To improve the theoretical prediction of the anomalous dipole moments of the $\tau$-neutrino, we have carried out a study through the processes $e^{+}{e}^{-}\to (\gamma ,Z)\to {\nu }_{\tau }{\overline{\nu }}_{\tau }\gamma$ 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 $e^{+}{e}^{-}\to (\gamma ,Z)\to {\nu }_{\tau }{\overline{\nu }}_{\tau }\gamma$ 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 $\mathcal{L}=10$, 50, 100, 200, 500, 1000, 1500, 2000, $3000{\mathrm{fb}}^{-1}$, 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 $e^{+}{e}^{-}\to (\gamma ,Z)\to {\nu }_{\tau }{\overline{\nu }}_{\tau }\gamma$ and $\gamma e^{-}\to \tau {\overline{\nu }}_{\tau }{\nu }_e$, as well as on the dipole moments ${\tilde{\kappa }}_{{\nu }_{\tau }}$ and ${\tilde{d}}_{{\nu }_{\tau }}$ 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.

• Received 15 September 2018
• Revised 26 September 2018

DOI:https://doi.org/10.1103/PhysRevD.98.095013

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Published by the American Physical Society