Cohen-Macaulay Du Bois singularities with a torus action of complexity one

Using Altmann-Hausen-S\"u\ss\ description of T-varieties via divisorial fans and K\'ovacs-Schwede-Smith characterization of Du Bois singularities we prove that any rational T-variety of complexity one which is Cohen-Macaulay and Du Bois has rational singularities. In higher complexity, we prove an analogous result in the case where the Chow quotient of the T-variety has Picard rank one and trivial geometric genus.Comment: 16 page