Status on the transversity parton distribution: the dihadron fragmentation functions way

We report on the extraction of dihadron fragmentation functions (DiFF) from the semiinclusive production of two hadron pairs in back-to-back jets in e+e- annihilation. A nonzero asymmetry in the correlation of azimuthal orientations of opposite $\pi^+\pi^-$ pairs is related to the transverse polarization of fragmenting quarks through a significant polarized DiFF. A combined analysis of this asymmetry and the spin asymmetry in the SIDIS process $ep^{\uparrow}\to e'(\pi^+\pi^-)X$ has led to the first extraction of the u and d-flavor transversity parton distribution function in the framework of collinear factorization.