We study the Sivers single spin asymmetry of the Drell-Yan lepton pair production in the small-$x$ regime. We find that in the corresponding kinematic region the spin asymmetry calculated in the small-$x$ approach is consistent with either the usual transverse-momentum-dependent factorization formalism or the collinear factorization formalism, respectively. We estimate the Sivers asymmetry for both polarized $\mathrm{p}+\mathrm{p}$ and $\mathrm{p}+\mathrm{A}$ collisions and argue that the Drell-Yan production is an interesting and unique probe for both the transverse spin physics and the small-$x$ saturation effect.

• Received 3 January 2013

DOI:https://doi.org/10.1103/PhysRevD.87.034038