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We estimate the single-spin asymmetries (SSA) which provide the access totransversity as well as to Boer-Mulders and Sivers PDFs via investigation ofthe single-polarized Drell-Yan (DY) processes with $ pp$, $pD$ and $DD$collisions available to RHIC, NICA, COMPASS, and J-PARC. The feasibility ofthese SSA is studied with the new generator of polarized DY events. Theperformed estimations demonstrate that there exist the such kinematical regionswhere SSA are presumably measurable. The most useful for PDFs extraction arethe limiting kinematical ranges, where one can neglect the sea PDFscontributions which occur at large values of Bjorken x. It is of interest thaton the contrary to the Sivers PDF, the transversity PDF is presumablyaccessible only in the especial kinematical region. On the contrary to theoption with the symmetric collider mode (RHIC, NICA), this is of importance forthe COMPASS experiment and the future J-PARC facility where the fixed targetmode is available.

Transversity and T-odd PDFs from Drell-Yan processes with $pp$, $pD$ and $DD$ collisions