Possible deviations in tau polarization in e-e+--> tau - tau + due to exotic-lepton mixing.

Abstract

The $\ensuremath{\tau}$ polarization ${P}_{\ensuremath{\tau}}(s,cos\ensuremath{\theta})$ as a function of the production polar angle $\ensuremath{\theta}$, the mean $\ensuremath{\tau}$ polarization in the forward hemisphere ${〈{P}_{\ensuremath{\tau}}(s)〉}_{F}$, and the total mean $\ensuremath{\tau}$ polarization ${〈{P}_{\ensuremath{\tau}}(s)〉}_{T}$ in the process ${e}^{\ensuremath{-}}{e}^{+}\ensuremath{\rightarrow}{\ensuremath{\tau}}^{\ensuremath{-}}{\ensuremath{\tau}}^{+}$ are reexamined with the inclusion of mixing between ordinary ($l=e,\ensuremath{\tau}$) and exotic (${E}_{l}$) leptons of type (i) vector singlet (VS), (ii) vector doublet (VD), and (iii) mirror (M) for c.m. energies around the $Z$ peak. For $\sqrt{s}\ensuremath{\sim}{M}_{Z}$, the deviations from standard-model expectations are much less for the M lepton mixing in comparison to those due to the VS or VD lepton mixing. Around the $Z$ peak, the VS (VD) mixing induces negative (positive) deviations. At $\sqrt{s}\ensuremath{\sim}{M}_{Z}$, for the presently allowed mixing element square, ${|{U}_{{\ensuremath{\tau}E}_{\ensuremath{\tau}}}|}^{2}=0.02$, the expected relative deviations are (i) -11.4% (+13.0%) in ${P}_{\ensuremath{\tau}}(cos\ensuremath{\theta}=0.75)$, (ii) -11.8% (+13.5%) in ${〈{P}_{\ensuremath{\tau}}(s)〉}_{F}$, and (iii) -23.2% (+27.0%) in ${〈{P}_{\ensuremath{\tau}}(s)〉}_{T}$, for VS (VD) types of mixed exotic leptons.