Investigation of Quark Distributions in a Family of Pentaquarks using the Thomas-Fermi Quark Model

TL;DR

This paper employs the Thomas-Fermi quark model to analyze quark distributions in multi-pentaquarks, revealing distinct distributions for light, charm, and anti-charm quarks and uncovering a pattern of spherical arrangements.

Contribution

It introduces a novel application of the Thomas-Fermi model to multi-pentaquarks, deriving conditions for quark distributions across different flavors.

Findings

Three distinct Thomas-Fermi functions for different quark flavors

Color interaction probabilities averaged over configurations

Pattern of spherical quark distributions

Abstract

Using the Thomas-Fermi quark model, a collective, spherically symmetric density of states is created to represent a gas of interacting fermions with various degeneracies at zero temperature. Over a family of multi-pentaquarks, color interaction probabilities are obtained after averaging over all the possible configurations. It is found that three different Thomas-Fermi functions are necessary for light, charm, and anti-charm quarks. These are assumed to be linearly related by proportionality constants resulting in consistency conditions. We analyze these conditions and find that they lead to an interesting pattern of spherical quark distributions.