NJL model approach to diquarks and baryons in quark matter

TL;DR

This paper models baryons as quark-diquark bound states in quark matter using the NJL model, exploring their thermodynamics and stability at finite temperature and density, including the effects of diquark dissociation.

Contribution

It introduces a novel approach to describe baryons as quark-diquark bound states within the NJL model, accounting for Mott dissociation and phase space effects in medium.

Findings

Baryons remain bound beyond diquark Mott temperature due to phase space effects.

The nucleon mass follows in-medium quark and diquark masses towards chiral restoration.

Baryons are described as Borromean states where the three-quark system is bound despite unbound diquarks.

Abstract

We describe baryons as quark-diquark bound states at finite temperature and density within the NJL model for chiral symmetry breaking and restoration in quark matter. Based on a generalized Beth-Uhlenbeck approach to mesons and diquarks we present in a first step the thermodynamics of quark-diquark matter which includes the Mott dissociation of diquarks at finite temperature. In a second step we solve the Bethe-Salpeter equation for the baryon as a quark-diquark bound state in quark-diquark matter. We obtain a stable, bound baryon even beyond the Mott temperature for diquark dissociation since the phase space occupation effect (Pauli blocking for quarks and Bose enhancement for diquarks) in the Bethe-Salpeter kernel for the nucleon approximately cancel so that the nucleon mass follows the in-medium behaviour of the quark and diquark masses towards chiral restoration. In this situation the baryon is obtained as a "borromean" three-quark state in medium because the two-particle state (diquark) is unbound while the three-particle state (baryon) is bound.