2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174799We show that the transverse double spin asymmetry (DSA) in the Drell-Yan process contributed only from the Sivers functions can be picked out by the weighting function $\frac{Q_T}{M^2}(\cos(ϕ-ϕ_{S_1})\cos(ϕ-ϕ_{S_2})+3\sin(ϕ-ϕ_{S_1})\sin(ϕ-ϕ_{S_2}))$. The asymmetry is proportional to the product of two Sivers functions from each hadron $f_{1T}^{\perp(1)}\times f_{1T}^{\perp (1)}$. Using two sets of Sivers functions extracted from the semi-inclusive deeply elastic scattering data at HERMES, we estimate this asymmetry in the $p^\uparrow\bar{p}^\uparrow$ Drell-Yan process which is possible to be performed in HESR at GSI. The prediction of DSA in the Drell-Yan process contributed by the function $g_{1T}(x,\Vec k_T^2)$, which can be extracted by the weighting function $\frac{Q_T}{M^2}(3\cos(ϕ-ϕ_{S_1})\cos(ϕ-ϕ_{S_2})+\sin(ϕ-ϕ_{S_1})\sin(ϕ-ϕ_{S_2}))$, is also given at GSI.6 latex pages, 2 figures, to appear in PRDHigh Energy Physics - Phenomenologytext