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We show that the transverse double spin asymmetry (DSA) in the Drell-Yanprocess contributed only from the Sivers functions can be picked out by theweighting function$\frac{Q_T}{M^2}(\cos(\phi-\phi_{S_1})\cos(\phi-\phi_{S_2})+3\sin(\phi-\phi_{S_1})\sin(\phi-\phi_{S_2}))$.The asymmetry is proportional to the product of two Sivers functions from eachhadron $f_{1T}^{\perp(1)}\times f_{1T}^{\perp (1)}$. Using two sets of Siversfunctions extracted from the semi-inclusive deeply elastic scattering data atHERMES, we estimate this asymmetry in the $p^\uparrow\bar{p}^\uparrow$Drell-Yan process which is possible to be performed in HESR at GSI. Theprediction 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$\frac{Q_T}{M^2}(3\cos(\phi-\phi_{S_1})\cos(\phi-\phi_{S_2})+\sin(\phi-\phi_{S_1})\sin(\phi-\phi_{S_2}))$,is also given at GSI.

Double transverse spin asymmetry in the $p^\uparrow\bar{p}^\uparrow$ Drell-Yan process from Sivers functions