Search for exclusive Higgs and $Z$ boson decays to $\phi\gamma$ and $\rho\gamma$ with the ATLAS detector

A search for the exclusive decays of the Higgs and $Z$ bosons to a $\phi$ or $\rho$ meson and a photon is performed with a $pp$ collision data sample corresponding to an integrated luminosity of up to 35.6 $fb^{-1}$ collected at $\sqrt{s}=13$ TeV with the ATLAS detector at the CERN Large Hadron Collider. These decays have been suggested as a probe of the Higgs boson couplings to light quarks. No significant excess of events is observed above the background, as expected from the Standard Model. Upper limits at 95% confidence level were obtained on the branching fractions of the Higgs boson decays to $\phi\gamma$ and $\rho\gamma$ of $4.8\times10^{-4}$ and $8.8\times10^{-4}$, respectively. The corresponding 95% confidence level upper limits for the $Z$ boson decays are $0.9\times10^{-6}$ and $25\times10^{-6}$ for $\phi\gamma$ and $\rho\gamma$, respectively.