Probing the electromagnetic properties of the neutrinos at future lepton colliders

In this study, we explore the non-standard $\nu \overline{\nu }\gamma \gamma $ couplings parametrized by dimension-seven operators via ${e}^{+}{e}^{-}\to \nu \overline{\nu }\gamma $ process at the FCC-ee/CEPC and ${\mu }^{+}{\mu }^{-}\to \nu \overline{\nu }\gamma $ process at the Muon Colliders. For the detailed Monte Carlo simulation, all signal and relevant background events are produced within the framework of Madgraph where non-standard $\nu \overline{\nu }\gamma \gamma $ couplings are implemented. After passing through Pythia for parton showering and hadronization, detector effects are included via tuned corresponding detector cards for each collider in Delphes. Projected sensitivities on $\nu \overline{\nu }\gamma \gamma $ couplings are obtained at a 5σ confidence level without and with 5% systematic uncertainties for the FCC-ee/CEPC and the Muon Colliders, showcasing the complementarity between lepton colliders. Our best limit on the anomalous $\nu \overline{\nu }\gamma \gamma $ couplings even with 5% systematic uncertainties for muon collider with $\sqrt{s}=10$ TeV and ${L}_{int}=10$ ab$^{−1}$ are found to be fourteen orders of magnitude stronger than the upper bound obtained from rare decay $Z\to \gamma \gamma \nu \overline{\nu }$ analysis using LEP data.