Resummation in Transversely Polarized Drell - Yan Process

Hard processes with polarized nucleon beams enable us to study spin-dependent dynamics of QCD and the spin structure of nucleon. The helicity distribution ∆q(x) of quarks within nucleon has been measured in polarized DIS experiments, and ∆G(x) of gluons has also been estimated from the scaling violations of them. On the other hand, the transversity distribution δq(x), i.e. the distribution of transversely polarized quarks inside transversely polarized nucleon, can not be measured in inclusive DIS due to its chiral-odd nature,1 and remains as the last unknown distribution at the leading twist. Transversely polarized Drell-Yan (tDY) process is one of the processes where the transversity distribution can be measured, and has been undertaken at RHIC-Spin experiment. We compute the 1-loop QCD corrections to tDY at a measured QT and azimuthal angle φ of the produced lepton in the dimensional regularization scheme. For this purpose, the phase space integration inD-dimension, separating out the relevant transverse degrees of freedom, is required to extract the ∝cos(2φ) part of the cross section characteristic of the spin asymmetry of tDY.1 The calculation is rather cumbersome compared with the corresponding calculation in unpolarized and longitudinally polarized cases, and has not been performed so far. We obtain the NLO