On the existence of glueballs

Lattice gauge calculations require the existence of glueballs. In particular a scalar glueball is firmly predicted at a mass of 1700 MeV. This prediction has led to an intense study of scalar isoscalar interactions and to the discovery of several states. The number of scalar states observed seems to exceed the number of states which can be accommodated in the quark model. None of these states has a decay pattern which is consistent with that of a pure glueball but mixing of scalar q over-bar q states with the scalar glueball provides for a reasonable interpretation of the data. In this paper we scrutinize the evidence for these states and their production characteristics. The f0(1370) - a cornerstone of all q over-bar q-glueball mixing scenarios - is shown to be likely of non-q over-bar q nature. The remaining scalar states then do fit into a nonet classification. If this interpretation should be correct there would be no room for resonant scalar gluon-gluon interactions, no room for the scalar glueball.