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.
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