Observation of Longitudinal-Longitudinal Interactions at High $p_T^Z$ and Studies of the Radiation Amplitude Zero Effect in $W^\pm Z$ Events with the ATLAS Detector at the Large Hadron Collider

Polarization of vector bosons offers unique avenues for exploring the Standard Model (SM) of particle physics and effects going beyond. Two such approaches investigate delicate gauge cancellations at high energies in $W^\pm Z$ events where both bosons are transversally polarized (TT) and the energy dependence of the fraction of events where both bosons are longitudinally polarized (00). The former is known as the radiation amplitude zero (RAZ) effect. To achieve this, events with leptonically decaying $W^\pm Z$ bosons are selected in the Run 2 data of the ATLAS experiment at the LHC. This data was recorded at a center-of-mass energy of $\sqrt{s}=13$ TeV and encompasses an integrated luminosity of $140$ fb$^{-1}$. The fraction of doubly longitudinally polarized events in a region with $p_T^{WZ} < 70$ GeV and $100 < p_T^Z \leq 200$ GeV is measured to be $18.9\pm^{3.4}_{3.3}(\text{stat.})\pm^{2.4}_{2.2}(\text{syst.})\%$. When the $p_T^Z$ cut is changed to $p_T^Z > 200$ GeV, the value is determined to be $13\pm^{9}_{8}(\text{stat.})\pm^{2}_{2}(\text{syst.})\%$. The former is accompanied by a significance of $5.2\sigma$ over the null hypothesis that no 00 state exists. If the measurement is performed with a more restricted model, evidence for the 00 state is also found in the $p_T^Z >200$ GeV region with a significance of $3.2\sigma$. Using $100 < p_T^Z \leq 200$ GeV, a lower bound of $2.8\sigma$ is determined for the significance of rejecting the hypothesis that the fractions of longitudinally polarized $W^\pm$ and $Z$ bosons are independent of each other. The RAZ effect is probed through the unfolding of the $\Delta Y(WZ)$ and $\Delta Y(\ell_WZ)$ observables for the TT polarization state and the sum of polarizations in regions requiring $p_T^{WZ}$ to be smaller than $10,20,40$, or $70$ GeV, or unconstrained. Here, the effect is realized as a reduction of the differential cross-section around $\Delta Y=0$. A depth variable ($D$) is introduced to quantify the size of this dip and measured to be $0.68\pm0.10$ and $0.29\pm0.06$ for the TT state in the region with $p_T^{WZ} < 70$ GeV using $\Delta Y(WZ)$ and $\Delta Y(\ell_WZ)$, respectively. The former represents an estimated significance of $D/\Delta D = 7.0$ and indicates a precise measurement of the depth.