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A search for the decay of the Higgs boson to a $Z$ boson and a light,pseudoscalar particle, $a$, decaying respectively to two leptons and to twophotons is reported. The search uses the full LHC Run 2 proton-proton collisiondata at $\sqrt{s}=13$ TeV, corresponding to 139 fb$^{-1}$ collected by theATLAS detector. This is one of the first searches for this specific decay modeof the Higgs boson, and it probes unexplored parameter space in models withaxion-like particles (ALPs) and extended scalar sectors. The mass of the $a$particle is assumed to be in the range 0.1-33 GeV. The data are analysed in twocategories: a merged category where the photons from the $a$ decay arereconstructed in the ATLAS calorimeter as a single cluster, and a resolvedcategory in which two separate photons are detected. The main backgroundprocesses are from Standard Model $Z$ boson production in association withphotons or jets. The data are in agreement with the background predictions, andupper limits on the branching ratio of the Higgs boson decay to $Za$ times thebranching ratio $a\to\gamma\gamma$ are derived at the 95% confidence level andthey range from 0.08% to 2% depending on the mass of the $a$ particle. Theresults are also interpreted in the context of ALP models.

Search for the decay of the Higgs boson to a $Z$ boson and a light pseudoscalar particle decaying to two photons