This Letter reports measurements of differential cross sections for the production of two Z bosons in association with jets in proton-proton collisions at $\sqrt{s} =$ 8 and 13 TeV. The analysis is based on data samples collected at the LHC with the CMS detector, corresponding to integrated luminosities of 19.7 and 35.9 fb$^{-1}$ at 8 and 13 TeV, respectively. The measurements are performed in the leptonic decay modes ZZ $\to\ell^+ \ell^- \ell'^+ \ell'^-$, where $\ell,\ell' =$ e, $\mu$. The differential cross sections as a function of the jet multiplicity, the transverse momentum $p_\mathrm{T}$, and pseudorapidity of the $p_\mathrm{T}$-leading and subleading jets are presented. In addition, the differential cross sections as a function of variables sensitive to the vector boson scattering, such as the invariant mass of the two $p_\mathrm{T}$-leading jets and their pseudorapidity separation, are reported. The results are compared to theoretical predictions and found in good agreement within the theoretical and experimental uncertainties.
Data from Fig. 2 upper right panel. The $\textrm{pp} \to \textrm{ZZ}\to \ell\ell\ell^{\prime}\ell^{\prime}$ differential cross section at $\sqrt{s} = 13$ TeV as a function of the jet multiplicity with $|\eta_{j}| < 4.7$.
Data from Fig. 3 upper right panel. The $\textrm{pp} \to \textrm{ZZ}\to \ell\ell\ell^{\prime}\ell^{\prime}$ normalized differential cross section at $\sqrt{s} = 13$ TeV as a function of the jet multiplicity with $|\eta_{j}| < 4.7$.
Data from Fig. 2 lower right panel. The $\textrm{pp} \to \textrm{ZZ}\to \ell\ell\ell^{\prime}\ell^{\prime}$ differential cross section at $\sqrt{s} = 13$ TeV as a function of the jet multiplicity with $|\eta_{j}| < 2.4$.