  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 distribution of the unpolarized cross sections in
the Q^2 range from 2 to 100 GeV^2. In addition, the matching is established
between our evolution and the Collins-Soper-Sterman resummation with
b*-prescription and Konychev-Nodalsky parameterization of the non-perturbative
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.
