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Searches for the exclusive decays of the Higgs boson to an $\omega$ meson anda photon or a $K^{*}$ meson and a photon can probe flavour-conserving andflavour-violating Higgs boson couplings to light quarks, respectively. Searchesfor these decays, along with the analogous $Z$ boson decay to an $\omega$ mesonand a photon, are performed with a $pp$ collision data sample corresponding tointegrated luminosities of up to 134 fb$^{-1}$ collected at $\sqrt{s}=13$ TeVwith the ATLAS detector at the CERN Large Hadron Collider. The obtained 95%confidence-level upper limits on the respective branching fractions are ${\calB}(H\rightarrow\omega\gamma)< 5.5\times 10^{-4}$, ${\cal B}(H\rightarrowK^{*}\gamma)< 2.2\times10^{-4}$ and ${\cal B}(Z\rightarrow\omega\gamma)<3.9\times 10^{-6}$. The limits for $H\rightarrow \omega\gamma$and $Z\rightarrow \omega\gamma$ are 370 times and 140 times the Standard Modelexpected values, respectively. The result for $Z\rightarrow \omega\gamma$corresponds to a two-orders-of-magnitude improvement over the limit obtained bythe DELPHI experiment at LEP.

Search for exclusive Higgs and $Z$ boson decays to $\omega\gamma$ and Higgs boson decays to $K^{*}\gamma$ with the ATLAS detector