  We present predictions of the unweighted and weighted double spin asymmetries
related to the transversal helicity distribution $g_{1T}$ and the longitudinal
transversity distribution $h_{1L}^\perp$, 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.
