Search for the electromagnetic properties of the neutrinos at the HL-LHC and the FCC-hh

The $\nu \bar{\nu }\gamma \gamma$ couplings parametrized with the non-standard dimension-seven operators defined by the Effective Field Theory framework are investigated through the process $pp\to \nu \bar{\nu }\gamma$ at the High Luminosity-LHC and the Future Circular proton-proton Collider. The effective Lagrangian of $\nu \bar{\nu }\gamma \gamma$ couplings is implemented into FeynRules to generate a UFO module inserted into Madgraph to generate both background and signal events. These events are then passed through Pythia 8 for parton showering and Delphes to include realistic detector effects. The sensitivities on $\nu \bar{\nu }\gamma \gamma$ couplings are obtained at $95\mathrm{\%}$ confidence level. We show that the analysis of the signal emerging from the process $pp\to \nu \bar{\nu }\gamma$ allows to improve constraints on $\nu \bar{\nu }\gamma \gamma$ couplings given by the LEP collaboration.