Comparative analysis of the transversities and the longitudinally polarized distribution functions of the nucleon

A first empirical extraction of the transversity distributions for the $u$- and $d$-quarks has been done by Anselmino {\it et al.} based on the combined global analysis of the measured azimuthal asymmetries in semi-inclusive deep inelastic scatterings and those in $e^+ e^- \to h_1 h_2 X$ processes. Although with large uncertainties, the determined transversity distributions already appear to reveal a remarkable qualitative difference with the corresponding longitudinally polarized distributions. We point out that this difference contains very important information on internal spin structure of the nucleon.Comment: 12 pages, 2 figure