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We discuss the double-spin asymmetries in transversely polarized Drell-Yan process, calculating all-order gluon resummation corrections up to the next-to-leading logarithmic accuracy. This resummation is relevant when the transverse-momentum of the produced lepton pair is small, and reproduces the (fixed-order) next-to-leading QCD corrections upon integrating over . The resummation corrections in -collision behave differently compared with -collision cases, and are small at the kinematics in the proposed GSI experiments. This fact allows us to predict large value of the double-spin asymmetries at GSI, using recent empirical information on the transversity.

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