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

Abstract

We 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 $\frac{Q_T}{M^2}(\cos (\ddot{I}•-\ddot{I}{•}_{S_1})\cos (\ddot{I}•-\ddot{I}{•}_{S_2})+3\sin (\ddot{I}•-\ddot{I}{•}_{S_1})\sin (\ddot{I}•-\ddot{I}{•}_{S_2}))$. 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 $\frac{Q_T}{M^2}(3\cos (\ddot{I}•-\ddot{I}{•}_{S_1})\cos (\ddot{I}•-\ddot{I}{•}_{S_2})+\sin (\ddot{I}•-\ddot{I}{•}_{S_1})\sin (\ddot{I}•-\ddot{I}{•}_{S_2}))$, is also given at GSI.

6 latex pages, 2 figures, to appear in PRD