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The recently discovered scalar resonance at the LHC is now almost confirmedto be a Higgs Boson, whose CP properties are yet to be established. At the ILCwith and without polarized beams, it may be possible to probe these propertiesat high precision. In this work, we study the possibility of probing departuresfrom the pure CP-even case, by using the decay distributions in the process$e^+ e^- \to t \bar{t} \Phi$, with $\Phi$ mainly decaying into a $b\bar b$pair. We have compared the case of a minimal extension of the SM case (Model I)with an additional pseudoscalar degree of freedom, with a more realistic casenamely the CP-violating Two-Higgs Doublet Model (Model II) that permits a moregeneral description of the couplings. We have considered the ILC with$\sqrt{s}=800$\,GeV and integrated luminosity of $300\, {\rm fb}^{-1}$. Ourmain findings are that even in the case of small departures from the CP-evencase, the decay distributions are sensitive to the presence of a CP-oddcomponent in Model II, while it is difficult to probe these departures in ModelI unless the pseudoscalar component is very large. Noting that the proposeddegrees of beam polarization increases the statistics, the process demonstratesthe effective role of beam polarization in studies beyond the Standard Model.Further, our study shows that an indefinite CP Higgs would be a sensitivelaboratory to physics beyond the SM.

Probing the indefinite CP nature of the Higgs Boson through decay distributions in the process $e^+e^-\to t\bar{t}\Phi$