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

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