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

Searches for the exclusive decays of Higgs and Z bosons into a vector quarkonium state and a photon are performed in the mu(+)mu(-) gamma final state with a proton-proton collision data sample corresponding to an integrated luminosity of 139 fb(-1) collected at root s = 13 TeV with the ATLAS detector at the CERN Large Hadron Collider. The observed data are compatible with the expected backgrounds. The 95% confidence-level upper limits on 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 x 10(-4), 10.5x10(-4), and (2.5, 4.2, 3.4) x10(-4), respectively, assuming Standard Model production of the Higgs boson. The corresponding 95% CL upper limits on the branching fractions of the Z boson decays are 1.2 x 10(-6), 2.4 x 10(-6), and (1.1, 1.3, 2.4) x10(-6). An observed 95% CL interval of (-133, 175) is obtained for the kappa(c)/kappa(gamma) ratio of Higgs boson coupling modifiers, and a 95% CL interval of (-37, 40) is obtained for kappa(b)/kappa(gamma).