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Decays of the 125 GeV Higgs boson into a Z boson and a $\rho^0$(770) or$\phi$(1020) meson are searched for using proton-proton collision datacollected by the CMS experiment at the LHC at $\sqrt{s} = $ 13 TeV. Theanalysed data set corresponds to an integrated luminosity of 137 fb$^{-1}$.Events are selected in which the Z boson decays into a pair of electrons or apair of muons, and the $\rho$ and $\phi$ mesons decay into pairs of pions andkaons, respectively. No significant excess above the background model isobserved. As different polarization states are possible for the decay productsof the Z boson and $\rho$ or $\phi$ mesons, affecting the signal acceptance,scenarios in which the decays are longitudinally or transversely polarized areconsidered. Upper limits at the 95% confidence level on the Higgs bosonbranching fractions into Z$\rho$ and Z$\phi$ are determined to be 1.04-1.31%and 0.31-0.40%, respectively, where the ranges reflect the consideredpolarization scenarios; these values are 740-940 and 730-950 times larger thanthe respective standard model expectations. These results constitute the firstexperimental limits on the two decay channels.

Search for decays of the 125 GeV Higgs boson into a Z boson and a $\rho$ or $\phi$ meson