We examine the QCD evolution for the transverse momentum dependent observables in hard processes of semi-inclusive hadron production in deep inelastic scattering and Drell-Yan lepton pair production in $pp$ collisions, including the spin-average cross sections and Sivers single transverse spin asymmetries. We show that the evolution equations derived by a direct integral of the Collins-Soper-Sterman evolution kernel from low to high $Q$ can describe well the transverse momentum distributions of the unpolarized cross sections in the $Q^2$ range from 2 to $100{\mathrm{GeV}}^2$. In addition, the matching is established between our evolution and the Collins-Soper-Sterman resummation with $b_{*}$ prescription and Konychev-Nodalsky parametrization of the nonperturbative form factors, which are formulated to describe the Drell-Yan lepton pair and $W/Z$ boson production in hadronic collisions. With these results, we present the predictions for the Sivers single transverse spin asymmetries in Drell-Yan lepton pair production and $W^{\pm }$ boson production in polarized $pp$ and ${\pi }^{-}p$ collisions for several proposed experiments. We emphasize that these experiments will not only provide crucial test of the sign change of the Sivers asymmetry but also provide important opportunities to study the QCD evolution effects.

• Received 11 September 2013

DOI:https://doi.org/10.1103/PhysRevD.88.114012