Azimuthal asymmetries in single polarized proton-proton Drell-Yan processes

We study the azimuthal asymmetries in proton-proton Drell-Yan processes with one incident proton being transversely or longitudinally polarized. We consider particularly the asymmetries contributed by the leading-twist chiral-odd quark distributions. We analyze the asymmetries with $\sin (2\varphi +{\varphi }_S)$ and $\sin (2\varphi -{\varphi }_S)$ modulations in transverse single polarized $p^{\uparrow }p$ Drell-Yan and $\sin 2\varphi$ asymmetries in longitudinal single polarized $p^{\to }p$ Drell-Yan at RHIC, J-PARC, E906 (Fermi Lab) and NICA (JINR). We show that the measurements of the asymmetries in those facilities can provide valuable information of the chiral-odd structure of the nucleon both in the valence and sea regions.