  We present the full next-to-leading order (NLO) corrected inclusive cross
section $d^3\Delta \sigma/dQ^2/dy/dp_T$ for massive lepton pair production in
longitudinally polarized proton-proton collisions $p + p\to l^+l^- + 'X'$. Here
$'X'$ denotes any inclusive hadronic state and Q represents the invariant mass
of the lepton pair which has transverse momentum p_T and rapidity y. All QCD
partonic subprocesses have been included provided the lepton pair is created by
a virtual photon, which is a valid approximation for $Q<50{\rm GeV}$. Like in
unpolarized proton-proton scattering the dominant subprocess is given by
$q(\bar q) + g \to \gamma^* + 'X'$ so that massive lepton pair production
provides us with an excellent method to measure the spin density of the gluon.
Our calculations are carried out using the method of n-dimensional
regularization by making a special choice for the $\gamma_5$-matrix. Like in
the case of many other prescriptions evanescent counter terms appear. They are
determined by computing the NLO coefficient functions for $d\Delta\sigma/dQ^2$
and the polarized cross section for Higgs production using both n-dimensional
regularization and a four dimensional regularization technique in which the
$\gamma_5$-matrix is uniquely defined. Our calculations reveal that the
non-singlet polarized coefficient function equals the unpolarized one up to a
minus sign. We give predictions for double longitudinal spin asymmetry
measurements at the RHIC.
