Andreas Windisch, Markus Q. Huber, Reinhard Alkofer
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 non-analytic 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 non- perturbative 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 light-like momenta, which can be attributed to the employed Born approximation.
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http://arxiv.org/abs/1212.2175
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