  The anomalous weak dipole moments of the tau lepton are measured in a data
sample collected by ALEPHfrom 1990 to 1995 corresponding to an integrated
luminosity of 155pb-1. Tau leptons produced in the reaction e+e- -> tau+tau- at
energies close to the Z mass are studied using their semileptonic decays to pi,
rho, a_1 -> pi 2pi0 or a_1 -> 3 pi. The real and imaginary components of both
the anomalous weak magnetic dipole moment and the CP-violating anomalous weak
electric dipole moment, Re,mu_tau, Im,mu_tau, Re, d_tau and Im, d_tau, are
measured simultaneously by means of a likelihood fit built from the full
differential cross section. No evidence of new physics is found. The following
bounds are obtained 95% CL: |Re, mu_tau | < 1.14 x 10-3, |Im}, mu_tau | < 2.65
x 10-3, |Re}, d_tau | < 0.91 x 10-3, and |Im, d_tau | < 2.01 x 10-3.

High Energy Physics - Experiment