Full NLO electroweak corrections to Z-boson pair production at the Large Hadron Collider

We report on a recent calculation of the full next-to-leading-order electroweak corrections to Z-boson pair production with subsequent decays into four charged leptons. Using the complete matrix elements at leading order and next-to-leading order in the electroweak coupling for the processes $pp\to\mu^+\mu^-e^+e^-$ and $pp \to\mu^+\mu^-\mu^+\mu^-$, this includes all off-shell effects of intermediate massive vector bosons and photons. We employ a gauge-invariant splitting for the electroweak corrections into purely weak and photonic corrections. The latter show the well-known radiative tails near kinematical thresholds or resonances. The former are generically at the level of $\sim-5\%$ for the fiducial cross section and reach several $-10\%$ in the high-energy tails of distributions due to logarithms of electroweak origin. The impact of interference effects due to equal-flavour leptons in the final state can reach the order of $5\%$ in off-shell-sensitive regions. Photon-induced contributions are included in our calculation, but turn out to be phenomenologically unimportant.