On the breaking of collinear factorization in QCD

TL;DR

This paper analyzes the breaking of collinear factorization in QCD for non-inclusive hadron-hadron observables by studying SL collinear limits in a color-space formalism. It shows that amplitude-level factorization violations arise from non-commuting Coulomb/Glauber exchanges, but QCD cross sections remain factorized at one and two loops due to cancellations, with no new effects at two loops. The work identifies the physical origin of violations and links them to the broader structure of soft gluon dynamics, including super-leading and non-global logarithms, and predicts a genuine cross-section violation at three loops for colored incoming partons. These results have implications for understanding the underlying event and gap survival, and set a framework for higher-order factorization analyses in non-inclusive observables.

Abstract

We investigate the breakdown of collinear factorization for non-inclusive observables in hadron-hadron collisions. For pure QCD processes, factorization is violated at the three-loop level and it has a structure identical to that encountered previously in the case of super-leading logarithms. In particular, it is driven by the non-commutation of Coulomb/Glauber gluon exchanges with other soft exchanges. Beyond QCD, factorization may be violated at the two-loop level provided that the hard subprocess contains matrix element contributions with phase differences between different colour topologies.