We present next-to-leading order predictions for double transverse-spin asymmetries in Drell-Yan dilepton production initiated by proton-antiproton scattering. The kinematic region of the proposed PAX experiment at GSI: 30 s 200 GeV 2 and 2 M 7 GeV is examined. The Drell-Yan asymmetries turn out to be large, in the range 20-40%. Measuring these asymmetries would provide the cleanest determination of the quark transversity distributions.
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