Analysis of the $Hb\bar{b}$ coupling constant and $CP$-violation effects at the future $e^+e^-$-collider

The $e^+e^- \to b\bar{b}\nu \bar {\nu}$ process, where $\upsilon$ is an electron, muon, or $\tau$-lepton neutrino, is analyzed in detail for the general form of the coupling constant of a Higgs boson with $b$ quarks, with the $({m_b}/{v}) (a + i \gamma_5 b) $ parameterization of the $Hb\bar{b}$ interaction. This process is shown to be highly sensitive to this coupling constant. Experiments at the future with $\sqrt{s}= 500-GeV$ linear collider will provide limits of 2 and 20% for deviations of the parameters $a$ and $b$, respectively, from their Standard Model values. Results concerning the $e^+e^- \to b\bar{b} \nu \bar{\nu}$ process in combination with the independent measurements of the partial width ($\Gamma_{H \to b\bar{b}}$ can testify to the $CP$ origin of the Higgs sector of the theory.