A global analysis of the experimental data on azimuthal asymmetries in semi-inclusive deep inelastic scattering (SIDIS), from the HERMES and COMPASS Collaborations, and in e + e − → h1h2X processes, from the Belle Collaboration, is performed. It results in the extraction of the Collins fragmentation function and, for the first time, of the transversity distribution function for u and d quarks. These turn out to have opposite signs and to be sizably smaller than their positivity bounds. Predictions for the azimuthal asymmetry A sin(φ h +φ S ) U T , as will soon be measured at JLab and COMPASS operating on a transversely polarized proton target, are then presented.

We study the Sivers effect in the transverse single spin asymmetries (SSA) for pion and kaon production in semi-inclusive deep inelastic scattering (SIDIS) processes. We perform a fit of Awhich, by including recent high statistics experimental data for pion and kaon production from HER-MES and COMPASS Collaborations, allows a new determination of the Sivers distribution functions for quarks and antiquarks with u, d and s flavours. Estimates for forthcoming SIDIS experiments at COMPASS and JLab are given.

The role of intrinsic k(perp) in inclusive and semi-inclusive Deep Inelastic Scattering processes (lp -> lhX) is studied with exact kinematics within QCD parton model at leading order; the dependence of the unpolarized cross section on the azimuthal angle between the leptonic and the hadron production planes (Cahn effect) is compared with data and used to estimate the average values of k(perpendicular to) both in quark distribution and fragmentation functions. The resulting picture is applied to the description of the weighted single spin asymmetry A(UT)(pi)(sin(phi)-phi(S)) recently measured by the HERMES collaboration at DESY; this allows to extract some simple models for the quark Sivers functions. These are compared with the Sivers functions which succeed in describing the data on transverse single spin asymmetries in p(uparrow) p -> pi X processes; the two sets of functions are not inconsistent. The extracted Sivers functions give predictions for the COMPASS measurement of A(UT)(pi)(sin(phi)-phi(S)) in agreement with recent preliminary data, while their contribution to HERMES A(UL)(pi) sin(phi) is computed and found to be small. Predictions for A(UT)(K)(sin(phi)-phi(S)) for kaon production at HERMES are also given

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.

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