Determination of CP-violating Higgs couplings with transversely-polarized beams at the ILC

We study possible CP-violation effect of the Higgs to Z boson coupling at the future e⁺ e⁻ collider (ILC). We find that the azimuthal angular distribution of the muon pair, produced by e⁺ e⁻ → H Z → H μ⁺ μ⁻, can be sensitive to such a CP-violation effect when we apply initial transversely polarized beams. Based on this angular distribution, we construct a CP sensitive asymmetry, and obtain this asymmetry by Whizard simulation. By comparing the SM prediction with 2σ range of this asymmetry, we estimate the discovery limit of the CP-odd coupling in $HZZ$ interaction.