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

A study of the order alpha(s)(2) corrections to the Drell-Yan (non-singlet) differential cross section for incoming states of arbitrary longitudinal helicities is presented. The transverse momentum distributions, q(T), 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)over bar> scheme and the 't 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)over bar> scheme helicity is not conserved along the quark lines, unless a finite renormalization is done and one adapts the physical (<(MS)over bar>(p)) scheme. This aspect of the calculation is similar to the O(alpha(s)(2)) polarized production of single and double photons. Our spin-averaged unpolarized differential cross sections agree with the EMP calculations. (C) 1998 Elsevier Science B.V.