NLO differential distributions of massive lepton-pair production in longitudinally polarized proton-proton collisions

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.