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 3 Δσ/ dQ 2/ dy/ dp T for massive lepton pair production in longitudinally polarized proton–proton collisions p+p→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 GeV. Like in unpolarized proton–proton scattering the dominant subprocess is given by q( q ̄ )+g→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.