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

Abstract

The BEC-BCS (Bose-Einstein condensation-Bardeen-Cooper-Shriffer) 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.

Authors:
; ;  [1]
  1. Physics Department, Tsinghua University, Beijing 100084 (China)
Publication Date:
OSTI Identifier:
21020517
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 9; Other Information: DOI: 10.1103/PhysRevD.75.096004; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BARYONS; BCS THEORY; BOSE-EINSTEIN CONDENSATION; CHARGE DENSITY; CHIRAL SYMMETRY; COLOR MODEL; GROUND STATES; ISOSPIN; PION CONDENSATION; POTENTIALS; QUANTUM CHROMODYNAMICS; QUARKS; SUPERCONDUCTORS; VECTOR MESONS

Citation Formats

Sun Gaofeng, He Lianyi, and Zhuang Pengfei. BEC-BCS crossover in the Nambu-Jona-Lasinio model of QCD. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.096004.
Sun Gaofeng, He Lianyi, & Zhuang Pengfei. BEC-BCS crossover in the Nambu-Jona-Lasinio model of QCD. United States. doi:10.1103/PHYSREVD.75.096004.
Sun Gaofeng, He Lianyi, and Zhuang Pengfei. Tue . "BEC-BCS crossover in the Nambu-Jona-Lasinio model of QCD". United States. doi:10.1103/PHYSREVD.75.096004.
@article{osti_21020517,
title = {BEC-BCS crossover in the Nambu-Jona-Lasinio model of QCD},
author = {Sun Gaofeng and He Lianyi and Zhuang Pengfei},
abstractNote = {The BEC-BCS (Bose-Einstein condensation-Bardeen-Cooper-Shriffer) 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.},
doi = {10.1103/PHYSREVD.75.096004},
journal = {Physical Review. D, Particles Fields},
number = 9,
volume = 75,
place = {United States},
year = {Tue May 01 00:00:00 EDT 2007},
month = {Tue May 01 00:00:00 EDT 2007}
}
  • 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 themore » 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.« less
  • We study the QCD phase structure in the three-flavor Nambu-Jona-Lasinio model, incorporating the interplay between the chiral and diquark condensates induced by the axial anomaly. We demonstrate that for an appropriate range of parameters of the model, the interplay leads to the low temperature critical point in the phase structure predicted by a previous Ginzburg-Landau analysis. We also show that a Bose-Einstein condensate (BEC) of diquark molecules emerges in the intermediate density region, and as a result, a BEC-BCS crossover is realized with increasing quark chemical potential.
  • We study the interplay between the chiral and the deconfinement transitions, both at high temperature and high quark chemical potential, by a nonlocal Nambu-Jona-Lasinio model with the Polyakov loop in the mean field approximation and requiring neutrality of the ground state. We consider three forms of the effective potential of the Polyakov loop: two of them with a fixed deconfinement scale, cases I and II, and the third one with a {mu} dependent scale, case III. In cases I and II, at high chemical potential {mu} and low temperature T, the main contribution to the free energy is due tomore » the Z(3)-neutral three-quark states, mimicking the quarkyonic phase of the large N{sub c} phase diagram. On the other hand, in case III the quarkyonic window is shrunk to a small region. Finally we comment on the relations of these results to lattice studies and on possible common prospects. We also briefly comment on the coexistence of quarkyonic and color superconductive phases.« less
  • Using the standard auxiliary field method, we derive from the extended Nambu{endash}Jona-Lasinio model an effective meson action containing vector and axial-vector mesons in addition to Goldstone bosons. The vector and axial-vector mesons in this effective action transform as gauge fields of hidden local symmetry {ital G}{sub local}=[U({ital n}){sub {ital L}}{times}U({ital n}){sub {ital R}}]{sub local}. Here, the realization of enlarged hidden local symmetry is accomplished via the introduction of two kinds of {open_quote}{open_quote}compensating{close_quote}{close_quote} fields. For obtaining the intrinsic-parity-violating part of the action, we generalize the standard gauged Wess-Zumino-Witten action such that it also contains two kinds of {open_quote}{open_quote}compensators{close_quote}{close_quote} in addition tomore » the usual Goldstone bosons as well as the vector and axial-vector mesons. This generalized gauged Wess-Zumino-Witten action turns out to have {ital G}{sub global}{times}{ital G}{sub local} symmetry, where {ital G}{sub global} is the usual U({ital n}){sub {ital L}}{times}U({ital n}){sub {ital R}} global chiral symmetry while {ital G}{sub local} is the U({ital n}){sub {ital L}}{times}U({ital n}){sub {ital R}} hidden local symmetry. This means that {ital G}{sub local} has no gauge anomaly and its associated vector and axial-vector mesons can be regarded as gauge bosons of {ital G}{sub local}. The introduction of the coupling with the external electroweak fields requires us to gauge some appropriate subgroup of {ital G}{sub global}. To make it consistent with the anomaly structure of QCD is a nontrivial problem. We explain how this can be done, following the recent suggestion by several authors. {copyright} {ital 1996 The American Physical Society.}« less