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We study the analytic structure of the two-point function of the operator F2which is expected to describe a scalar glueball. The calculation of theinvolved integrals is complicated by nonanalytic structures in the integrands,which we take into account properly by identifying cuts generated by angularintegrals and deforming the contours for the radial integration accordingly.The obtained locations of the branch points agree with Cutkosky's cut rules. Asinput we use different nonperturbative Landau gauge gluon propagators withdifferent analytic properties as obtained from lattice and functionalcalculations. All of them violate positivity and describe thus gluons absentfrom the asymptotic physical space. The resulting spectral densities for theglueball candidate show a cut but no poles for lightlike momenta, which can beattributed to the employed Born approximation.

On the analytic structure of scalar glueball operators at Born level