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The potential of the process $\gamma \gamma \rightarrow \tau\bar{\tau}\gamma$ is examined in a model-independent way using the effectiveLagrangian approach for the ILC which is designed with standard configurationsof 0.25 TeV/2000 fb$^{-1}$, 0.35 TeV/200 fb$^{-1}$ and 0.5 TeV/4000 fb$^{-1}$.The limits obtained for $\tilde{a}_{\tau}$ and $\tilde{{d}_{\tau}}$ parametersdefining the anomalous $\tau \bar{\tau}\gamma$ couplings at $95\%$ confidencelevel and systematic uncertainties of $\delta_{sys}=0,5,10 \%$ are comparedwith the experimental results. The best limits obtained without systematicerror on the anomalous couplings are $-0.00082<\tilde{a}_{\tau}<0.00050$ and$|\tilde{{d}_{\tau}}|<3.5969 \times 10^{-18}$ $e\,cm$, respectively. Thus, ourresults show that $\gamma \gamma$ collisions at the ILC lead to a remarkableimprovement in the existing experimental limits on the anomalous magnetic andelectric dipole moments of the tau lepton.

Model-independent study on the anomalous $\tau \bar{\tau}\gamma$ couplings at the ILC