Model-independent sensibility studies for the anomalous dipole moments of the ${\nu }_{\tau }$ at the CLIC based ${e}^{+}{e}^{-}$ and $\gamma {e}^{-}$ colliders

To improve the theoretical prediction of the anomalous dipole moments of the $\tau $-neutrino, we have carried out a study through the processes ${e}^{+}{e}^{-}\to \left(\gamma ,Z\right)\to {\nu }_{\tau }{\overline{\nu }}_{\tau }\gamma $ and $\gamma {e}^{-}\to \tau {\overline{\nu }}_{\tau }{\nu }_{e}$, which represent an excellent and useful option in determination of these anomalous parameters. Furthermore, we consider the effective Lagrangian formalism which induces contributions to the dipole moments of the tau-neutrino. To study the potential of the processes ${e}^{+}{e}^{-}\to \left(\gamma ,Z\right)\to {\nu }_{\tau }{\overline{\nu }}_{\tau }\gamma $ and $\gamma {e}^{-}\to \tau {\overline{\nu }}_{\tau }{\nu }_{e}$ we apply a future high-energy and high-luminosity linear electron-positron collider, such as the CLIC, with $\sqrt{s}=380$, 1500, 3000 GeV and $L=10$, 50, 100, 200, 500, 1000, 1500, 2000, $3000\text{}\text{}{\mathrm{fb}}^{-1}$, and we consider systematic uncertainties of ${\delta }_{\mathrm{sys}}=0%$, 5%, 10%. Furthermore, we including initial state radiation plus beamstrahlung effects. With these elements, we present a comprehensive and detailed sensitivity study on the total cross section of the processes ${e}^{+}{e}^{-}\to \left(\gamma ,Z\right)\to {\nu }_{\tau }{\overline{\nu }}_{\tau }\gamma $ and $\gamma {e}^{-}\to \tau {\overline{\nu }}_{\tau }{\nu }_{e}$, as well as on the dipole moments ${\stackrel{˜}{\kappa }}_{{\nu }_{\tau }}$ and ${\stackrel{˜}{d}}_{{\nu }_{\tau }}$ at the 95% C.L., showing the feasibility of such processes at the CLIC at the ${e}^{+}{e}^{-}$ and $\gamma {e}^{-}$ modes with unpolarized and polarized electron-positron beams.