Nested soft-collinear subtractions in NNLO QCD computations

We discuss a modification of the next-to-next-to-leading order (NNLO) subtraction scheme based on the residue-improved sector decomposition that reduces the number of double-real emission sectors from five to four. In particular, a sector where energies and angles of unresolved particles vanish in a correlated fashion is redundant and can be discarded. This simple observation allows us to formulate a transparent iterative subtraction procedure for double-real emission contributions, to demonstrate the cancellation of soft and collinear singularities in an explicit and (almost) process-independent way and to write the result of a NNLO calculation in terms of quantities that can be computed in four space-time dimensions. We illustrate this procedure explicitly in the simple case of $\mathcal O(\alpha _\mathrm{s}^2)$ gluonic corrections to the Drell–Yan process of $q \bar{q}$ annihilation into a lepton pair. We show that this framework leads to fast and numerically stable computation of QCD corrections.