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

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 $\epsilon$. 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.

26 pages, 1 figure

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• Collinear functions for QCD resummations
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• The NNLO quark beam function for jet-veto resummation
• Expansion by regions meets angular integrals
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Double-Real-Virtual and Double-Virtual-Real Corrections to the Three-Loop Thrust Soft Function
• One-loop corrections to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD
• Asymptotic behavior of angular integrals in the massless limit
• Angular integrals with three denominators via IBP, mass reduction, dimensional shift, and differential equations
• QCD Beyond Leading Power