  Accurate measurement of spin-dependent parton distributions in production of
electroweak bosons with polarized proton beams at the Relativistic Heavy Ion
Collider depends on good understanding of QCD radiation at small transverse
momenta $q_T$ of vector bosons. We present a theoretical formalism for
small-$q_T$ resummation of the cross sections for production of virtual
photons, W, and Z bosons, with the subsequent decay of these bosons into lepton
pairs, for arbitrary longitudinal polarizations of the proton beams.
