The chirally-odd twist-3 distribution e(x)

Properties of the nucleon twist-3 distribution function e(x) are reviewed. It is emphasized that the QCD equations of motion imply the existence of a delta-function at x=0 in e(x), which gives rise to the pion-nucleon sigma-term. According to the resulting ``practical'' DIS sum rules the first and the second moment of e(x) vanish, a situation analogue to that of the pure twist-3 distribution function $\bar{g}_2(x)$.Comment: 19 pages, 3 figures, new references and figures adde

Azimuthal asymmetries and Collins analyzing power

Spin azimuthal asymmetries in pion electro-production in deep inelastic scattering off longitudinally polarized protons, measured by HERMES, are well reproduced theoretically with no adjustable parameters. Predictions for azimuthal asymmetries for a longitudinally polarized deuteron target are given. The z-dependence of the Collins fragmentation function is extracted. The first information on e(x) is extracted from CLAS A_LU asymmetry.Comment: 5 pages, 7 figures. Talk presented by A.V. Efremov at DIS2002, Cracow, Poland, 30 April to 4 May 2002. To appear in Acta Physica Polonica

Transversity in Drell-Yan process of polarized protons and antiprotons in PAX experiment

Estimates are given for the double spin asymmetry in lepton-pair production from collisions of transversely polarized protons and antiprotons for the kinematics of the recently proposed PAX experiment at GSI on the basis of predictions for the transversity distribution from the chiral quark soliton model.Comment: 4 pages, 2 eps-figures, style files. To be published in Proceedings of 16th Intern. spin physics symposium, October 10-16, Trieste, Ital

Collins Effect in SIDIS and in e+e−{\bf e^+e^-} Annihilation

We review the present understanding of the nucleon transversity distribution and Collins fragmentation function, based on Ref.\cite{Efremov:2006qm}, and discuss how Drell-Yan experiments will improve it.Comment: Talk at Moscow ICHEP 26.7-2.8.2006 and Kyoto Symposium on Spin Physics 2-7.10.2006, 5 pages, 5 figures, AIP style files included. Some pictures chenged, one reference added, typos and some errors in formulas are correcte