Nested soft-collinear subtractions in NNLO QCD computations

Understand

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 $O(\alpha_s^2)$ gluonic corrections to the Drell-Yan process of $q \bar q$ annihilation into a lepton pair.