Heavy quark polarizations of $e^{+}{e}^{-}\to q\bar{q}h$ in the general two Higgs doublet model

The polarizations of the heavy quark ($q=t$ or $b$) in the process $e^+e^- \to q \bar q h$ have been calculated in the general two Higgs doublet model. The CP violating normal polarization of the top quark can reach 8%, and $2 \sim 3%$ for the bottom quark, while it is zero in the standard model. The longitudinal and transverse polarizations of the bottom quark can be significantly different from those in SM and consequently could aslo be used as the probe of the new physics.