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We discuss the Drell-Yan process at a measured transverse-momentum $Q_T$ ofthe produced lepton pair in collisions of transversely polarized protons andantiprotons, to be observed at the proposed spin experiments at GSI. The largelogarithmic contributions from multiple soft gluon emission, accompanying theDrell-Yan mechanism at small $Q_T$, are resummed to all orders in QCDperturbation theory up to next-to-leading logarithmic (NLL) accuracy. Numericalevaluation shows the impact of the NLL as well as LL effect on the dilepton$Q_T$ spectra. For the corresponding $Q_T$-dependent spin asymmetry $\aqt$, theLL effect gives significant modification while the NLL effect is marginal,leading to QCD prediction that $\aqt$ at GSI is flat at small and moderate$Q_T$ and almost equals the conventional asymmetry $A_{TT}$ associated with the$Q_T$-integrated cross sections. This flat behavior in turn allows us to useanalytic saddle-point evaluation of the resummation formula in the limit$Q_T\to 0$, not only to obtain quantitative estimate of $\aqt$, but also toclarify mechanisms behind the relation $\aqt \simeq A_{TT}$ characteristic of$p\bar{p}$ collisions at GSI.

Double-spin asymmetries for small-Q_T Drell-Yan pair production in transversely polarized p\bar{p} collisions