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The increase in luminosity and center of mass energy at the FCC-hh will openup new clean channels where BSM contributions are enhanced at high energy. Inthis paper we study one such channel, $Wh \to \ell\nu\gamma\gamma$. We estimatethe sensitivity to the $\mathcal{O}_{\varphi q}^{(3)}$, $\mathcal{O}_{\varphi{W}}$, and $\mathcal{O}_{\varphi \widetilde {W}}$ SMEFT operators. We find thatthis channel will be competitive with fully leptonic $WZ$ production in settingbounds on $\mathcal{O}_{\varphi q}^{(3)}$. We also find that the doubledifferential distribution in the $p_T^h$ and the leptonic azimuthal angle canbe exploited to enhance the sensitivity to $\mathcal{O}_{\varphi \widetilde{W}}$. However, the bounds on $\mathcal{O}_{\varphi {W}}$ and$\mathcal{O}_{\varphi \widetilde {W}}$ we obtain in our analysis, thoughcomplementary and more direct, are not competitive with those coming from othermeasurements such as EDMs and inclusive Higgs measurements.

A New Precision Process at FCC-hh: the diphoton leptonic Wh channel