Nambu-Jona-Lasinio model description of weakly interacting Bose condensate and BEC-BCS crossover in dense QCD-like theories
Abstract
QCD-like theories possess a positively definite fermion determinant at finite baryon chemical potential μB and the lattice simulation can be successfully performed. While the chiral perturbation theories are sufficient to describe the Bose condensate at low density, to describe the crossover from Bose-Einstein condensation (BEC) to BCS superfluidity at moderate density we should use some fermionic effective model of QCD, such as the Nambu-Jona-Lasinio model. In this paper, using two-color two-flavor QCD as an example, we examine how the Nambu-Jona-Lasinio model describes the weakly interacting Bose condensate at low density and the BEC-BCS crossover at moderate density. Near the quantum phase transition point μB=mπ (mπ is the mass of pion/diquark multiplet), the Ginzburg-Landau free energy at the mean-field level can be reduced to the Gross-Pitaevskii free energy describing a weakly repulsive Bose condensate with a diquark-diquark scattering length identical to that predicted by the chiral perturbation theories. The Goldstone mode recovers the Bogoliubov excitation in weakly interacting Bose condensates. The results of in-medium chiral and diquark condensates predicted by chiral perturbation theories are analytically recovered. The BEC-BCS crossover and meson Mott transition at moderate baryon chemical potential as well as the beyond-mean-field corrections are studied. Part of our results can also be applied to real QCD at finite baryon or isospin chemical potential.
- Publication:
-
Physical Review D
- Pub Date:
- November 2010
- DOI:
- 10.1103/PhysRevD.82.096003
- arXiv:
- arXiv:1007.1920
- Bibcode:
- 2010PhRvD..82i6003H
- Keywords:
-
- 11.10.Wx;
- 12.38.-t;
- 25.75.Nq;
- Finite-temperature field theory;
- Quantum chromodynamics;
- Quark deconfinement quark-gluon plasma production and phase transitions;
- High Energy Physics - Phenomenology;
- Condensed Matter - Superconductivity;
- Nuclear Theory
- E-Print:
- 29 pages + 9 figures. Published version in PRD