Search for the exotic decay of the Higgs boson into a Z boson and a light pseudoscalar decaying into two photons in pp collisions at $\sqrt{s}=13~\mathrm{TeV}$

A search for the exotic decay of the Higgs boson to a Z boson and a light pseudoscalar particle, decaying, respectively, to two leptons and two photons, is presented. The search is based on proton-proton collision data at a center-of-mass energy of $\sqrt{s}=13~\mathrm{TeV}$, collected by the CMS detector and corresponding to an integrated luminosity of $138~\mathrm{fb}^{-1}$. The analysis probes pseudoscalar masses ($m_a$) between 1 and 30$~\mathrm{GeV}$, leading to two pairs of well-isolated leptons and photons. No significant deviation from the standard model expectation is observed. Upper limits at $95\%$ confidence level are set on the product of the Higgs boson production cross section and its branching to two leptons and two photons. The observed (expected) limits range from 17.8 (17.9)$~\mathrm{fb}$ for $m_{a} = 1~\mathrm{GeV}$ to 4.7 (6.9)$~\mathrm{fb}$ for $m_{a} = 30~\mathrm{GeV}$. Limits on axion-like particle models are also reported.