Spin dependent Drell Yan in QCD to O({alpha}{sub s}{sup 2}) (I). (The non-singlet sector)

Abstract

A study of the order {alpha}{sub s}{sup 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{sub T}, of the lepton pair are studied and the calculations of Ellis, Martinelli, and Petronzio (EMP) are extended to include polarized initial states. The authors use the {ovr MS} scheme and the t`Hooft-Veltman regularization for the helicity projectors. From the 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. They show that in the {ovr MS} scheme helicity is not conserved along the quark lines, unless a finite renormalization is done and one adapts the physical ({ovr MS{sub p}}) scheme. This aspect of the calculation is similar to the O({alpha}{sub s}{sup 2}) polarized production of single and double photons. The spin averaged unpolarized differential cross sections agree with the EMP calculations.

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