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Title: Thermodynamics of the Polyakov-Nambu-Jona-Lasinio model with nonzero baryon and isospin chemical potentials

Abstract

We have extended the Polyakov-Nambu-Jona-Lasinio (PNJL) model for two degenerate flavors to include the isospin chemical potential ({mu}{sub I}). All the diagonal and mixed derivatives of pressure with respect to the quark number (proportional to baryon number) chemical potential ({mu}{sub 0}) and isospin chemical potential up to sixth order have been extracted at {mu}{sub 0}={mu}{sub I}=0. These derivatives give the generalized susceptibilities with respect to quark and isospin numbers. Similar estimates for the flavor diagonal and off-diagonal susceptibilities are also presented. Comparison to lattice QCD (LQCD) data of some of these susceptibilities for which LQCD data are available show similar temperature dependence, though there are some quantitative deviations above the crossover temperature. We have also looked at the effects of instanton induced flavor mixing coming from the U{sub A}(1) chiral symmetry breaking 't Hooft determinantlike term in the NJL part of the model. The diagonal quark number and isospin susceptibilities are completely unaffected. The off-diagonal susceptibilities show significant dependence near the crossover. Finally we present the chemical potential dependence of specific heat and speed of sound within the limits of chemical potentials where neither diquarks nor pions can condense.

Authors:
; ;  [1];  [2]
  1. Department of Theoretical Physics, Tata Institute, of Fundamental Research, Homi Bhabha Road, Mumbai 400 005 (India)
  2. (India)
Publication Date:
OSTI Identifier:
21020487
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.75.094015; (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; BARYON NUMBER; BARYONS; CHIRAL SYMMETRY; COMPARATIVE EVALUATIONS; FLAVOR MODEL; INSTANTONS; ISOSPIN; LATTICE FIELD THEORY; PIONS; POTENTIALS; QUANTUM CHROMODYNAMICS; QUARKS; SOUND WAVES; SPECIFIC HEAT; SYMMETRY BREAKING; TEMPERATURE DEPENDENCE; THERMODYNAMICS

Citation Formats

Mukherjee, Swagato, Mustafa, Munshi G., Ray, Rajarshi, and Theory Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700 064. Thermodynamics of the Polyakov-Nambu-Jona-Lasinio model with nonzero baryon and isospin chemical potentials. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.094015.
Mukherjee, Swagato, Mustafa, Munshi G., Ray, Rajarshi, & Theory Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700 064. Thermodynamics of the Polyakov-Nambu-Jona-Lasinio model with nonzero baryon and isospin chemical potentials. United States. doi:10.1103/PHYSREVD.75.094015.
Mukherjee, Swagato, Mustafa, Munshi G., Ray, Rajarshi, and Theory Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700 064. Tue . "Thermodynamics of the Polyakov-Nambu-Jona-Lasinio model with nonzero baryon and isospin chemical potentials". United States. doi:10.1103/PHYSREVD.75.094015.
@article{osti_21020487,
title = {Thermodynamics of the Polyakov-Nambu-Jona-Lasinio model with nonzero baryon and isospin chemical potentials},
author = {Mukherjee, Swagato and Mustafa, Munshi G. and Ray, Rajarshi and Theory Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700 064},
abstractNote = {We have extended the Polyakov-Nambu-Jona-Lasinio (PNJL) model for two degenerate flavors to include the isospin chemical potential ({mu}{sub I}). All the diagonal and mixed derivatives of pressure with respect to the quark number (proportional to baryon number) chemical potential ({mu}{sub 0}) and isospin chemical potential up to sixth order have been extracted at {mu}{sub 0}={mu}{sub I}=0. These derivatives give the generalized susceptibilities with respect to quark and isospin numbers. Similar estimates for the flavor diagonal and off-diagonal susceptibilities are also presented. Comparison to lattice QCD (LQCD) data of some of these susceptibilities for which LQCD data are available show similar temperature dependence, though there are some quantitative deviations above the crossover temperature. We have also looked at the effects of instanton induced flavor mixing coming from the U{sub A}(1) chiral symmetry breaking 't Hooft determinantlike term in the NJL part of the model. The diagonal quark number and isospin susceptibilities are completely unaffected. The off-diagonal susceptibilities show significant dependence near the crossover. Finally we present the chemical potential dependence of specific heat and speed of sound within the limits of chemical potentials where neither diquarks nor pions can condense.},
doi = {10.1103/PHYSREVD.75.094015},
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}
}
  • We study the phase diagram of two-flavor dense QCD at finite isospin and baryon chemical potentials in the framework of the Nambu-Jona-Lasinio model. We focus on the case with arbitrary isospin chemical potential {mu}{sub I} and small baryon chemical potential {mu}{sub B{<=}{mu}B}{sup {chi}}where {mu}{sub B}{sup {chi}}is the critical chemical potential for the first-order chiral phase transition to happen at {mu}{sub I}=0. The {mu}{sub I}-{mu}{sub B} phase diagram shows a rich phase structure since the system undergoes a crossover from a Bose-Einstein condensate of charged pions to a BCS superfluid with condensed quark-antiquark Cooper pairs when {mu}{sub I} increases at {mu}{submore » B}=0, and a nonzero baryon chemical potential serves as a mismatch between the pairing species. We observe a gapless pion condensation phase near the quadruple point ({mu}{sub I},{mu}{sub B})=(m{sub {pi}},M{sub N}-1.5m{sub {pi}}) where m{sub {pi}}, M{sub N} are the vacuum masses of pions and nucleons, respectively. The first-order chiral phase transition becomes a smooth crossover when {mu}{sub I}>0.82m{sub {pi}}. At very large isospin chemical potential, {mu}{sub I}>6.36m{sub {pi}}, an inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell superfluid phase, appears in a window of {mu}{sub B}, which should in principle exist for arbitrary large {mu}{sub I}. Between the gapless and the Larkin-Ovchinnikov-Fulde-Ferrell phases, the pion superfluid phase and the normal quark matter phase are connected by a first-order phase transition. In the normal phase above the superfluid domain, we find that charged pions are still bound states even though {mu}{sub I} becomes very large, which is quite different from that at finite temperature. Our phase diagram is in good agreement with that found in imbalanced cold atom systems.« less
  • We extend the Polyakov-loop improved Nambu-Jona-Lasinio model to 2+1 flavor case to study the chiral and deconfinement transitions of strongly interacting matter at finite temperature and nonzero chemical potential. The Polyakov loop, the chiral susceptibility of light quarks (u and d), and the strange quark number susceptibility as functions of temperature at zero chemical potential are determined and compared with the recent results of lattice QCD simulations. We find that there is always an inflection point in the curve of strange quark number susceptibility accompanying the appearance of the deconfinement phase, which is consistent with the result of lattice QCDmore » simulations. Predictions for the case at nonzero chemical potential and finite temperature are made as well. We give the phase diagram in terms of the chemical potential and temperature and find that the critical end point moves down to low temperature and finally disappears with the decrease of the strength of the 't Hooft flavor-mixing interaction.« less
  • A nonlocal covariant extension of the two-flavor Nambu and Jona-Lasinio model is constructed, with built-in constraints from the running coupling of QCD at high-momentum and instanton physics at low-momentum scales. Chiral low-energy theorems and basic current algebra relations involving pion properties are shown to be reproduced. The momentum-dependent dynamical quark mass derived from this approach is in agreement with results from Dyson-Schwinger equations and lattice QCD. At finite temperature, inclusion of the Polyakov loop and its gauge invariant coupling to quarks reproduces the dynamical entanglement of the chiral and deconfinement crossover transitions as in the (local) Polyakov-loop-extended Nambu and Jona-Lasiniomore » model, but now without the requirement of introducing an artificial momentum cutoff. Steps beyond the mean-field approximation are made including mesonic correlations through quark-antiquark ring summations. Various quantities of interest (pressure, energy density, speed of sound, etc.) are calculated and discussed in comparison with lattice QCD thermodynamics at zero chemical potential. The extension to finite quark chemical potential and the phase diagram in the (T,{mu})-plane are also discussed.« less
  • We discuss the isentropic trajectories on the QCD phase diagram in the temperature and the quark chemical potential plane using the Nambu-Jona-Lasinio model with the Polyakov loop coupling. We impose a constraint on the strange quark chemical potential so that the strange quark density is zero, which is the case in the ultra relativistic heavy-ion collisions. We compare our numerical results with the truncated estimates by the Taylor expansion in terms of the chemical potential to quantify the reliability of the expansion used in the lattice QCD simulation. We finally discuss the strange quark chemical potential induced by the strangenessmore » neutrality condition and relate it to the ratio of the Polyakov loop and the anti-Polyakov loop.« less
  • The Monte-Carlo method is applied to the Polyakov-loop extended Nambu-Jona-Lasinio model. This leads beyond the saddle-point approximation in a mean-field calculation and introduces fluctuations around the mean fields. We study the impact of fluctuations on the thermodynamics of the model, both in the case of pure gauge theory and including two quark flavors. In the two-flavor case, we calculate the second-order Taylor expansion coefficients of the thermodynamic grand canonical partition function with respect to the quark chemical potential and present a comparison with extrapolations from lattice QCD. We show that the introduction of fluctuations produces only small changes in themore » behavior of the order parameters for chiral symmetry restoration and the deconfinement transition. On the other hand, we find that fluctuations are necessary in order to reproduce lattice data for the flavor nondiagonal quark susceptibilities. Of particular importance are pion fields, the contribution of which is strictly zero in the saddle point approximation.« less