Precision study on $ZZ\gamma$ production including $Z$-boson leptonic decays at the ILC

TL;DR

This paper provides precise predictions for the $ZZ\gamma$ production process at the ILC, including NLO electroweak corrections and high order initial state radiation effects, crucial for accurate experimental analysis.

Contribution

It presents the first comprehensive calculation of NLO EW and high order ISR corrections for $ZZ\gamma$ production with leptonic $Z$ decays at the ILC, incorporating spin correlations.

Findings

NLO EW corrections significantly suppress the LO cross section.

High order ISR effects are prominent near the production threshold.

Corrections are less significant at higher energies.

Abstract

We report on the precision predictions for the $e^+e^-\to ZZ\gamma$ 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 investigate the corresponding NLO EW and h.o.ISR relative corrections. We also study the leptonic decays of the final $Z$-boson pair by adopting the {\sc 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.