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

We consider QCD radiative corrections to $ZZ$ production for all experimentally relevant leptonic processes. We report on a novel computation of next-to-next-to-leading-order (NNLO) corrections to the diboson signature with two charged leptons and missing transverse energy ($\ell\ell$+$E_T^{\rm miss}$). 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 also study processes with four charged leptons: $\ell\ell\ell\ell$ and $\ell\ell\ell'\ell'$. For the first time NNLO accuracy is achieved for a process mixing two double-resonant diboson topologies ($ZZ/W^+W^-\to\ell\ell\nu_\ell\nu_\ell$). We find good agreement with ATLAS data at 8 TeV. NNLO corrections are large (5-20% and more), and interference effects between $ZZ$ and $W^+W^-$ resonances turn out to be negligible in most cases.