We summarize the latest achievements about the extraction of the transversity parton distribution and proton tensor charge based on an analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets. Recently released data for proton and deuteron targets by HERMES and COMPASS allow for a flavor separation of the valence components of transversity. At variance with the Collins effect, this extraction is performed in the framework of collinear factorization and relies on di-hadron fragmentation functions. The latter have been taken from the first recent analysis of the semi-inclusive production of two pion pairs in back-to-back jets in e+e- annihilation. We also comment on the possibility of isolating new azimuthally asymmetric correlations of opposite pion pairs, which could arise when a fragmenting quark crosses parity-odd domains localized in Minkowski space-time and induced by the topologically nontrivial QCD background (the so-called theta vacuum).
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