Spin-dependent Drell-Yan in QCD to O(αs2) (I). The non-singlet sector Original Research Article

A study of the order αs2 corrections to the Drell-Yan (non-singler) differential cross section for incoming states of arbitrary longitudinal helicities is presented. The transverse momentum distributions, qT, of the lepton pair are studied and the calculations of Ellis, Martinelli, and Petronzio (EMP) are extended to include polarized initial states. We use the MS scheme and the ʹt Hooft-Veltman regularization for the helicity projectors. From our results one can obtain the bulk of the totally inclusive NNLO cross section for the production of a Drell-Yan pair in the non-singlet sector by a simple integration over the virtual photon momentum. We show that in the MS scheme helicity is not conserved along the quark lines, unless a finite renormalization is done and one adapts the physical (MSp) scheme. This aspect of the calculation is similar to the O(αs2) polarized production of single and double photons. Our spin-averaged unpolarized differential cross sections agree with the EMP calculations.