  We study parity-even and parity-odd polarization observables for the process
$p \, p \to l^{\pm} \, X$, where the lepton comes from the decay of a
$W$-boson. By using the collinear twist-3 factorization approach, we consider
the case when one proton is transversely polarized, while the other is either
unpolarized or longitudinally polarized. These observables give access to two
particular quark-gluon-quark correlation functions, which have a direct
relation to transverse momentum dependent parton distributions. We present
numerical estimates for RHIC kinematics. Measuring, for instance, the
parity-even transverse single spin correlation would provide a crucial test of
our current understanding of single spin asymmetries in the framework of QCD.
