Transversity and Collins functions from SIDIS and e+e- data

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 AUTsin(S+h), as will soon be measured at JLab and COMPASS operating on a transversely polarized proton target, are then presented.