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

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