Transversity and Collins functions from SIDIS ande+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 $e^{+}{e}^{-}\to h_1{h}_{2}X$ 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 azimuthal asymmetry $A_{UT}^{\sin ({\varphi }_S+{\varphi }_h)}$, as will soon be measured at JLab and COMPASS operating on a transversely polarized proton target, are then presented.