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We calculate the double-spin transverse asymmetries for the Drell-Yan lepton pair production in p-p and p-anti p collisions. We assume the transverse and the longitudinal polarization densities to be equal at a very small scale, as it is suggested by confinement model results. Using a global fit for the longitudinal distributions, we find transverse asymmetries of order of 10^-2 at most, in the accessible kinematic regions.

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