The Thomas-Fermi Quark Model: Non-Relativistic Aspects

TL;DR

This paper explores the non-relativistic Thomas-Fermi quark model, incorporating spin interactions, to describe baryons and exotic multi-quark states, demonstrating its effectiveness in fitting known spectra and predicting new states.

Contribution

It introduces a generalized spin-flavor interaction into the Thomas-Fermi quark model and applies it to baryons and multi-quark states, including the H-dibaryon, showing its versatility.

Findings

The model fits the low energy spectrum of octet and decuplet baryons.

It predicts spatial flavor separation even in degenerate states.

The model can be used to estimate properties of exotic multi-quark states.

Abstract

The first numerical investigation of non-relativistic aspects of the Thomas-Fermi (TF) statistical multi-quark model is given. We begin with a review of the traditional TF model without an explicit spin interaction and find that the spin splittings are too small in this approach. An explicit spin interaction is then introduced which entails the definition of a generalized spin "flavor". We investigate baryonic states in this approach which can be described with two inequivalent wave functions; such states can however apply to multiple degenerate flavors. We find that the model requires a spatial separation of quark flavors, even if completely degenerate. Although the TF model is designed to investigate the possibility of many-quark states, we find surprisingly that it may be used to fit the low energy spectrum of almost all ground state octet and decuplet baryons. The charge radii of such states are determined and compared with lattice calculations and other models. The low energy fit obtained allows us to extrapolate to the six-quark doubly strange {\it H}-dibaryon state, flavor symmetric strange states of higher quark content and possible six quark nucleon-nucleon resonances. The emphasis here is on the {\it systematics} revealed in this approach. We view our model as a versatile and convenient tool for quickly assessing the characteristics of new, possibly bound, particle states of higher quark number content.