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We study the single transverse spin asymmetries in the single inclusiveparticle production within the framework of the generalized parton model (GPM).By carefully analyzing the initial- and final-state interactions, we includethe process-dependence of the Sivers functions into the GPM formalism. Themodified GPM formalism has a close connection with the collinear twist-3approach. Within the new formalism, we make predictions for inclusive $\pi^0$and direct photon productions at RHIC energies. We find the predictions areopposite to those in the conventional GPM approach.

Process dependent Sivers function and implications for single spin asymmetry in inclusive hadron production