Searches for the exclusive decays of the Higgs boson into $D^*\gamma$ and of the $Z$ boson into $D^0\gamma$ and $K^0_s\gamma$ can probe flavour-violating Higgs and $Z$ boson couplings to light quarks. Searches for these decays are performed with a $pp$ collision data sample corresponding to an integrated luminosity of $136.3$ fb$^{-1}$ collected at $\sqrt{s}=13$ TeV between 2016-2018 with the ATLAS detector at the CERN Large Hadron Collider. In the $D^*\gamma$ and $D^0\gamma$ channels, the observed (expected) 95$\%$ confidence-level upper limits on the respective branching fractions are ${\cal B}(H\rightarrow D^*\gamma)< 1.0 (1.2)\times 10^{-3}$, ${\cal B}(Z\rightarrow D^0\gamma)< 4.0 (3.4)\times 10^{-6}$, while the corresponding results in the $K^0_s\gamma$ channel are ${\cal B}(Z\rightarrow K^0_s\gamma)< 3.1 (3.0)\times 10^{-6}$.
Numbers of observed and expected background events for the $m_{\mathcal{M}\gamma}$ ranges of interest. Each expected background and the corresponding uncertainty is obtained by integrating the total pdf after a background-only fit to the data, where the uncertainty does not take into account statistical fluctuations in each mass range. Expected Higgs and $Z$ boson signal contributions, with their corresponding total systematic uncertainty, are shown for reference branching fractions of $10^{-3}$ and $10^{-6}$, respectively. Entries are marked with a dash when there is no signal of that type in the specified range.
Observed and expected (with the corresponding $\pm1\sigma$ intervals) 95% CL upper limits on the branching fractions for $H\rightarrow D^*\gamma$, $Z\rightarrow D^0\gamma$ and $Z\rightarrow K^0_s\gamma$. Standard Model production of the Higgs boson is assumed. The corresponding upper limits on the production cross-section times branching fraction $\sigma\times\mathcal{B}$ are also shown.
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