Study of worm-gear-T function $g_{1T}$ with semi-inclusive DIS data

The worm-gear-T function parameterizes the probability to find a longitudinally polarized quark inside a transversely polarized hadron. We extract it from data on polarized semi-inclusive deep-inelastic scattering (SIDIS) measured at COMPASS and HERMES. As a theoretical model, we use a Wandzura-Wilczek-type approximation at the next-to-leading order. We find that, at present, the data quality is insufficient to determine the worm-gear-T function faithfully. We also provide predictions for the transverse single-spin asymmetry associated with the worm-gear-T function, which could be measured in weak-boson production at STAR.