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We discuss the double-spin asymmetries in transversely polarized Drell-Yanprocess, calculating all-order gluon resummation corrections up to thenext-to-leading logarithmic accuracy. This resummation is relevant when thetransverse-momentum Q_T of the produced lepton pair is small, and reproducesthe (fixed-order) next-to-leading QCD corrections upon integrating over Q_T.The resummation corrections behave differently between pp- andp\bar{p}-collision cases and are small for the latter case at the kinematics inthe proposed GSI experiments. This fact allows us to predict large value of thedouble-spin asymmetries at GSI, using the recent empirical information on thetransversity.

Double Transverse-Spin Asymmetries for Drell-Yan Process in pp and  p\bar{p} Collisions: Role of Nonleading QCD Corrections at Small Transverse  Momentum