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 Ο(ϵ$^{0}$) results for NNLO beam and soft functions available in the literature by Gaunt et al. (JHEP 4:113, 2014), Gaunt et al. (JHEP 8:20, 2014), Boughezal et al. (Phys Rev D 96:34001, 2017), Monni et al. (JHEP 8:10, 2011) and Kelley et al. (Phys Rev D 84:45022, 2011).