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Description
A search for the Higgs boson decay to a $Z$ boson and a photon in the $\ell\ell\gamma$ ($\ell = e, \mu$) final state is performed using $pp$ collisions at $\sqrt{s}=13.6~\mathrm{TeV}$ recorded with the ATLAS detector at the Large Hadron Collider during 2022--2024, corresponding to an integrated luminosity of $165~\mathrm{fb}^{-1}$. The signal yield, normalised to the Standard Model prediction, is measured to be $\mu = 0.9^{+0.7}_{-0.6}$, compared to an expected value of $\mu = 1.0 \pm 0.7$. This corresponds to an observed (expected) signal significance of $1.4$ ($1.5$) standard deviations for the background-only hypothesis. This result is combined with that of a similar search performed with $140~\mathrm{fb}^{-1}$ of $\sqrt{s}=13~\mathrm{TeV}$ $pp$ collisions to provide the most stringent expected sensitivity to date to this rare decay, namely an observed (expected) signal strength of $\mu = 1.3^{+0.6}_{-0.5}$ ($\mu = 1.0^{+0.6}_{-0.5}$), corresponding to an observed (expected) significance of $2.5$ ($1.9$) standard deviations. The measurement is consistent with the Standard Model expectation.
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