# Nested soft-collinear subtractions in NNLO QCD computations

## TL;DR

This paper introduces a simplified NNLO subtraction scheme for QCD calculations that reduces computational complexity and enhances numerical stability, demonstrated through gluonic corrections to the Drell-Yan process.

## Contribution

It presents a modified subtraction scheme that reduces sectors and simplifies NNLO QCD computations, making them more efficient and process-independent.

## Key findings

- Reduced the number of double-real emission sectors from five to four.
- Demonstrated explicit cancellation of singularities in a process-independent way.
- Achieved faster and more stable numerical computations for QCD corrections.

## Abstract

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. We show that this framework leads to fast and numerically stable computation of QCD corrections.