Precision study of ZZγ production including Z-boson leptonic decays at the ILC

We report on the precision predictions for the e(+) e(-). ZZ gamma process including Z-boson leptonic decays at the ILC in the standard model (SM). The calculation includes the full next-to-leading (NLO) electroweak (EW) corrections and high order initial state radiation (h.o. ISR) contributions. We find that the NLO EW corrections heavily suppress the LO cross section, and the h.o. ISR effects are notable near the threshold while become small in high energy region. We present the LO and the NLO EW + h.o. ISR corrected distributions of the transverse momenta of final Z-boson and photon as well as the Z-pair invariant mass, and we investigate the corresponding NLOEW and h.o. ISR relative corrections. We also study the leptonic decays of the final Z-boson pair by adopting the MadSpin method where the spin correlation effect is involved. We conclude that both the h.o. ISR effects and the NLO EW corrections are important in exploring the ZZ gamma production at the ILC.