  In order to measure spin-dependent parton distributions in production of weak
bosons using the non-hermetic detectors of the Relativistic Heavy Ion Collider,
an accurate model for distributions of charged leptons from the W boson decay
is needed. We discuss the predictions for production and decay of the W bosons
based on a calculation for resummation of large logarithmic contributions
originating from multiple soft gluon radiation. We compare the predictions for
the spin-dependent resummed cross sections with the corresponding
next-to-leading order results. We show that the lepton-level asymmetries can be
reliably predicted by the resummation calculation and directly compared to the
experimental data. A program for the numerical analysis of such cross sections
in $\gamma ^{*}, W^{\pm},$ and $Z^{0}$ boson production is also presented.
