$ZZγ$ production in the NLO QCD+EW accuracy at the LHC

Abstract: In this paper we present the first study of the impact of the $\mathcal{O}(\alpha)$ EW correction to the $pp \to ZZ \gamma+X$ process at the CERN Large Hadron Collider (LHC). The subsequent $Z$-boson leptonic decays are considered at the leading order using the MadSpin method, which takes into account the spin-correlation and off-shell effects from the $Z$-boson decays. We provide numerical results of the integrated cross section and the kinematic distributions for this process. In coping with final-state photon-jet separation in the QCD real emission and photon-induced processes, we adopt both the Frixione isolated-photon plus jets algorithm and the phenomenological quark-to-photon fragmentation function method for comparison. We find that the next-to-leading order (NLO) EW correction to the $ZZ\gamma$ production can be sizeable and amounts to about $-7\%$ of the integrated cross section, and provides a non$-$negligible contribution to the kinematic distributions, particularly in the high energy region. We conclude that the NLO EW correction should be included in precision theoretical predictions in order to match future experimental accuracy.