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   Abstract The production of Z boson pairs in proton–proton ( $${\mathrm{p}} {\mathrm{p}} $$ p p ) collisions, $${{\mathrm{p}} {\mathrm{p}} \rightarrow ({\mathrm{Z}}/\gamma ^*)({\mathrm{Z}}/\gamma ^*) \rightarrow 2\ell 2\ell '}$$ p p → ( Z / γ ∗ ) ( Z / γ ∗ ) → 2 ℓ 2 ℓ ′ , where $${\ell ,\ell ' = {\mathrm{e}}}$$ ℓ , ℓ ′ = e or $${{\upmu }}$$ μ , is studied at a center-of-mass energy of 13 $$\,\text {TeV}$$ TeV with the CMS detector at the CERN LHC. The data sample corresponds to an integrated luminosity of 137 $$\,\text {fb}^{-1}$$ fb - 1more », collected during 2016–2018. The $${\mathrm{Z}} {\mathrm{Z}} $$ Z Z production cross section, $$\sigma _{\text {tot}} ({\mathrm{p}} {\mathrm{p}} \rightarrow {\mathrm{Z}} {\mathrm{Z}} ) = 17.4 \pm 0.3 \,\text {(stat)} \pm 0.5 \,\text {(syst)} \pm 0.4 \,\text {(theo)} \pm 0.3 \,\text {(lumi)} \text { pb} $$ σ tot ( p p → Z Z ) = 17.4 ± 0.3 (stat) ± 0.5 (syst) ± 0.4 (theo) ± 0.3 (lumi) pb , measured for events with two pairs of opposite-sign, same-flavor leptons produced in the mass region $${60< m_{\ell ^+\ell ^-} < 120\,\text {GeV}}$$ 60 < m ℓ + ℓ - < 120 GeV is consistent with standard model predictions. Differential cross sections are also measured and agree with theoretical predictions. The invariant mass distribution of the four-lepton system is used to set limits on anomalous $${\mathrm{Z}} {\mathrm{Z}} {\mathrm{Z}} $$ Z Z Z and $${{\mathrm{Z}} {\mathrm{Z}} \gamma }$$ Z Z γ couplings.« less