A measurement of $\tau$ lepton polarization using the L3 detector at LEP

W e rep ort on the measuremen t of the a v erage p olarization and forw ard-bac kw ard p olarization asymmetry of tau leptons pro duced in electron-p ositron collisions at the Large Electron P ositron (LEP) collider at the Europ ean Lab oratory for P article Ph ysics (CERN). The data w as collected using the L3 detector during 1990, 1991, 1992, and 1993 and consists of appro ximately 86 000 Z -> pi + pi - events. The tau p olarization w as determined as a function of the pro duction p olar angle using the follo wing 1-prong deca y mo des: t - -> e-v e v t, t- -> u-vuvt, t- -> pi-vt, t- -> p-vt and t- -> a1vt. F rom this measuremen tw e obtain the follo wing ratio of v ector- to axial-v ector w eak neutral couplings for taus and electrons: g V =g A = 0 : 0752 0 : 0063(stat : ) 0 : 00 45(s yst : ), g e V =g e A =0 : 0791 0 : 0099 (stat : ) 0 : 00 25(syst : ). This is consisten t with the h yp othesis of e - T univ ersalit y of the w eak neutral curren t. Assuming lepton univ ersalit y ,w e nd the e ectiv ew eak mixing angle sin 2 e W =0 : 2309 0 : 0016.