xi_\ell$, $(\xi\delta)_\ell$ (with $\ell ={\rm e}, \mu$) and $\eta_\mu$ are extracted from the energy spectra of the charged decay leptons and from their energy–energy correlations. A new method involving a global likelihood fit of Monte Carlo generated events with complete detector simulation and background treatment has been applied to the data recorded at center-of-mass energies close to $\sqrt{s} =m_{\rm Z^0}$ corresponding to an integrated luminosity of 155 pb$^{-1}$. If e-$\mu$ universality is assumed and inferring the $\tau$ polarization from neutral current data, the measured Michel parameters are: \[ \begin{array}{l@{\quad}l} \rho = 0.781 \pm 0.028 \pm 0.018, & \xi = 0.98 \pm 0.22 \pm 0.10, \eta = 0.027 \pm 0.055 \pm 0.005, & \xi\delta = 0.65 \pm 0.14 \pm 0.07, \end{array} \] where the value of $\eta$ has been constrained using the published OPAL measurements of the leptonic branching ratios and the $\tau$ lifetime. Limits on non-standard coupling constants and on the masses of new gauge bosons are obtained. The results are in agreement with the V–A prediction of the Standard Model.