  In this paper, we extend the study of Drell-Yan processes with antiproton
beams already presented in a previous work. We consider the fully polarized
$\bar{p}^\uparrow p^\uparrow \to \mu^+ \mu^- X$ process, because this is the
simplest scenario for extracting the transverse spin distribution of quarks, or
transversity, which is the missing piece to complete the knowledge of the
nucleon spin structure at leading twist. We perform Monte Carlo simulations for
transversely polarized antiproton and proton beams colliding at a
center-of-mass energy of interest for the future HESR at GSI. The goal is to
possibly establish feasibility conditions for an unambiguous extraction of the
transversity from data on double spin asymmetries.
