  We show that hard-scattering factorization is violated in the production of
high-p_T hadrons in hadron-hadron collisions, in the case that the hadrons are
back-to-back, so that k_T factorization is to be used. The explicit
counterexample that we construct is for the single-spin asymmetry with one beam
transversely polarized. The Sivers function needed here has particular
sensitivity to the Wilson lines in the parton densities. We use a greatly
simplified model theory to make the breakdown of factorization easy to check
explicitly. But the counterexample implies that standard arguments for
factorization fail not just for the single-spin asymmetry but for the
unpolarized cross section for back-to-back hadron production in QCD in
hadron-hadron collisions. This is unlike corresponding cases in e^+e^-
annihilation, Drell-Yan, and deeply inelastic scattering. Moreover, the result
endangers factorization for more general hadroproduction processes.
