Abstract: This Letter reports measurements of differential cross sections for the production of two Z bosons in association with jets in proton?proton collisions at 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 35.9fb?1 at 8 and 13?TeV, respectively. The measurements are performed in the leptonic decay modes ZZ??+????+???, where ?,??=e,?. The differential cross sections as a function of the jet multiplicity, the transverse momentum pT, and pseudorapidity of the pT -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 pT -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.

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