Longitudinal quark polarization in transversely polarized nucleons

Accounting for transverse momenta of the quarks, a longitudinal quark spin asymmetry exists in a transversely polarized nucleon target. The relevant leading quark distribution $g_{1T}(x, k_T^2)$ can be measured in semi-inclusive deep-inelastic scattering. The average $k_T^2$ weighted distribution function $g_{1T}^{\mathrm{}\left(1\right)\mathrm{}}$ can be obtained directly from the inclusive measurement of $g_2$.