We present a study of the polarization observables of the $W$ and $Z$ bosons in the process $p p to W^pm Zto e^pm u_e mu^+mu^-$ at the 13 TeV Large Hadron Collider. The calculation is performed at next-to-leading order, including the full QCD corrections as well as the electroweak corrections, the latter being calculated in the double-pole approximation. The results are presented in the helicity coordinate system adopted by ATLAS and for different inclusive cuts on the di-muon invariant mass. We define left-right charge asymmetries related to the polarization fractions between the $W^+ Z$ and $W^- Z$ channels and we find that these asymmetries are large and sensitive to higher-order effects. Similar findings are also presented for charge asymmetries related to a P-even angular coefficient.
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