New sets of parameters (“tunes”) for the underlying-event (UE) modelling of the pythia8, pythia6 and herwig++ Monte Carlo event generators are constructed using different parton distribution functions. Combined fits to CMS UE proton–proton ((mathrm {p}mathrm {p})) data at (sqrt{s} = 7, ext {TeV} ) and to UE proton–antiproton ((mathrm {p}overline{mathrm{p}} )) data from the CDF experiment at lower (sqrt{s}), are used to study the UE models and constrain their parameters, providing thereby improved predictions for proton–proton collisions at 13(, ext {TeV}). In addition, it is investigated whether the values of the parameters obtained from fits to UE observables are consistent with the values determined from fitting observables sensitive to double-parton scattering processes. Finally, comparisons are presented of the UE tunes to “minimum bias” (MB) events, multijet, and Drell–Yan (( mathrm{q} overline{mathrm{q}} ightarrow mathrm{Z}/ gamma ^* ightarrow ) lepton-antilepton+jets) observables at 7 and 8(, ext {TeV}), as well as predictions for MB and UE observables at 13(, ext {TeV}).
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