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We recently estimated pion+X production via proton collisions with apolarized proton target to enable the Collins fragmentation function to bedetermined via future experiments. In the present article we first estimate theSilvers differential cross section obtianed from experiments with the targetproton having both positive and negative polarizations, and then estimate theSivers Function using quark distribution functions.

Sivers Differential Cross Section for $\pi+X$ Production via $p^{\uparrow}+p$ Collisions, and the Quark Sivers Function