Transverse momentum distribution of Drell-Yan pair in transversely polarized proton-proton collision

We discuss the QCD predictions for the transverse momentum ($Q_T$) distribution of Drell-Yan pair, produced in collisions of transversely polarized protons. We compute the 1-loop QCD corrections to transversely polarized Drell-Yan process at a measured $Q_T$ and azimuthal angle of the produced lepton in the dimensional regularization scheme. We also include soft gluon effects at small $Q_T$ by all-order resummation of logarithmically enhanced contributions up to next-to-leading logarithmic accuracy. We demonstrate that the soft gluon resummation leads to a well- defined, finite prediction of the cross section for all region of $Q_T$. We show the numerical results of the cross section using the transversity distributions $\delta q(x,Q^2 )$ which satisfy the Soffer inequality. We also discuss role of nonperturbative corrections related to the intrinsic transverse momentum distributions of partons inside protons, and present the results for the transverse double-spin asymmetry $A_{TT}$.