QCD and electroweak corrections to ZZ plus jet production with Z-boson leptonic decays at the LHC

In this paper we present the full next-to-leading-order (NLO) QCD + NLO electroweak (EW) corrections to the Z-boson pair production in association with a hard jet at the LHC. The subsequent Z-boson leptonic decays are included by adopting both the naive narrow-width approximation and MADSPIN methods for comparison. Since the ZZ + jet production is an important background for single Higgs boson production and new physics searches at hadron colliders, the theoretical predictions with high accuracy for the hadronic production of ZZ + jet are necessary. We present the numerical results of the integrated cross section and various kinematic distributions of final particles, and conclude that it is necessary to take into account the spin correlation and finite-width effects from the Z-boson leptonic decays. We also find that the NLO EW correction is quantitatively non-negligible in matching the experimental accuracy at the LHC, particularly in the high-transverse-momentum region.