General Helicity Formalism for Two-hadron Production in $e^+e^-$ Collisions and the $\Lambda$ Polarizing Fragmentation Function

We present the complete structure of the azimuthal dependences and polarization observables for two-hadron production in $e^+e^-$ annihilation processes within a transverse momentum dependent (TMD) approach adopting the helicity formalism. The leading-twist TMD fragmentation functions (TMD-FFs) for spin-1/2 hadrons are fully accounted for. The role of the polarizing FF, together with its extraction from Belle data for the transverse polarization of $\Lambda$'s, are discussed as well. Finally, predictions for SIDIS processes at EIC are presented.