Determination of CP-violating $HZZ$ interaction with polarised beams at the ILC

We study possible CP-violation effects of the 125 GeV Higgs to Z boson coupling at the 250 GeV ILC with transverse and longitudinal beam polarisation via the process e⁺ e⁻ → HZ → H μ⁻μ⁺. We explore the azimuthal angular distribution of the muon pair from the Z boson decay, and constructe CP-odd observables sensitive to CP-violation effects, where we derived this observable both by analytical calculations and by Whizard simulations. Particularly, we can construct two CP-odd observables with the help of transversely-polarised initial beams and improve the statistical significance of CP-violation effects by combining two measurements. We defined the asymmetries between the signal regions with different signs of the CP-odd observables, and determine the CP-violation effect by comparing with the SM 95% C.L. upper bound. In this paper, we setup a scenario which assumes that the total cross-section is always fixed while CP-violation is varying, and such a scenario helps us to determine the intrinsic CP-mixing angle limit around |ξCP|~ 0.03 with (90%, 40%) polarised electron-positron beams and 5 ab⁻¹ integrated luminosity. In addition, we determine the CP-odd coupling limit |cHZZ|~ 0.01 as well, where we suppose that the SM tree-level cross-section is fixed and the CP-violation is the varying additional contribution. Comparing with the analysis with unpolarised beams, the sensitivity to the CP-violation effect can be improved by transverse or longitudinal polarisation.