Separation of soft and collinear infrared limits of QCD squared matrix elements

TL;DR

The paper addresses the overlap of soft and collinear infrared singularities in QCD calculations of jet cross sections. It introduces a simple, color-structure-based separation of soft and collinear limits, using soft-gluon insertion rules and a fixed gauge to isolate color-diagonal soft terms from collinear contributions, enabling straightforward subtraction and extension to higher orders. The authors provide explicit formulations for NLO and multi-emission configurations, and show that the separation enables helicity-dependent subtraction terms and Monte Carlo summation over helicities, with potential reductions in CPU time and easier integration into parton-shower algorithms. This approach offers a simple, automatable alternative to traditional double-subtraction schemes, with clear benefits for high-multiplicity final states at the LHC and beyond.

Abstract

We present a simple way of separating the overlap between the soft and collinear factorization formulae of QCD squared matrix elements. We check its validity explicitly for single and double unresolved emissions of tree-level processes. The new method makes possible the definition of helicity-dependent subtraction terms for regularizing the real contributions in computing radiative corrections to QCD jet cross sections. This implies application of Monte Carlo helicity summation in computing higher order corrections.

Figures (1)

• Figure 1: General structure of infrared factorization at any perturbative order. (From Ref. Catani:1999ss with permission of S. Catani.)