Spin asymmetries at RHIC and polarized parton distributions

We discuss polarized parton distributions and their effects on spin asymmetries at RHIC. In particular, transversity distributions and transverse spin asymmetry are studied. First, we show the $Q^2$ evolution difference between a transversity distribution and a corresponding longitudinally polarized distribution. The difference could be an important test of perturbative QCD in high-energy spin physics. Then, the transverse spin asymmetry $A_{TT}$ is calculated with possible transversity distributions. Next, we study antiquark flavor asymmetry $\Delta_{_T} \bar u/ \Delta_{_T} \bar d$ in the transversity distributions by using a simple model. Its effects on the transverse spin asymmetry are also discussed.