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We consider QCD radiative corrections to $ZZ$ production for allexperimentally relevant leptonic processes. We report on a novel computation ofnext-to-next-to-leading-order (NNLO) corrections to the diboson signature withtwo charged leptons and missing transverse energy ($\ell\ell$+$E_T^{\rmmiss}$). All relevant final states are considered: $\ell\ell\nu_\ell\nu_\ell$,$\ell\ell\nu_{\ell'}\nu_{\ell'}$ and $\ell\nu_{\ell}\ell'\nu_{\ell'}$. We alsostudy processes with four charged leptons: $\ell\ell\ell\ell$ and$\ell\ell\ell'\ell'$. For the first time NNLO accuracy is achieved for aprocess mixing two double-resonant diboson topologies($ZZ/W^+W^-\to\ell\ell\nu_\ell\nu_\ell$). We find good agreement with ATLASdata at 8 TeV. NNLO corrections are large (5-20% and more), and interferenceeffects between $ZZ$ and $W^+W^-$ resonances turn out to be negligible in mostcases.

$ZZ$ production at the LHC: NNLO predictions for $2\ell2\nu$ and $4\ell$ signatures