Measurements of $\gamma \gamma \to \mbox{Higgs}$ and $\gamma \gamma \to W^{+}W^{-}$ in $e^{+}e^{-}$ collisions at the Future Circular Collider

The measurements of the two-photon production of the Higgs boson and of $W^{\pm}$ boson pairs in $e^{+}e^{-}$ collisions at the Future Circular Collider (FCC-ee) are investigated. The processes $e^{+}e^{-}\xrightarrow{\gamma \gamma}e^+\,{\rm H}\,e^-,e^+\,{\rm W^+W^-}\,e^-$ are computed using the effective photon approximation for electron-positron beams, and studied in their ${\rm H}\to b\bar{b}$ and ${\rm W^+W^-}\to 4j$ decay final-states including parton showering and hadronization, jet reconstruction, $e^\pm$ forward tagging, and realistic experimental cuts. After selection criteria, up to 75 Higgs bosons and 6600 $\rm W^{\pm}$ pairs will be reconstructed on top of controllable continuum backgrounds at $\sqrt{s} = $240 and 350 GeV for the total expected integrated luminosities, by tagging the scattered $e^\pm$ with near-beam detectors. A 5$\sigma$ observation of $\gamma \gamma \to$H is thereby warranted, as well as high-statistics studies of triple $\rm \gamma WW$ and quartic $\rm \gamma\gamma WW$ electroweak couplings, improving by at least factors of 2 and 10 the current limits on dimension-6 anomalous quartic gauge couplings.