We present predictions of the unweighted and weighted double spin asymmetries
related to the transversal helicity distribution g1T and the longitudinal
transversity distribution h1L⊥, two of eight leading-twist transverse
momentum dependent parton distributions (TMDs) or three-dimensional parton
distribution functions (3dPDFs), in the polarized proton-antiproton Drell-Yan
process at typical kinematics on the Facility for Antiproton and Ion Research
(FAIR). We conclude that FAIR is ideal to access the new 3dPDFs towards a
detailed picture of the nucleon structure.Comment: 6 latex pages, 5 figures, version for publication in EPJ