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^-→ h_1 h_2 X 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 Collins azimuthal asymmetry, as will soon be measured at JLab and COMPASS operating on a transversely polarized proton target, are then presented.