Nucleons or diquarks? Competition between clustering and color superconductivity in quark matter

TL;DR

This paper investigates the competition between nucleon formation and color superconductivity in quark matter using a generalized NJL model, revealing that diquark formation is favored at higher densities and questioning the role of confinement.

Contribution

It introduces a detailed comparison of nucleon and diquark stability in quark matter within a NJL framework, highlighting the dominance of diquark pairing at higher densities.

Findings

Nucleons are stable up to nuclear matter density.

Scalar diquarks become energetically favored beyond a quarter of nuclear matter density.

The model questions the ability to reproduce realistic baryonic phase diagrams without confinement.

Abstract

We study the instabilities of quark matter in the framework of a generalized Nambu--Jona-Lasinio model, in order to explore possible competition between three-quark clustering to form nucleons and diquark formation leading to color superconductivity. Nucleon and $\Delta$ solutions are obtained for the relativistic Faddeev equation at finite density and their binding energies are compared with those for the scalar and axial-vector diquarks found from the Bethe-Salpeter equation. In a model with interactions in both scalar and axial diquark channels, bound nucleons exist up to nuclear matter density. However, except at densities below about a quarter of that of nuclear matter, we find that scalar diquark formation is energetically favored. This raises the question of whether a realistic phase diagram of baryonic matter can be obtained from any model which does not incorporate color confinement.