  The worm-gear transverse momentum dependent (TMD) function $g_{1T}$ is one of
the eight leading-twist TMDs and has the probabilistic interpretation of
finding a longitudinally polarized quark inside a transversely polarized
hadron. In this work, we present the first simultaneous extraction of $g_{1T}$
from all the available experimental measurements. The study involves the
analysis of COMPASS, HERMES, and Jefferson Lab data on semi-inclusive
deep-inelastic scattering using Monte Carlo techniques. We also compare
$g_{1T}$ obtained from this experimental data with different theoretical
approaches, such as the large-$N_c$ approximation, the Wandzura-Wilczek-type
approximation, and lattice QCD.
