  We study the single spin asymmetries for the $D$-meson production, Drell-Yan
lepton-pair production and the direct-photon production in the $pp$ collision
induced by the twist-3 three-gluon correlation functions in the transversely
polarized nucleon. We present a corresponding polarized cross section formula
in the leading-order with respect to the QCD coupling and a model calculation
for the asymmetries, illustrating the sensitivity to the form of the
correlation functions.
