Energy evolution for the Sivers asymmetries in hard processes

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We investigate the energy evolution of the azimuthal spin asymmetries in semi-inclusive hadron production in deep inelastic scattering (SIDIS) and Drell-Yan lepton pair production in $pp$ collisions. The scale dependence is evaluated by applying an approximate solution to the Collins-Soper-Sterman evolution equation at one-loop order, which is adequate for moderate Q² variations. This describes well the unpolarized cross sections for the SIDIS and Drell-Yan process in the Q² range of 2.4--100 GeV². A combined analysis of the Sivers asymmetries in SIDIS from HERMES and COMPASS experiments and the predictions for the Drell-Yan process at RHIC at √S=200 GeV are presented. We further extend to the Collins asymmetries and find, for the first time, a consistent description for HERMES/COMPASS and BELLE experiments with the evolution effects. We emphasize an important test of the evolution effects by studying di-hadron azimuthal asymmetry in e⁺e^- annihilation at moderate energy range, such as at BEPC at √S=4.6 GeV.