NJL model approach to diquarks and baryons in quark matter

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.