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We describe how the nested soft-collinear subtraction scheme [1] can be usedto compute the next-to-next-to-leading order (NNLO) QCD corrections to theproduction of an arbitrary number of gluonic jets in hadron collisions. We showthat the infrared subtraction terms can be combined into recurring structuresthat in many cases are simple iterations of those terms known fromnext-to-leading order. The way that these recurring structures are identifiedand computed is fairly general, and can be applied to any partonic process. Asan example, we explicitly demonstrate the cancellation of all singularities inthe fully-differential cross section for the $q\bar{q} \to X + N g $ process atNNLO in QCD. The finite remainder of the NNLO QCD contribution, which arisesupon cancellation of all $\epsilon$-poles, is expressed via relatively simpleformulas, which can be implemented in a numerical code in a straightforwardway. Our approach can be extended to describe arbitrary processes at NNLO inQCD; the largest remaining challenge at this point is the combinatorics ofquark and gluon collinear limits.

A fresh look at the nested soft-collinear subtraction scheme: NNLO QCD corrections to $N$-gluon final states in $q\bar{q}$ annihilation