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Searches for the exclusive decays of Higgs and $Z$ bosons into a vectorquarkonium state and a photon are performed in the $\mu^+\mu^- \gamma$ finalstate with a proton$-$proton collision data sample corresponding to anintegrated luminosity of $139$ fb$^{-1}$ collected at $\sqrt{s}=13$ TeV withthe ATLAS detector at the CERN Large Hadron Collider. The observed data arecompatible with the expected backgrounds. The 95% confidence-level upper limitson the branching fractions of the Higgs boson decays into $J/\psi \gamma$,$\psi(2S) \gamma$, and $\Upsilon(1S,2S,3S) \gamma$ are found to be$2.0\times10^{-4}$, $10.5\times10^{-4}$, and $(2.5,4.2,3.4)\times10^{-4}$,respectively, assuming Standard Model production of the Higgs boson. Thecorresponding 95% CL upper limits on the branching fractions of the $Z$ bosondecays are $1.2\times10^{-6}$, $2.4\times10^{-6}$, and$(1.1,1.3,2.4)\times10^{-6}$. An observed 95% CL interval of $(-133,175)$ isobtained for the $\kappa_c/\kappa_\gamma$ ratio of Higgs boson couplingmodifiers, and a 95% CL interval of $(-37,40)$ is obtained for$\kappa_b/\kappa_\gamma$.

european physical journal. c, particles and fields

Searches for exclusive Higgs and $Z$ boson decays into a vector  quarkonium state and a photon using $139$ fb$^{-1}$ of ATLAS $\sqrt{s}=13$  TeV proton$-$proton collision data