Angular dependence in transverse momentum dependent diffractive parton distributions at small-$x$

Abstract: We discuss the angular dependence of the recently proposed transverse momentum dependent quark and gluon diffractive parton distributions at small-$x$. We introduce the difractive versions of the Sivers function and the elliptic gluon Wigner distribution and evaluate them in simple models with gluon saturation and study their geometric scaling properties. We also show that the diffractive version of the linearly polarized gluon distribution identically vanishes to leading order. These distributions enrich the physics opportunities for measuring semi-inclsuive diffractive DIS processes at the future electron-ion colliders.