CP violation in the annihilation $e^{+}~e^{-} \to t~\bar{t}$ within the Model-III of the two-Higgs-doublet extension

The CP-violating effects are studied in the electron-positron annihilation to produce $t\bar{t}$ pair within the Model-III of the two-Higgs-doublet extensions, which allows flavor changing neutral currents via Higgs exchanges. Complete analytical expressions for the form factors of the top quark electric and weak dipole moment induced in the framework of the model are presented. Several observables sensitive to the CP violation are calculated. The dependences of the CP-violating effects on Higgs boson masses and the possible phase angles are discussed. We find that the CP-violating observables can be of the order of $10^{-4}$ in general but may reach to $10^{-3}$ for the most favorable parameters in the model.