# Integrated triple-collinear counter-terms for the nested soft-collinear subtraction scheme

## TL;DR

This paper derives analytic integrated triple-collinear splitting functions crucial for NNLO QCD calculations, enhancing the efficiency and stability of subtraction schemes in hadron collision processes.

## Contribution

It provides the first complete analytic expressions for all integrated triple-collinear counter-terms in the nested soft-collinear subtraction scheme.

## Key findings

- All integrated subtraction terms are now known analytically.
- Improved efficiency and numerical stability in NNLO QCD computations.
- Facilitates the development of a general NNLO subtraction formula for hadron collisions.

## Abstract

We obtain analytic results for integrated triple-collinear splitting functions that emerge as collinear counter-terms in the context of the nested soft-collinear subtraction scheme arXiv:1702.01352 . With these results, all integrated subtraction terms required for NNLO QCD computations within this scheme are known analytically. In addition to improving efficiency and numerical stability of practical computations, the availability of these results will contribute towards establishing a general NNLO QCD subtraction formula for generic hard scattering processes in hadron collisions, similar to Catani-Seymour and FKS subtractions at NLO.