Space-like (vs. time-like) collinear limits in QCD: is factorization violated?

TL;DR

This paper investigates the breakdown of strict collinear factorization in space-like regions at higher-loop orders in QCD, proposing a generalized factorization approach that accounts for process dependence.

Contribution

It introduces a generalized all-order collinear factorization framework that incorporates process-dependent effects in space-like collinear limits at higher loops.

Findings

Strict collinear factorization fails at one-loop and higher in space-like regions.

Explicit two-loop amplitude results for multiparton collinear limits.

Implications for non-abelian logarithmic terms and mass singularity factorization.

Abstract

We consider the singular behaviour of QCD scattering amplitudes in kinematical configurations where two or more momenta of the external partons become collinear. At the tree level, this behaviour is known to be controlled by factorization formulae in which the singular collinear factor is universal (process independent). We show that this strict (process-independent) factorization is not valid at one-loop and higher-loop orders in the case of the collinear limit in space-like regions (e.g., collinear radiation from initial-state partons). We introduce a generalized version of all-order collinear factorization, in which the space-like singular factors retain some dependence on the momentum and colour charge of the non-collinear partons. We present explicit results on one-loop and two-loop amplitudes for both the two-parton and multiparton collinear limits. At the level of square amplitudes and, more generally, cross sections in hadron--hadron collisions, the violation of strict collinear factorization has implications on the non-abelian structure of logarithmically-enhanced terms in perturbative calculations (starting from the next-to-next-to-leading order) and on various factorization issues of mass singularities (starting from the next-to-next-to-next-to-leading order).