On the Analytic Structure of Scalar Glueball Operators

The correlator of the square of the Yang-Mills field-strength tensor corresponds to a scalar glueball, i.e., to a bound-state formed by gluonic ingredients only. It has quantum numbers 0++ and its mass, as predicted by different theoretical approaches, is expected to lie between 1 and 2 GeV. Here we restrict our considerations to the Born level, that is, we consider the correlator to zeroth order in the coupling. Gluonic self-interaction is taken into account indirectly by using non-perturbative gluon propagators. The employed closed expressions are motivated by lattice and Dyson-Schwinger studies. The analytic continuation of the integrals themselves is complicated by additional obstructive structures like branch cuts and poles that are induced by the inner integral in the complex plane of the outer integration variable. We deal with this problem by deforming the outer integration contour accordingly. For different input gluon propagators we find a positive glueball spectral density which is required for physical states. Poles are, however, absent which is most likely an artifact of working at Born level.