Polarized twist-three distributions $g_T$ and $h_L$ and the role of intrinsic transverse momentum

In a nonstandard way we split up the polarized quark distributions $g_T$ and $h_L$ into their twist-two, quark-mass, and interaction-dependent parts, emphasizing the sensitivity to quark intrinsic transverse momentum. We show how to derive the Burkhardt-Cottingham sum rule in this approach and derive a similar sum rule for the chiral-odd distribution $h_2$. The effect of intrinsic transverse momentum in experimental observables is illustrated in the calculation of the $\mathcal{O}(1\mathrm{/}Q)$ double-spin asymmetry $A_{LT}$ in Drell-Yan scattering.