  Within the so-called color gauge invariant generalized parton model, a TMD
scheme including initial- (ISI) and final-state (FSI) interactions, we present
a phenomenological analysis of available SSA data for pion and $D$-meson
production in $pp$ collisions. This allows us, for the first time, to put a
preliminary constraint on the two universal types of gluon Sivers function
entering the model. Predictions for SSAs in $J/\psi$ and direct photon
production, as well as a comparison with the simpler generalized parton model
(without ISIs and FSIs), are also presented.
