Factorization Violation and Scale Invariance

TL;DR

This paper demonstrates that pure Glauber ladder graphs do not violate factorization at the cross section level for single-scale observables, highlighting the role of soft gluons in factorization violation.

Contribution

It proves that pure Glauber graphs cancel at the cross section level for single-scale observables, challenging previous assumptions about their factorization-violating effects.

Findings

Pure Glauber ladder graphs cancel at the cross section level.

Factorization violation involves soft gluon graphs with Lipatov vertices.

Scale invariance of scattering amplitudes is key to the cancellation.

Abstract

Factorization violating effects in hadron scattering are due mainly to spectator-spectator interactions. While it is known that these interactions cancel in inclusive cross sections, like for the Drell-Yan process, not much is known about for what classes of observables factorization is violated. We show that for pure Glauber ladder graphs, all amplitude-level factorization violating effects completely cancel at cross section level for any single-scale observable (such as hadronic transverse energy or beam thrust). This result disproves previous claims that these pure Glauber graphs are factorization-violating. Our proof exploits scale invariance of two-to-two scattering amplitudes in an essential way. The leading factorization-violating effects therefore come from graphs with at least one soft gluon, involving the Lipatov vertex off of the Glauber ladders. This implies that real soft radiation must be involved in factorization-violation, shedding light on the connection between factorization-violation and the underlying event.