Di-hadron fragmentation in reduced dimensionality and $\Lambda$ hyperon beam-spin transfer

In this contribution, we focus on two types of dihadron fragmentation functions (diFF), the "strong-diFF" and the "weak-diFF", where the "strong" and "weak" labels the way the experimentally observed hadrons are formed. The strong-diFF is the more widely used dihadron fragmentation in this community, where in particular the chiral-odd "interference fragmentation function" is employed as a probe for transversity, the main theme of this workshop. We discuss limitations in the analysis of strong-diFF data arising through an incomplete integration of the differential cross section imposed by experimental constraints. In particular, we show that the usual application of momentum requirements together with integration over the polar angle of the hadrons in the di-hadron center-of-mass frame leads to a presently uncontrollable mixture of various partial-wave components of the di-hadron fragmentation function for charged-pion pairs, prohibiting precision extractions of di-hadron fragmentation functions from $e^{+}e^{-}$ annihilation, semi-inclusive deep-inelastic scattering, or proton-proton collision data. A prominent example of weak-diFF is the production and subsequent weak decay of $\Lambda$ hyperons into a pion and a proton. The weak decay reveals the polarization of the parent $\Lambda$ hyperon, a valuable tool to study spin phenomena. Preliminary HERMES data on the spin transfer from the lepton beam to final-state $\Lambda$ and $\bar{\Lambda}$ hyperons in semi-inclusive deep-inelastic scattering are presented. No sizable spin transfer is observed.