Measurement of Double Spin Asymmetry $A_{LT}$ in Semi-Inclusive Pion Electroproduction on a Transversely Polarized $^3$He Target

Double spin asymmetry $A_{LT}$ for the neutron was measured for the first time in Hall A at Jefferson Lab in semi-inclusive deep inelastic deep inelastic $^{3}He^{\uparrow}(\overrightarrow{e},e'\pi^{+/-})X$ reactions, using a 6 GeV polarized electron beam on a transversely polarized 3He target. The produced pions were detected in coincidence with the scattered electrons by a high-resolution spectrometer and a BigBite spectrometer. Kinematic coverage was focused on the valence quark region, $x \sim 0.1$-$0.4$, at $Q^2 \sim 1$-$3(\mathrm{GeV}/c)^2$. When combined with the world data, the new data will provide constraints on the $g^{q}_{1T}$ distribution functions, which describe the longitudinal polarization of up and down quarks for a transversely polarized nucleon. Current data analysis progress and preliminary results will be presented.