  We study the analytic structure of the two-point function of the operator F2
which is expected to describe a scalar glueball. The calculation of the
involved integrals is complicated by nonanalytic structures in the integrands,
which we take into account properly by identifying cuts generated by angular
integrals and deforming the contours for the radial integration accordingly.
The obtained locations of the branch points agree with Cutkosky's cut rules. As
input we use different nonperturbative Landau gauge gluon propagators with
different analytic properties as obtained from lattice and functional
calculations. All of them violate positivity and describe thus gluons absent
from the asymptotic physical space. The resulting spectral densities for the
glueball candidate show a cut but no poles for lightlike momenta, which can be
attributed to the employed Born approximation.
