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New neutral vector bosons $Z'$ decaying to charged gauge boson pairs $W^+W^-$are predicted in many scenarios of new physics, including models with anextended gauge sector such as $E_6$, left-right symmetric $Z^\prime_{\rm LRS}$and the sequential standard model $Z'_{\rm SSM}$. For these benchmark models wecalculate and present theoretical expectations for different values of the$Z^\prime$ mass $M_2$ and mixing parameter $\xi$. Our results are based on thenarrow width approximation which allows to make a convenient comparison ofexperiment to theoretical benchmark models. The diboson production allows toplace stringent constraints on the $Z$-$Z'$ mixing angle and the $Z'$ mass,which we determine by using data from $pp$ collisions at $\sqrt{s}=13$ TeVrecorded by the ATLAS detector at the CERN LHC, with integrated luminosity of$\sim$ 36 fb$^{-1}$. By comparing the experimental limits to the theoreticalpredictions for the total cross section of $Z'$ resonant production and itssubsequent decay into $W^+W^-$ pairs, we show that the derived constraints onthe mixing angle for the benchmark models are of the order of a few $\times10^{-4}$, i.e., greatly improved with respect to those derived from the globalanalysis of electroweak data. We combine the limits derived from dibosonproduction data with those obtained from the Drell--Yan process in order tosignificantly extend the exclusion region in the $M_{2}$-$\xi$ parameter plane.Also, we demonstrate that further improvement on the constraining of thismixing can be achieved through analysis of the full set of Run~II data.

Improved constraints on the mixing and mass of $Z'$ bosons from resonant diboson searches at the LHC at $\sqrt{s}=13$ TeV and predictions for Run II