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.

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