Z-boson quantum tomography at next-to-leading order

Abstract: We investigate the origin of the unusually large electroweak (EW) radiative effects observed in the extraction of the spin-density matrix and related observables at colliders, focusing on leptonic Z-boson decays. We compute the Z-boson-decay spin-density matrix at next-to-leading order (NLO) and find that, while its analytic structure remains essentially unchanged with respect to leading order, the EW corrections induce a sizeable $-35\%$ shift in the spin-analysing-power parameter $\eta_\ell$. This effect alone accounts for the striking size of the corrections. For boosted Z bosons, we further show that the treatment of photon radiation in lepton-dressing algorithms significantly affects the extraction of spin-density-matrix coefficients at NLO and must be carefully controlled. To address these challenges, we propose a quantum tomography procedure that is applicable to any final state with one or more on-shell Z bosons that is robust under higher-order corrections. We illustrate its validity and limitations in ${\textrm{pp}} \to {\textrm{ZZ}} \to 4\ell$ and in heavy ($M_{\textrm{H}}>2 M_{\textrm{Z}}$) Higgs-boson decay ${\textrm{H}}\to {\textrm{ZZ}} \to 4\ell$.