# Application of the Thomas Fermi Quark Model to Multiquark Mesons

## TL;DR

This paper applies the Thomas-Fermi quark model to investigate the stability and properties of multiquark mesons with multiple quark-antiquark pairs, revealing potential stability for certain multi-$Z$ mesons.

## Contribution

It introduces a novel application of the Thomas-Fermi model to multiquark mesons, deriving energy expressions and analyzing stability for heavy-light quark systems.

## Key findings

- Multi-$Z$ mesons may be stable for certain quark numbers.
- Energy trends suggest stability of multi-charmonium and multi-bottomonium systems.
- Quark interactions are primarily between quarks and antiquarks, simplifying the model.

## Abstract

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