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

Abstract

Abstract 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 $$\epsilon $$ ϵ . These higher order terms are needed for the computation of the next-to-next-to-next-to-leading order ($$\hbox {N}^3\hbox {LO}$$ N3LO ) zero-jettiness soft and beam functions. As a byproduct, we confirm the $${\mathcal {O}}{(\epsilon ^0)}$$ O(ϵ0) 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).