The most recent data on the weighted transverse single spin asymmetry A sin(φ h −φ S ) U T from HERMES and COMPASS collaborations are analysed within LO parton model with unintegrated parton distribution and fragmentation functions; all transverse motions are taken into account, with exact kinematics, in the elementary interactions. The overall quality of the data is such that, for the first time, a rather well constrained extraction of the Sivers function for u and d quarks is possible and is performed. Comparisons with models are made. Based on the extracted Sivers functions, predictions for A sin(φ h −φ S ) U T asymmetries at JLab are given; suggestions for further measurements at COM-PASS, with a transversely polarized hydrogen target and selecting favourable kinematical ranges, are discussed. Predictions are also presented for Single Spin Asymmetries (SSA) in Drell-Yan processes at RHIC and GSI.

The Sivers distributions recently extracted from semi-inclusive deep inelastic scattering data [1] are used to compute estimates for Sivers asymmetries in Drell-Yan processes which are being planned at several facilities (RHIC, COMPASS, J-PARC, PAX, PANDA, NICA (JINR) and SPASCHARM (IHEP)). Most of these asymmetries turn out to be large and could allow a clear test of the predicted sign change of the Sivers distributions when active in SIDIS and Drell-Yan processes. This is regarded as a fundamental test of our understanding, within QCD and the factorization scheme, of single spin asymmetries.

We present an update of a previous global analysis of the experimental data on azimuthal asymmetries in semiinclusive deep inelastic scattering (SIDIS), from the HERMES and COMPASS Collaborations, and in e + e − → h1h2X processes, from the Belle Collaboration. Compared to the first extraction, a more precise determination of the Collins fragmentation function and the transversity distribution function for u and d quarks is obtained.

We construct an improved implementation for combining transverse-momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suitable for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard W + Y prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. We further argue that questions regarding the shape and Q-dependence of the cross sections at lower Q are largely governed by the matching to the Y -term.

In the leading order of QCD parton model of Semi Inclusive Deep Inelastic Scattering (SIDIS) the double spin asymmetry ALT arises due to the longitudinal polarization of quarks in the transversely polarized nucleon. The corresponding k1T can be related to ordinary helicity distribution g1(x) measured in DIS. Using recent parameterizations for (un)polarized distribution and fragmentation functions we calculated ALT asymmetry on transversely polarized proton and deuteron targets for different types hadron production. The predictions are given for COMPASS, HERMES and JLab energies. The role of Lorentz invariance relations and positivity constraints are discussed.