Glueballs, Hybrids and Q\bar Q Mesons

Lattice gauge calculations predict the existence of glueballs. In particular a scalar glueball is firmly expected at a mass of about 1730 MeV. This prediction has led to an intense study of scalar isoscalar interactions and to the discovery of new meson resonances. The number of scalar states observed seems to exceed the number of states which can be accommodated in the quark model even when two states, the a_0(980) and f_0(980), are interpreted as K Kbar bound states and are removed from the list. However, none of these states has a decay pattern which is consistent with that of a pure glueball. A reasonable interpretation of the number of states and of their decay pattern is found only when mixing of scalar q qbar states with the scalar glueball is taken into account. In this paper we scrutinize the evidence for these states and their production characteristics. The f_0(1370) - a cornerstone of all qbar q-glueball mixing scenarios - is shown to be likely of non-qbar 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. We also discuss the status of mesons with exotic quantum numbers, of mesons which cannot possibly have qbar q structure, and argue that these are, most likely, four-quark states and not excitations of the gluon string providing the binding between quark and antiquark.