NNLO zero-jettiness beam and soft functions to higher orders in the dimensional-regularization parameter $ϵ$

We present the calculation of the next-to-next-to-leading order (NNLO) zero-jettiness beam and soft functions, up to the second order in the expansion in the dimensional regularization parameter $ϵ$. These higher order terms are needed for the computation of the next-to-next-to-next-to-leading order (N${}^3$LO) zero-jettiness soft and beam functions. As a byproduct, we confirm the $O({ϵ}^0)$ results for NNLO beam and soft functions available in the literature.