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Spin Dependent Drell-Yan beyond Leading Order: Non-Singlet Virtual corrections to $O(α_s^2)$

We present parton-level analytical results for the next-to-leading order non-singlet virtual and real corrections to the Drell-Yan differential cross-section. The dependence of the differential cross section on the helicity of the initial state partons is shown explicitly (the spins of the final state partons are summed). The calculation is implemented in dimensional regularization within the $\bar{MS}$ scheme and with the t'Hooft Veltman prescriptions for the n-dimensional $γ_5$. Both the polarized initial state and the unpolarized cross sections can be obtained from our result. Our unpolarized cross section agrees with the previous result of Ellis, Martinelli and Petronzio in the non-singlet sector.