Probing CPV mixing in the Higgs sector in VBF at 1 TeV ILC

With the current precision of measurements by the ATLAS and CMS experiments, it cannot be excluded that a SM-like Higgs boson is a CP violating mixture of CP-even and CP-odd states. We explore this possibility here, assuming Higgs boson production in ZZ-fusion, at 1 TeV ILC, with unpolarized beams. The full simulation of SM background and fast simulation of the signal is performed, simulating 8 ab$^{-1}$ of data collected with the ILD detector. We demonstrate that the CP mixing angle $\Psi_{\mathrm{CP}}$ between scalar and pseudoscalar states can be measured with the statistical uncertainty of 3.8 mrad at 68% CL, corresponding to 1.44 $\cdot 10^{-5}$ for the CP parameter $f_\mathrm{CP}$, for the pure scalar state. This is the first result on sensitivity of an $e^{+}e^{-}$ collider to measure $f_\mathrm{CP}$ in the Higgs production vertex in vector boson fusion.