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

We recently measured the neutron double spin asymmetry $A_{LT}$ in the semi-inclusive deep inelastic $^{3}He^{\uparrow}(\overrightarrow{e},e'\pi^{+/-})X$ reactions with polarized electron beam and a transversely polarized $^3$He target. The measurement was performed in Jefferson Lab Hall A, using a 6 GeV polarized electron beam scattered from a 40 cm polarized 3He target. The produced pions were detected by the left high-resolution spectrometer in coincidence with the scattered electrons detected by the BigBite spectrometer. The kinematic coverage focused on the valence quark region, $x \sim 0.13$-$0.41$, at $Q^2 \sim 1.31$-$3.10(\mathrm{GeV}/c)^2$. When combined with the world data, the new data will provide constraints on the $g^{q}_{1T}$ distribution functions. These distribution functions describe the longitudinal polarization of up and down quarks in the valence region for a transversely polarized nucleon. Current data analysis progress will be presented in this talk.