Polarized vector boson scattering in the fully leptonic WZ and ZZ channels at the LHC

Isolating the scattering of longitudinal weak bosons at the LHC is an important tool to probe the ElectroWeak Symmetry Breaking mechanism. Separating polarizations of $W$ and $Z$ bosons is complicated, because of non resonant contributions and interference effects. Additional care is necessary when considering $Z$ bosons, due to the $\gamma/Z$ mixing in the coupling to charged leptons. We propose a method to define polarized signals in $Z\!Z$ and $W^+\!Z$ scattering at the LHC, which relies on the separation of weak boson polarizations at the amplitude level in Monte Carlo simulations. After validation in the absence of lepton cuts, we investigate how polarized distributions are affected by a realistic set of kinematic cuts (and neutrino reconstruction, when needed). The total and differential polarized cross sections computed at the amplitude level are well defined, and their sum reproduces the full results, up to non negligible but computable interference effects which should be included in experimental analyses. We show that polarized cross sections computed using the reweighting method are inaccurate, particularly at large energies. We also present two procedures which address the model independent extraction of polarized components from LHC data, using Standard Model angular distribution templates.