Spin-spin coupling at small $x$: Worm-gear and pretzelosity TMDs

We study the small-$x$ asymptotics of the leading-twist quark transverse momentum dependent parton distribution functions (TMDs) which encode couplings between the polarization of the quarks and that of their parent hadron, with at least one of the two polarizations in the transverse direction: the two worm-gear TMDs $g_{1T}$ and $h_{1L}^{\perp }$, and the pretzelosity $h_{1T}^{\perp }$. We apply the light cone operator treatment which has been developed in recent years to rewrite the TMD operator definitions at small-$x$ in terms of polarized dipole amplitudes, finding that in the flavor nonsinglet sector all three TMDs reduce in the small-$x$ limit to previously known polarized dipole amplitudes, and thus the large-$N_c$, linearized, double logarithmic approximation (DLA) asymptotics have all been solved for previously. We have compiled these asymptotics together with those of the other five flavor nonsinglet, leading-twist quark TMDs into a single unified table.