Do glueballs contribute in heavy ion collisions?

In heavy ion collision simulations many hadron states and/or parton degrees of freedom are included in order to obtain the observables. Meson spectroscopy, for example, considers the $0^{++}$ meson as a mixture of $q\bar{q}$ and glue. This fact is usually not considered in heavy ion collision physics. In the present work we consider two extreme possibilities for the constitution of the $0^{++}$ meson, either as a pure glueball or as $q\bar{q}$-meson. The scattering amplitude and cross-sections with constituent interchange are determined for the two situations. The comparison showed that the glueball-glueball elastic scattering cross-section for a color singlet state is between one to two orders of magnitude smaller than the corresponding $q\bar{q}$ state. The $2^{++}$ glueball-glueball interaction is also evaluated with similar behavior. Thus, glueball-glueball scattering is not very likely to introduce significant changes in heavy ion collision observables.