  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.
