Transverse Spin Dependent Drell Yan in QCD to $O({\alpha }_s^2)$ at Large $p_T$ (I). Virtual Corrections and Methods for the Real Emissions

We investigate the role of the transverse spin dependence in Drell Yan lepton pair production to NLO in QCD at parton level. In our analysis we deal with the large $p_T$ distributions. We give very compact expressions for the virtual $O({\alpha }_s^2)$ corrections to the cross section and show that the singularities factorize. The study is performed in the $\overline{MS}$ scheme in Dimensional Regularization, and with the t’Hooft-Veltman prescription for ${\gamma }_5$. A discussion of the structure of the real emissions is included, and detailed methods for the study of these contributions are formulated.