Weizsäcker-Williams TMDs at Small-x

We study the small-x asymptotics of the transverse spin dependent Weizsäcker-Williams (WW) transverse momentum dependent parton distribution functions (TMDs), as well as the dipole worm-gear TMD g_1T. We apply the Light-Cone Operator Treatment (LCOT) to simplify the operator definitions of the TMDs at small-x in terms of polarized dipole amplitudes which encode the polarization dependent scattering of a color dipole on the parent hadron's quark and gluon fields. We then derive and solve the corresponding evolution equations for the polarized dipole amplitudes in the leading double-logarithmic approximation in the large-$N_c$ limit, thus obtaining the small-x asymptotics of the TMDs.