We study the transverse momentum dependent (TMD) evolution of the Collins azimuthal asymmetries in e + e − annihilations and semi-inclusive hadron production in deep inelastic scattering (SIDIS) processes. All the relevant coefficients are calculated up to the next-to-leading logarithmic (NLL) order accuracy. By applying the TMD evolution at the approximate NLL order in the Collins-Soper-Sterman (CSS) formalism, we extract transversity distributions for u and d quarks and Collins fragmentation functions from current experimental data by a global analysis of the Collins asymmetries in back-to-back di-hadron productions in e + e − annihilations measured by BELLE and BABAR Collaborations and SIDIS data from HERMES, COMPASS, and JLab HALL A experiments. The impact of the evolution effects and the relevant theoretical uncertainties are discussed. We further discuss the TMD interpretation for our results, and illustrate the unpolarized quark distribution, transversity distribution, unpolarized quark fragmentation and Collins fragmentation functions depending on the transverse momentum and the hard momentum scale. We make detailed predictions for future experiments and discuss their impact.

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 Q 2 variations. This describes well the unpolarized cross sections for the SIDIS and Drell-Yan process in the Q 2 range of 2:4-100 GeV 2 . 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 ffiffiffi S p ¼ 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 þ e À annihilation at moderate energy range, such as at BEPC at ffiffiffi

We update the well-known BLNY fit to the low transverse momentum Drell-Yan lepton pair productions in hadronic collisions, by considering the constraints from the semi-inclusive hadron production in deep inelastic scattering (SIDIS) from HERMES and COMPASS experiments. We follow the Collins-Soper-Sterman (CSS) formalism with the b * -prescription. A universal non-perturbative form factor associated with the transverse momentum dependent quark distributions is found in the analysis with a new functional form different from that of BLNY. This releases the tension between the BLNY fit to the Drell-Yan data with the SIDIS data from HERMES/COMPASS in the CSS resummation formalism.