What is (not) a Glueball?

Full text: We present a short review on what glueballs are and how they can be described theoretically. In particular we discuss a scalar glueball, which is described by the two-point function of the square of the Yang-Mills eld strength tensor. The momentum-space operator corresponding to this correlator has been constructed such that different gluon-propagators in 2 and 4 dimensions can be plugged into the expression. While the gluon-propagators have been taken from non-perturbative studies, the correlator itself is of lowest order in the coupling. By analytic continuation we extend the solution to complex values of p2, the square of the external momentum. The structure of the correlator in the complex plane encodes important information of the propagating degree of freedom, such as its mass or whether it is a bound state or not. We perform this investigation numerically by applying a specifically developed procedure which involves Graphics Processing Units to carry out this computationally intensive task. This tool allows us to investigate a variety of gluon propagators of different origin, without having to deal with the limitations present due to their complicated integral representations. The aim of this talk is to present not only the procedure used throughout the study, but also to stress what is not sufficient to get a glueball, restricting the ingredients of this highly interesting, experimentally hard-to-prove objects. (author)