Double-spin transverse asymmetries in Drell-Yan processes

We calculate the double-spin transverse asymmetries for the Drell-Yan lepton pair production in $\mathrm{pp}$ and $\overline{p}p$ collisions. We assume the transverse and the longitudinal polarization densities to be equal at a very small scale, as 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.