Doubly-polarized $WZ$ hadronic production at NLO QCD+EW: Calculation method and further results

The doubly-polarized production of $W^\pm Z$ pairs at the Large Hadron Collider (LHC) is presented at next-to-leading order (NLO) accuracy both for the electroweak (EW) and QCD corrections, including a detailed description of the calculational method using the double-pole approximation. Numerical results at the 13 TeV LHC are presented in particular for the $W^- Z$ case in the $e^-\bar{\nu}_e \mu^+\mu^-$ channel using ATLAS fiducial cuts and for polarized distributions defined in the $WZ$ center-of-mass system. The NLO EW corrections relative to the NLO QCD predictions are found to be smaller than $5\%$ in most kinematic distributions, but can reach the level of $10\%$ in some distributions such as lepton transverse momentum distributions or rapidity separation between the electron and the $Z$ boson. EW corrections are not uniform for different polarizations. A comparison between the new ATLAS measurement of polarization fractions to our theoretical prediction is presented.