BEC-BCS crossover in the Nambu-Jona-Lasinio model of QCD

Abstract

The BEC-BCS crossover in QCD at finite baryon and isospin chemical potentials is investigated in the Nambu-Jona-Lasinio model. The diquark condensation in two color QCD and the pion condensation in real QCD would undergo a BEC-BCS crossover when the corresponding chemical potential increases. We determined the crossover chemical potential as well as the BEC and BCS regions. The crossover is not triggered by increasing the strength of attractive interaction among quarks but driven by changing the charge density. The chiral symmetry restoration at finite temperature and density plays an important role in the BEC-BCS crossover. For real QCD, strong couplings in diquark and vector meson channels can induce a diquark BEC-BCS crossover in color superconductor, and in the BEC region the chromomagnetic instability is fully cured and the ground state is a uniform phase.

Bose—Einstein Condensation in Strong-Coupling Quark Color Superconductor near Flavor SU(3) Limit

“…Keeping it in mind that our concerned three-flavor superconductor is a fictional phase being valid near the flavor SU(3) limit, the magnitude of µ could not be identified with the baryon density of strongly interacting matter in realistic situations. In addition, strong coupling strength like G d /G s ∼ 1.1 − 1.5 had been used for studying quark superconducting phase and the BEC possibility in it [10,11,14,17]. There, exploring the BCS-BEC crossover physics was actually limited in the scope of strong-coupling quark superconductivity and the phase transition to the confined hadronic phase was not incorporated yet.…”

“…BEC displays a strong correlation in the coordinate space whereas BCS does a strong correlation in the momentum space. The BCS-BEC crossover physics in the scope of quark color superconductivity has attracted much attention and been investigated by a variety of QCD models [9,10,11,12,13,14,15,16,17,18]. For the strong-coupling regime, people usually apply the phenomenological models such as the Nambu Jona-Lasinio (NJL) model with both quark-antiquark and quark-quark interactions.…”

Pions in the quark matter phase diagram

“…On the example of the pion we will explain the physics of the Mott transition. The detailed investigation of the quantized diquark fluctuations, which are also a prerequisite of the formation of baryons, will be given elsewhere [30,35,36].…”

“…Recently, this transition became accessible to laboratory experiments with ultracold gases of fermionic atoms coupled via Feshbach resonances with a strength tunable by applying external magnetic fields [24,25,26,27,28]. The BEC-BCS crossover transition in quark matter is of particular theoretical interest due to the additional relativistic regime it offers [9,29,30].…”

Phase diagram of dense two-color QCD within lattice simulations

“…The properties of QC 2 D were studied theoretically within the following approaches: ChPT [2][3][4], the NJL model [5][6][7], FRG [8,9], random matrix theory [10][11][12]. Principally, these studies have revealed the following phase structure of low temperature QC 2 D with three subsequent phases: (1) 0 < µ < µ c (hadronic phase), (2) µ c < µ < µ d ("baryon onset" with a superfluid condensate due to Bose-Einstein condensation [BEC]) and (3) µ d < µ (the phase with diquark condensation due to the Bardeen-Cooper-Schrieffer mechanism [BCS] [13]).…”