  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 $\epsilon$. 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 $O(\epsilon^0)$ results for NNLO beam and soft functions available
in the literature.
