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

A search for the exclusive decays of the Higgs and $Z$ bosons to a $\varphi$ or $\rho$ meson and a photon is performed with a $pp$ collision data sample corresponding to an integrated luminosity of up to 35.6 $f{b}^{-1}$ 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$\mathrm{\%}$ confidence level were obtained on the branching fractions of the Higgs boson decays to $\varphi \gamma$ and $\rho \gamma$ of $5.0\times {10}^{-4}$ and $10.4\times {10}^{-4}$, respectively. The corresponding 95$\mathrm{\%}$ confidence level upper limits for the $Z$ boson decays are $0.7\times {10}^{-6}$ and $4.0\times {10}^{-6}$ for $\varphi \gamma$ and $\rho \gamma$, respectively.