Measurement of the $\mathrm{pp}\to\mathrm{WZ}$ inclusive and differential cross sections, polarization angles and search for anomalous gauge couplings at $\sqrt{s} = 13~\mathrm{TeV}$

The associated production of a $\mathrm{W}$ and a $\mathrm{Z}$ boson is studied in multileptonic final states produced in proton-proton collisions at a centre-of-mass energy of $\sqrt{s} = 13~\mathrm{TeV}$ using $137~\mathrm{fb}^{-1}$ of data collected with the CMS detector. A measurement of the total production cross section yields a result of $\sigma_{\textrm{Tot}}(\mathrm{pp} \rightarrow \mathrm{WZ}) = 50.6 \pm 0.8~(\mathrm{stat}) \pm 1.5~(\textrm{syst}) \pm 1.1~(\mathrm{lumi}) \pm 0.5~(\textrm{theo})~\mathrm{pb}$. Measurements of the fiducial and differential cross sections, for several key observables, are also performed in all the different final state lepton flavour and charge compositions. All results are compared with theoretical predictions computed up to next-to-next-to-leading order in quantum chromodynamics plus next-to-leading order in electroweak theory and for different sets of parton distribution functions. Several interpretations of the results are performed to study the properties of the $\mathrm{W}$ and $\mathrm{Z}$ bosons in $\mathrm{WZ}$ production, including direct measurements of the charge asymmetry and vector boson polarization states. The first observation of longitudinally polarized $\mathrm{W}$ bosons in $\mathrm{WZ}$ production is reported. An interpretation of the results in terms of a search for the presence of anomalous gauge couplings is performed and leads to new constraints on the presence of beyond-the-standard-model anomalies in the $\mathrm{WWZ}$ triple gauge coupling.