  The analytic structure of the non-perturbative gluon propagator contains
information on the absence of gluons from the physical spectrum of the theory.
We study this structure from numerical solutions in the complex momentum plane
of the gluon and ghost Dyson-Schwinger equations in Landau gauge Yang-Mills
theory. The resulting ghost and gluon propagators are analytic apart from a
distinct cut structure on the real, timelike momentum axis. The propagator
violates the Osterwalder-Schrader positivity condition, confirming the absence
of gluons from the asymptotic spectrum of the theory.
