BCS–BEC crossover and stability in a Nambu–Jona-Lasinio model with diquark–diquark repulsion

Abstract

We investigate the equation of state (EoS) along the BCS-BEC crossover for a quark system described by a Nambu-Jona-Lasinio model with multi-fermion interactions. Together with attractive channels for particle-antiparticle (GS) and particle-particle (GD) interactions, a multi-fermion channel with coupling λ that accounts for the diquark-diquark repulsion is also considered. The chiral and diquark condensates are found in the mean-field approximation for different values of the coupling constants. The parameter values where the BCS-BEC crossover can take place are found, and the EoS is used to identify the stability region where the BEC regime has positive pressure. We discuss how the particle density and the repulsive diquark-diquark interaction affect the stability window in the GS − GD plane and find the profile of the pressure versus the density for various values of λ and GD. The effects of λ and GD in the BCS-BEC crossover tend to compensate each other, allowing for a feasible region of densities where the crossover can occur with positive pressure. These results, although mainly qualitative, should serve as a preliminary step in the microscopic analysis required to determine the feasibility of the BCS-BEC crossover and its realization in more realistic models of dense QCD that can be relevant for applications to neutron stars.

BEC-BCS crossover in a cold and magnetized two color NJL model

“…It has been argued, however, that in the flavor SU(3) NJL model the axial anomaly might induce a BEC-BCS crossover for more conventional values of r [9,10]. Other possibility has been proposed in [11]. Contrary to what happens for N c = 3, the situation for the N c = 2 NJL model is quite clear.…”

Meson spectral functions at finite temperature and isospin density with the functional renormalization group

“…The BEC-BCS crossover, which is a hot topic in and beyond condensed matter and ultracold fermion gas, has been extended to relativistic fermion superfluid. Different from the normal situation where the BEC-BCS crossover is induced by increasing the attractive coupling among fermions [15][16][17][18][19][20][21][22][23], there exists a BEC-BCS crossover in pion superfluid, controlled by the isospin density and chiral symmetry restoration [24,25], similar to the case in two-color QCD system [26][27][28]. In the superfluid phase close to the critical isospin density, the deconfinement does not yet happen, the system is in the BEC state of pions.…”

Combined chiral and diquark fluctuations along QCD critical line and enhanced baryon production with parity doubling

“…In such a region of the T -µ plane, the chiral symmetry is partially restored and simultaneously the diquark correlations are strong, which may imply that there exists a significant amount of preformed diquarks [20,21,22]. Furthermore, if the baryon number density is relatively low, we can expect the BCS-BEC crossover [23,24,25,26,27] toward lower density where the inter-quark interaction is stronger while the mean interquark distance is smaller and hence the formation of bound diquark states in the configuration space is expected. On the basis of this observation, we can speculate that the proliferation of the baryons may happen in the final state of heavy-ion collision if the system enters this phase.…”