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

Abstract

We present the full next-to-leading order (NLO) corrected inclusive cross section $d^3Δσ/dQ^2/dy/dp_T$ 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 $q(\bar q) + g \to γ^* + 'X'$ 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 $γ_5$-matrix. Like in the case of many other prescriptions evanescent counter terms appear. They are determined by computing the NLO coefficient functions for $dΔσ/dQ^2$ and the polarized cross section for Higgs production using both n-dimensional regularization and a four dimensional regularization technique in which the $γ_5$-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.

56 pages, LaTeX, 20 postscript figures. We have changed the discussion of the various regularization schemes in the penultimate paragraph of section 1 and in the text between Eq. (2.17) and Eq. (2.18). Furthermore a more careful comparison between our results and those in refs. [13],[14] for the quark-anti-quark channel reveals that we have full agreement. Further some misprints like the ones occuring in Eq. (2.61) and table 1 in section 4 are corrected