MC simulation of vector boson production in polarized proton collisions

We present a Monte Carlo (MC) study of $W^{\pm}$ and $Z_{0}$ production of longitudinally polarized proton collisions at a center of mass (CMS) energy of $500\,{\rm GeV}$. All results were obtained with the SPHINX MC code. We consider two different types of polarized parton distributions with large and small gluon polarization. Various spin asymmetries are found to be sensitive to the shape of the polarized gluon distribution between $0.1\stackrel{<}{\sim}x\stackrel{<}{\sim}0.5$. The asymmetries are approximately constant with respect to the transverse momentum carried by the $W^{\pm}$ and $Z_{0}$, {\em except} if the first moment of the gluon polarization is large. In this case some $W^{\pm}$ asymmetries show a significant variation with transverse momentum.