Spin Dependent Drell-Yan in QCD to Order Alpha-Strong Squared: The Non-Singlet Sector

Sanghyeon Chang, Claudio Coriano, R. D. Field, and L. E. Gordon

Institute for Fundamental Theory, Department of Physics, University of Florida, Gainesville, FL 32611

Abstract

A study of the order alpha-strong squared corrections to the Drell-Yan (non-singlet) differential cross section for incoming states of arbitrary longitudinal helicities is presented. The transverse momentum distributions, 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 MSbar 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 MSbar scheme helicity is not conserved along the quark lines, unless a finite renormalization is done and one adapts the physical MSbar_P scheme. This aspect of the calculation is similar to the order alpha-strong squared polarized production of single and double photons. Our spin averaged unpolarized differential cross sections agree with the EMP calculations.