Nambu-Jona-Lasinio model description of weakly interacting Bose condensate and BEC-BCS crossover in dense QCD-like theories

Journal Article · Mon Nov 01 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.096003· OSTI ID:21503832

Lianyi, He ^[1]

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1. Frankfurt Institute for Advanced Studies and Institute for Theoretical Physics, J. W. Goethe University, 60438 Frankfurt am Main (Germany)

QCD-like theories possess a positively definite fermion determinant at finite baryon chemical potential {mu}{sub B} 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 {mu}{sub B}=m{sub {pi}} (m{sub {pi}} 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.

• OSTI ID: 21503832
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 9; Other Information: DOI: 10.1103/PhysRevD.82.096003; (c) 2010 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BARYONS
BCS THEORY
BOSE-EINSTEIN CONDENSATION
CHIRALITY
COMPUTERIZED SIMULATION
EXCITATION
FREE ENERGY
GINZBURG-LANDAU THEORY
ISOSPIN
LATTICE FIELD THEORY
MASS
MEAN-FIELD THEORY
PERTURBATION THEORY
PHASE TRANSFORMATIONS
PIONS
QUANTUM CHROMODYNAMICS
SCATTERING LENGTHS
SUPERFLUIDITY
WEAK INTERACTIONS
BASIC INTERACTIONS
BOSONS
CONSTRUCTIVE FIELD THEORY
DIMENSIONS
ELEMENTARY PARTICLES
ENERGY
ENERGY-LEVEL TRANSITIONS
FERMIONS
FIELD THEORIES
HADRONS
INTERACTIONS
LENGTH
MESONS
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
PSEUDOSCALAR MESONS
QUANTUM FIELD THEORY
SIMULATION
THERMODYNAMIC PROPERTIES