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Searches for the exclusive decays of the Higgs and $Z$ bosons into a$J/\psi$, $\psi(2S)$, or $\Upsilon(nS)$ ($n=1,2,3$) meson and a photon areperformed with a $pp$ collision data sample corresponding to an integratedluminosity of 36.1 fb$^{-1}$ collected at $\sqrt{s}=13$ TeV with the ATLASdetector at the CERN Large Hadron Collider. No significant excess of events isobserved above the expected backgrounds, and 95% confidence-level upper limitson the branching fractions of the Higgs boson decays to $J/\psi\gamma$,$\psi(2S)\gamma$, and $\Upsilon(nS)\gamma$ of $3.5\times10^{-4}$,$2.0\times10^{-3}$, and $(4.9,5.9,5.7)\times10^{-4}$, respectively, areobtained assuming Standard Model production. The corresponding 95%confidence-level upper limits for the branching fractions of the $Z$ bosondecays are $2.3\times10^{-6}$, $4.5\times10^{-6}$ and$(2.8,1.7,4.8)\times10^{-6}$, respectively.

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Searches for exclusive Higgs and $Z$ boson decays into $J/\psi\gamma$,  $\psi(2S)\gamma$, and $\Upsilon(nS)\gamma$ at $\sqrt{s}=13$ TeV with the  ATLAS detector