The Bonn nuclear quark model revisited

TL;DR

This paper revisits the Bonn quark model, providing exact solutions for its lowest energy states, analyzing color symmetry breaking, and evaluating the effectiveness of coherent and BCS states in describing these states.

Contribution

It offers the first exact solutions for the model's lowest energy states and assesses the performance of different state approximations in describing color symmetry breaking.

Findings

Ground state is not color symmetric except in a narrow quark number range.

Glauber coherent and BCS states describe the ground state remarkably well.

The model sheds light on controversial aspects of color superconductivity.

Abstract

We present the exact solutions to the equations of the lowest energy states of the colored and color-symmetric sectors of the Bonn quark model, which is SU(3) symmetric and is defined in terms of an effective pairing force with $su(4)$ algebraic structure. We show that the groundstate of the model is not color symmetrical except for a narrow interval in the range of possible quark numbers. We also study the performance of the Glauber coherent state, as well as of superconducting states of the BCS type, with respect to the description, not only of the absolute (colored) groundstate, but also of the minimum energy state of the color-symmetrical sector, finding that it is remarkably good. We use the model to discuss, in a schematic context, some controversial aspects of the conventional treatment of color superconductivity.