  We calculate the transverse momentum distribution for the production of
massive lepton-pairs in longitudinally polarized proton-proton reactions at
collider energies within the context of perturbative quantum chromodynamics.
For values of the transverse momentum Q_T greater than roughly half the pair
mass Q, Q_T > Q/2, we show that the differential cross section is dominated by
subprocesses initiated by incident gluons, provided that the polarized gluon
density is not too small. Massive lepton-pair differential cross sections
should be a good source of independent constraints on the polarized gluon
density, free from the experimental and theoretical complications of photon
isolation that beset studies of prompt photon production. We provide
predictions for the spin-averaged and spin-dependent differential cross
sections as a function of Q_T at energies relevant for the Relativistic Heavy
Ion Collider (RHIC) at Brookhaven, and we compare these with predictions for
real prompt photon production.
