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The possibility of the existence of mesons with two or more quark-antiquarkpairs is investigated with a new application of the Thomas-Fermi (TF)statistical quark model. Quark color couplings are treated in a mean fieldmanner similar to a previous application to baryons, and short and conciseexpressions for energies are derived. We find that, on average, quarks onlyinteract with antiquarks in such systems. The TF differential equation isconstructed and systems with heavy-light quark content are examined. Threetypes of mesonic systems are defined. In the case of charm quarks,multi-charmonium, multi-$Z$ meson and multi-$D$ meson family types areexamined. System analogs for bottom quarks are also constructed. Quantitativetrends for system energies of mesonic quark matter are extracted as a functionof the number of quark pairs. We find indications from energy plots thatmulti-$Z$ type mesons (and their bottom quark analogs) are actually stable fora range of quark number pairs. At this initial stage we have not yet includedexplicit spin interaction couplings between quarks, but we can take one levelof degeneracy into account in our two-inequivalent TF function construction.

Application of the Thomas Fermi Quark Model to Multiquark Mesons