  We study the single transverse-spin asymmetry for inclusive light-hadron
productions in the proton-proton collision, $\pphx$ ($h=\pi,K,\eta$), for the
RHIC kinematics based on the twist-3 mechanism in the collinear factorization.
The analysis includes all the contributions from the soft-gluon pole and the
soft-fermion pole for the twist-3 quark-gluon correlation functions in the
transversely polarized proton. After discussing the flavor decomposition and
the $P_T$-dependence of the asymmetry obtained in the previous analysis at the
center-of-mass energy $\sqrt{S}=62.4$ and 200 GeV, we will give a prediction
for the asymmetry at $\sqrt{S}=500$ GeV and also for the $\eta$-meson
production. We found slightly smaller asymmetry at $\sqrt{S}=500$ GeV for
$\pi^{\pm,0}$ and $K^+$ compared with those at the lower energies. The
asymmetry for the $\eta$-meson turned out to be significantly larger than that
for $\pi^0$.
