Predictions for Anomalous tau+ tau- gamma Production at LEP 1

We calculate distributions for tau+ tau- gamma production at LEP 1 taking into account a potentially existing anomalous magnetic moment a_tau of the tau lepton. The existing upper limits for |a_tau| are known from the dependence of the decay Z -> tau+ tau- gamma on (a_tau)^2 and are of the order of (1 - 5)%. We show that such limits are also sensitive to linear terms in a_tau, which are of equal importance at |a_tau| ~ (1 - 2)% and dominate below this value. Contributions from an electric dipole moment d_tau do not interfere with the electromagnetic vertex or with the anomalous magnetic moment. Appropriate formulae are derived.