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

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 ηℓ. 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 pp → ZZ → 4ℓ and in heavy (MH > 2MZ) Higgs boson decay H → ZZ → 4ℓ.