TAU-POLARIZATION AT THE Z-PEAK FROM THE ACOLLINEARITY BETWEEN BOTH TAU-DECAY PRODUCTS

We discuss the possibility of measuring the tau-polarization distribution at the Z peak by studying the angular correlated distributions between the decay products Of the tau-pairs. We give explicit formulae for the energy-energy correlation and for the acollinearity distribution of the decay products of the tau-pairs, for both the cross section and the forward-backward asymmetry, as a function of the tau-Polarization and the Z-polarization. These distributions provide an independent method of measuring the tau-polarization, with a sensitivity comparable to the one that can be achieved by studying the energy spectrum of the produced pion in the decay-tau --> pi-nu(tau), and possibly better systematic errors. This new technique thus offers the prospect to achieve an increased precision in the determination of the electroweak mixing angle.