NambuJonaLasinio model description of weakly interacting Bose condensate and BECBCS crossover in dense QCDlike theories
Abstract
QCDlike theories possess a positively definite fermion determinant at finite baryon chemical potential μ_{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 BoseEinstein condensation (BEC) to BCS superfluidity at moderate density we should use some fermionic effective model of QCD, such as the NambuJonaLasinio model. In this paper, using twocolor twoflavor QCD as an example, we examine how the NambuJonaLasinio model describes the weakly interacting Bose condensate at low density and the BECBCS crossover at moderate density. Near the quantum phase transition point μ_{B}=m_{π} (m_{π} is the mass of pion/diquark multiplet), the GinzburgLandau free energy at the meanfield level can be reduced to the GrossPitaevskii free energy describing a weakly repulsive Bose condensate with a diquarkdiquark 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 inmedium chiral and diquark condensates predicted by chiral perturbation theories are analytically recovered. The BECBCS crossover and meson Mott transition at moderate baryon chemical potential as well as the beyondmeanfield 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;
 Finitetemperature field theory;
 Quantum chromodynamics;
 Quark deconfinement quarkgluon plasma production and phase transitions;
 High Energy Physics  Phenomenology;
 Condensed Matter  Superconductivity;
 Nuclear Theory
 EPrint:
 29 pages + 9 figures. Published version in PRD