  The correlation between the longitudinal polarization of a fragmenting quark
and the transverse momenta of the produced hadrons was predicted over two
decades ago. Nevertheless, experimental searches in the electron-positron
annihilation process, both through the so-called jet handedness measurements by
the {\tt SLD} Collaboration and more recently via the measurements of the
azimuthal asymmetry containing the helicity-dependent dihadron fragmentation
function (DiFF) by the $\textrm{BELLE}$ Collaboration, did not yield a signal.
We will first discuss our recent explanation of the zero result at
$\textrm{BELLE}$, and the two new methods for accessing the helicity-dependent
DiFFs both in the electron-positron annihilation experiments, and in the
semi-inclusive deep inelastic scattering (SIDIS) experiments with a
longitudinally polarized target. We will also for the first time describe yet
another, new method for accessing the helicity-dependent DiFFs in SIDIS using
polarized beam asymmetry. Finally, we will present a new Monte Carlo
calculation of the specific Fourier moments of the helicity-dependent DiFF
entering in to the new asymmetries, performed within the extended quark-jet
model, and compare the results to those for the interference DiFF.
