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We carry out a study in the approach of a dimension-8 effective field theoryon the anomalous quartic $WW\gamma\gamma$ couplings that arise from the process$pp \to W\gamma\gamma$ at the Future Circular Collider-hadron hadron (FCC-hh).The process is sensitive to the $WW\gamma\gamma$ vertex, and future projectionson the anomalous $f_ {M,i}/\Lambda^4$ and $ f_ {T,j}/\Lambda^4$ couplings canbe put by measurements of $W\gamma\gamma$ production. We illustrate the physicsopportunities and reach of the FCC-hh operating for a high integratedluminosity scenario of ${\cal L}=1, 5, 10, 30$ ${\rm ab}^{-1}$ of proton-protoncollisions at a center-of-mass energy of $\sqrt{s}=100$ TeV and systematicuncertainties of $\delta_{sys}=0\%, 3\%, 5\%, 10\%$. Production cross-sectionsof the signal and the sensitivity constraints on the anomalous $f_{M,i}/\Lambda^4$ and $ f_ {T,j}/\Lambda^4$ couplings at $95\%$ C.L. areidentified through the leptonic and hadronic decay modes of the $W$-boson. TheFCC-hh sensitivity on these anomalous couplings is expected might reach up tothe order of magnitude ${\cal O}(10^{-4}-10^1)$. These sensitivity perspectivesindicate that the $pp \to W\gamma\gamma$ channel at the FCC-hh has a greaterpotential to search for the anomalous quartic $WW\gamma\gamma$ couplings and tosearch for new physics than present colliders.

Future projections on the anomalous $WW\gamma\gamma$ couplings in hadron-hadron interactions at the FCC-hh