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The measurement of the luminosity recorded by the CMS detector installed at LHC interaction point 5, using proton–proton collisions at $$\sqrt{s}=13\,{\text {TeV}} $$ s = 13 TeV in 2015 and 2016, is reported. The absolute luminosity scale is measured for individual bunch crossings using beam-separation scans (the van der Meer method), with a relative precision of 1.3 and 1.0% in 2015 and 2016, respectively. The dominant sources of uncertainty are related to residual differences between the measured beam positions and the ones provided by the operational settings of the LHC magnets, the factorizability of the proton bunch spatial density functions in the coordinates transverse to the beam direction, and the modeling of the effect of electromagnetic interactions among protons in the colliding bunches. When applying the van der Meer calibration to the entire run periods, the integrated luminosities when CMS was fully operational are 2.27 and 36.3 $$\,\text {fb}^{-1}$$ fb - 1 in 2015 and 2016, with a relative precision of 1.6 and 1.2%, respectively. These are among the most precise luminosity measurements at bunched-beam hadron colliders.

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 - 1 , 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.

A search for dark matter particles is performed using events with a Z boson candidate and large missing transverse momentum. The analysis is based on proton–proton collision data at a center-of-mass energy of 13$$\,\text {Te}\text {V}$$ Te , collected by the CMS experiment at the LHC in 2016–2018, corresponding to an integrated luminosity of 137$$\,\text {fb}^{-1}$$ fb - 1 . The search uses the decay channels $${\mathrm{Z}} \rightarrow {\mathrm{e}} {\mathrm{e}} $$ Z → e e and $${\mathrm{Z}} \rightarrow {{\upmu }{}{}} {{\upmu }{}{}} $$ Z → μ μ . No significant excess of events is observed over the background expected from the standard model. Limits are set on dark matter particle production in the context of simplified models with vector, axial-vector, scalar, and pseudoscalar mediators, as well as on a two-Higgs-doublet model with an additional pseudoscalar mediator. In addition, limits are provided for spin-dependent and spin-independent scattering cross sections and are compared to those from direct-detection experiments. The results are also interpreted in the context of models of invisible Higgs boson decays, unparticles, and large extra dimensions.

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