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To improve the theoretical prediction of the anomalous dipole moments of the$\tau$-neutrino, we have carried out a study through the process $\gamma e^-\to \tau \bar\nu_\tau \nu_e$, which represents an excellent and useful optionin determination of these anomalous parameters. To study the potential of theprocess $\gamma e^- \to \tau \bar\nu_\tau \nu_e$, we apply a future high-energyand high-luminosity linear electron-positron collider, such as the CLIC, with$\sqrt{s}=380, 1500, 3000\hspace{0.8mm}GeV$ and ${\cal L}=10, 50, 100, 200,500, 1000, 1500, 2000, 3000\hspace{0.8mm}fb^{-1}$, and we consider systematicuncertainties of $\delta_{sys}=0, 5, 10\%$. With these elements, we present acomprehensive and detailed sensitivity study on the total cross-section of theprocess $\gamma e^- \to \tau \bar\nu_\tau \nu_e$, as well as on the dipolemoments $\mu_{\nu_\tau}$ and $d_{\nu_\tau}$ at the $95\%$ C.L., showing thefeasibility of such process at the CLIC at the $\gamma e^-$ mode withunpolarized and polarized electron beams.

Model-independent sensibility studies for the anomalous dipole moments of the $\nu_\tau$ at the CLIC based $\gamma e^-$ colliders