Direct extraction of transversity and its accompanying t-odd distribution from the unpolarized and single- polarized Drell-Yan processes

The Drell-Yan processes with unpolarized colliding hadrons and with the single transversally polarized hadron are considered. The possibility of direct (without any model assumptions) extraction of both transversity and its accompanying T-odd parton distribution functions is discussed. For Drell-Yan processes measurements planned at GSI, the preliminary estimations demonstrate that it is quite real to extract both transversity and its accompanying T-odd PDF in the PAX conditions.