Torus invariant transverse K\"ahler foliations

In this paper, we show the convexity of the image of a moment map on a transverse symplectic manifold equipped with a torus action under a certain condition. We also study properties of moment maps in the case of transverse K\"ahler manifolds. As an application, we give a positive answer to the conjecture posed by Cupit-Foutou and Zaffran.