A decomposition splits the most singular dipole term of the N-jettiness soft function into an inclusive soft function and a remainder that is absent at NLO, finite at NNLO, and subtractable at N3LO, enabling NNLO results for up to five jets.
Sterman,Summation of Large Corrections to Short Distance Hadronic Cross-Sections, Nucl
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$N$-Jettiness Soft Functions Made Simple
A decomposition splits the most singular dipole term of the N-jettiness soft function into an inclusive soft function and a remainder that is absent at NLO, finite at NNLO, and subtractable at N3LO, enabling NNLO results for up to five jets.