Resummation of hadron collision cross sections, when the measurement imposes
a hierarchy of scales, relies on factorization. Cancellation of Glauber /
Coulomb gluons is a necessary condition for factorization. For Drell-Yan-like
processes, the known proofs of cancellation of Glauber gluons are not
applicable when jet vetoes are introduced, via jet algorithms or event shape
variables such as the beam thrust. A priori, this does not rule out the
possibility that an unknown new cancellation mechanism exists, or the
possibility that a generalized factorization formalism is correct. To resolve
the questions, we construct a direct counter-example in QCD with scalar quarks,
contradicting any form of factorization in which the two collinear sectors are
decoupled from each other. In the counter-example, decoupling of the two
collinear sectors implies zero dependence of the beam thrust distribution on
the longitudinal spin of the incoming hadrons, but we find a non-zero spin
asymmetry at leading power due to Glauber gluons exchanged between spectators.
We discuss implications for resumming large logarithms from jet vetoes.Comment: 21 pages, 5 figure