Model-independent study on the anomalous couplings at the ILC

The potential of the process $\gamma \gamma \to \tau \overline{\tau }\gamma $ is examined in a model-independent way using the effective Lagrangian approach for the International Linear Collider, a proposed electron-positron machine which is designed with standard configurations of 0.25 TeV/2000 fb$^{−1}$, 0.35 TeV/200 fb$^{−1}$ and 0.5 TeV/4000 fb$^{−1}$. The limits obtained for the tau lepton's anomalous magnetic dipole moment ${\stackrel{˜}{a}}_{\tau }$ and the tau lepton's anomalous electric dipole moment ${\stackrel{˜}{d}}_{\tau }$ defining the anomalous $\tau \overline{\tau }\gamma $ couplings at 95% confidence level and systematic uncertainties of ${\delta }_{sys}=0,5,10\text{%}$ are compared with the experimental results. The best limits obtained with ${\delta }_{sys}=0\text{%}$ on the anomalous couplings are $-0.00082<{\stackrel{˜}{a}}_{\tau }<0.00050$ and $|\stackrel{˜}{{d}_{\tau }}|<3.59×{10}^{-18}$ $e\phantom{\rule{0.2em}{0ex}}\text{cm}$, respectively. Also, the limits on the anomalous couplings do not improve proportionately to the luminosity due to the systematic error considered here. The reason of this situation is the systematic error which is much bigger than the statistical error. If the systematic error is improved, we expect better limits on the couplings. However, the best limits on the anomalous couplings for the process $\gamma \gamma \to \tau \overline{\tau }\gamma $ with $\sqrt{s}=500$ GeV, ${L}_{int}=4000$ fb$^{−1}$ and ${\delta }_{sys}=0\text{%}$ can be improved up to 4 times for ${\stackrel{˜}{a}}_{\tau }$ and 9 times for ${\stackrel{˜}{d}}_{\tau }$ according to case with ${\delta }_{sys}=10\text{%}$. Our results show that γγ collisions at the ILC give results up to one order of magnitude for ${\stackrel{˜}{a}}_{\tau }$ and two orders of magnitude for ${\stackrel{˜}{d}}_{\tau }$ better than the current experimental limits.