  The first results of a new application of the Thomas-Fermi statistical quark
model to mesonic matter is presented. Interesting aspects of the theory are
discussed, distinguishing such states from baryonic matter. A major motivation
of this study is the tetraquark states discovered by the Belle and other
collaborations and the possibility that stable multi-quark families of such
states exist. Similar to our previous baryonic study, we use a two-inequivalent
wave function approach to investigate aspects of multi-quark matter. We think
of our model as a tool for quickly assessing the characteristics of new,
possibly bound, particle states of higher quark number content, which can not
yet be examined by lattice methods.
