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We discuss the double-spin asymmetry \aqt in the transversely polarizedDrell-Yan process at small transverse-momentum Q_T of the produced dilepton.The soft gluon corrections relevant for small Q_T are resummed to all orders in\alpha_s, up to the next-to-leading logarithmic accuracy. We show that the softgluon corrections largely cancel in the spin asymmetry, but the significantcorrections still remain.The asymmetries \aqt are calculated for pp collisionat RHIC and J-PARC, and for p\bar{p} collision at GSI. A novel asymptoticformula for \aqt at small Q_T is presented, which provides a new approach toextract the transversity \delta q(x) from the experimental data.

Soft gluon resummation in Drell-Yan dilepton production at small transverse momentum: spin asymmetry and a novel asymptotic formula