# 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:

- Department of Theoretical Physics, Tata Institute, of Fundamental Research, Homi Bhabha Road, Mumbai 400 005 (India)
- (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}

}