Three-dimensional QCD phase diagram in the pNJL model
Abstract: Based on the three-flavor Polyakov-looped Nambu$-$Jona-Lasinio (pNJL) model, we have studied the structure of the three-dimensional QCD phase diagram with respect to the temperature, the baryon chemical potential, and the isospin chemical potential, by investigating the interplay among the chiral quark condensate, the pion condensate, and the Polyakov loop. While the pNJL model leads to qualitatively similar structure of the normal quark phase, the pion superfluid phase, and the Sarma phase as well as their phase boundaries, when compared to the NJL model, the inclusion of the Polyakov loop enlarges considerably the areas of the pion superfluid phase and the Sarma phase, and leads to critical end points at higher temperatures. With the contribution of the gluon dynamics effectively included, the present study is expected to give a more reliable prediction of the three-dimensional QCD phase diagram compared to that in the NJL model.
- C. Bernard, T. Burch, E. B. Gregory, D. Toussaint, Carleton E. DeTar, J. Osborn, Steven Gottlieb, U. M. Heller, and R. Sugar (MILC), “QCD thermodynamics with three flavors of improved staggered quarks,” Phys. Rev. D 71, 034504 (2005), arXiv:hep-lat/0405029 .
- Y. Aoki, G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Szabo, “The Order of the quantum chromodynamics transition predicted by the standard model of particle physics,” Nature 443, 675–678 (2006), arXiv:hep-lat/0611014 .
- A. Bazavov et al., “The chiral and deconfinement aspects of the QCD transition,” Phys. Rev. D 85, 054503 (2012), arXiv:1111.1710 [hep-lat] .
- F. Karsch, “Lattice QCD at high temperature and density,” Lect. Notes Phys. 583, 209–249 (2002), arXiv:hep-lat/0106019 .
- Shin Muroya, Atsushi Nakamura, Chiho Nonaka, and Tetsuya Takaishi, “Lattice QCD at finite density: An Introductory review,” Prog. Theor. Phys. 110, 615–668 (2003), arXiv:hep-lat/0306031 .
- Paulo F. Bedaque, “A complex path around the sign problem,” EPJ Web Conf. 175, 01020 (2018), arXiv:1711.05868 [hep-lat] .
- Nino M. Bratovic, Tetsuo Hatsuda, and Wolfram Weise, “Role of Vector Interaction and Axial Anomaly in the PNJL Modeling of the QCD Phase Diagram,” Phys. Lett. B 719, 131–135 (2013), arXiv:1204.3788 [hep-ph] .
- M. Asakawa and K. Yazaki, “Chiral Restoration at Finite Density and Temperature,” Nucl. Phys. A 504, 668–684 (1989).
- Kenji Fukushima, “Phase diagrams in the three-flavor Nambu-Jona-Lasinio model with the Polyakov loop,” Phys. Rev. D 77, 114028 (2008), [Erratum: Phys.Rev.D 78, 039902 (2008)], arXiv:0803.3318 [hep-ph] .
- Stefano Carignano and Michael Buballa, “Inhomogeneous chiral condensates in three-flavor quark matter,” Phys. Rev. D 101, 014026 (2020), arXiv:1910.03604 [hep-ph] .
- Xian-yin Xin, Si-xue Qin, and Yu-xin Liu, “Quark number fluctuations at finite temperature and finite chemical potential via the Dyson-Schwinger equation approach,” Phys. Rev. D 90, 076006 (2014), arXiv:2109.09935 [hep-ph] .
- Wei-jie Fu, Jan M. Pawlowski, and Fabian Rennecke, “QCD phase structure at finite temperature and density,” Phys. Rev. D 101, 054032 (2020), arXiv:1909.02991 [hep-ph] .
- Fei Gao and Jan M. Pawlowski, “QCD phase structure from functional methods,” Phys. Rev. D 102, 034027 (2020), arXiv:2002.07500 [hep-ph] .
- Marco Frasca and Marco Ruggieri, “Magnetic Susceptibility of the Quark Condensate and Polarization from Chiral Models,” Phys. Rev. D 83, 094024 (2011), arXiv:1103.1194 [hep-ph] .
- Bernd-Jochen Schaefer, Mathias Wagner, and Jochen Wambach, “Thermodynamics of (2+1)-flavor QCD: Confronting Models with Lattice Studies,” Phys. Rev. D 81, 074013 (2010), arXiv:0910.5628 [hep-ph] .
- D. T. Son and Misha A. Stephanov, “QCD at finite isospin density,” Phys. Rev. Lett. 86, 592–595 (2001), arXiv:hep-ph/0005225 .
- Lu-Meng Liu, Jun Xu, and Guang-Xiong Peng, “Three-dimensional QCD phase diagram with a pion condensate in the NJL model,” Phys. Rev. D 104, 076009 (2021a), arXiv:2108.09477 [hep-ph] .
- B. Klein, D. Toublan, and J. J. M. Verbaarschot, “The QCD phase diagram at nonzero temperature, baryon and isospin chemical potentials in random matrix theory,” Phys. Rev. D 68, 014009 (2003), arXiv:hep-ph/0301143 .
- A. Barducci, R. Casalbuoni, Giulio Pettini, and L. Ravagli, “A Calculation of the QCD phase diagram at finite temperature, and baryon and isospin chemical potentials,” Phys. Rev. D 69, 096004 (2004), arXiv:hep-ph/0402104 .
- A. Barducci, R. Casalbuoni, G. Pettini, and L. Ravagli, “A NJL-based study of the QCD critical line,” Phys. Rev. D 72, 056002 (2005), arXiv:hep-ph/0508117 .
- Lian-yi He, Meng Jin, and Peng-fei Zhuang, “Pion superfluidity and meson properties at finite isospin density,” Phys. Rev. D 71, 116001 (2005), arXiv:hep-ph/0503272 .
- D. Ebert and K. G. Klimenko, “Gapless pion condensation in quark matter with finite baryon density,” J. Phys. G 32, 599–608 (2006), arXiv:hep-ph/0507007 .
- Tao Xia, Lianyi He, and Pengfei Zhuang, “Three-flavor Nambu–Jona-Lasinio model at finite isospin chemical potential,” Phys. Rev. D 88, 056013 (2013), arXiv:1307.4622 [hep-ph] .
- Simon Roessner, Claudia Ratti, and W. Weise, “Polyakov loop, diquarks and the two-flavour phase diagram,” Phys. Rev. D 75, 034007 (2007), arXiv:hep-ph/0609281 .
- Zhao Zhang and Yu-xin Liu, “Two-flavor QCD phases and condensates at finite isospin chemical potential,” Phys. Rev. C 75, 035201 (2007a), arXiv:hep-ph/0603252 .
- Zhao Zhang and Yu-Xin Liu, “Coupling of pion condensate, chiral condensate and Polyakov loop in an extended NJL model,” Phys. Rev. C 75, 064910 (2007b), arXiv:hep-ph/0610221 .
- Takahiro Sasaki, Yuji Sakai, Hiroaki Kouno, and Masanobu Yahiro, “QCD phase diagram at finite baryon and isospin chemical potentials,” Phys. Rev. D 82, 116004 (2010), arXiv:1005.0910 [hep-ph] .
- Cheng-fu Mu, Lian-yi He, and Yu-xin Liu, “Evaluating the phase diagram at finite isospin and baryon chemical potentials in the Nambu-Jona-Lasinio model,” Phys. Rev. D 82, 056006 (2010).
- Prabal Adhikari, Jens O. Andersen, and Patrick Kneschke, “Pion condensation and phase diagram in the Polyakov-loop quark-meson model,” Phys. Rev. D 98, 074016 (2018), arXiv:1805.08599 [hep-ph] .
- Zhen-Yan Lu, Cheng-Jun Xia, and Marco Ruggieri, “Thermodynamics and susceptibilities of isospin imbalanced QCD matter,” Eur. Phys. J. C 80, 46 (2020), arXiv:1907.11497 [hep-ph] .
- B. B. Brandt, G. Endrodi, and S. Schmalzbauer, “QCD phase diagram for nonzero isospin-asymmetry,” Phys. Rev. D 97, 054514 (2018a), arXiv:1712.08190 [hep-lat] .
- Tamaz Khunjua, Konstantin Klimenko, and Roman Zhokhov, “Charged Pion Condensation in Dense Quark Matter: Nambu–Jona-Lasinio Model Study,” Symmetry 11, 778 (2019), arXiv:1912.08635 [hep-ph] .
- Kenji Fukushima, “Chiral effective model with the Polyakov loop,” Phys. Lett. B 591, 277–284 (2004), arXiv:hep-ph/0310121 .
- Claudia Ratti, Michael A. Thaler, and Wolfram Weise, “Phases of QCD: Lattice thermodynamics and a field theoretical model,” Phys. Rev. D 73, 014019 (2006), arXiv:hep-ph/0506234 .
- Kenji Fukushima and Tetsuo Hatsuda, “The phase diagram of dense QCD,” Rept. Prog. Phys. 74, 014001 (2011), arXiv:1005.4814 [hep-ph] .
- Kenji Fukushima and Vladimir Skokov, “Polyakov loop modeling for hot QCD,” Prog. Part. Nucl. Phys. 96, 154–199 (2017), arXiv:1705.00718 [hep-ph] .
- Pedro Costa, M. C. Ruivo, C. A. de Sousa, H. Hansen, and W. M. Alberico, “Scalar-pseudoscalar meson behavior and restoration of symmetries in SU(3) PNJL model,” Phys. Rev. D 79, 116003 (2009), arXiv:0807.2134 [hep-ph] .
- Wei-jie Fu, Zhao Zhang, and Yu-xin Liu, “2+1 flavor Polyakov-Nambu-Jona-Lasinio model at finite temperature and nonzero chemical potential,” Phys. Rev. D 77, 014006 (2008), arXiv:0711.0154 [hep-ph] .
- Gerard ’t Hooft, “Computation of the Quantum Effects Due to a Four-Dimensional Pseudoparticle,” Phys. Rev. D 14, 3432–3450 (1976), [Erratum: Phys.Rev.D 18, 2199 (1978)].
- Matthias F. M. Lutz, S. Klimt, and W. Weise, “Meson properties at finite temperature and baryon density,” Nucl. Phys. A 542, 521–558 (1992).
- Michael Buballa, “NJL model analysis of quark matter at large density,” Phys. Rept. 407, 205–376 (2005), arXiv:hep-ph/0402234 .
- Bastian B. Brandt, Gergely Endrodi, Eduardo S. Fraga, Mauricio Hippert, Jurgen Schaffner-Bielich, and Sebastian Schmalzbauer, “New class of compact stars: Pion stars,” Phys. Rev. D 98, 094510 (2018b), arXiv:1802.06685 [hep-ph] .
- Robert D. Pisarski, “Quark gluon plasma as a condensate of SU(3) Wilson lines,” Phys. Rev. D 62, 111501 (2000), arXiv:hep-ph/0006205 .
- Andrew W. Steiner, Sanjay Reddy, and Madappa Prakash, “Color neutral superconducting quark matter,” Phys. Rev. D 66, 094007 (2002), arXiv:hep-ph/0205201 .
- Kenji Fukushima, Chris Kouvaris, and Krishna Rajagopal, “Heating (gapless) color-flavor locked quark matter,” Phys. Rev. D 71, 034002 (2005), arXiv:hep-ph/0408322 .
- Stefan B. Ruester, Verena Werth, Michael Buballa, Igor A. Shovkovy, and Dirk H. Rischke, “The Phase diagram of neutral quark matter: Self-consistent treatment of quark masses,” Phys. Rev. D 72, 034004 (2005), arXiv:hep-ph/0503184 .
- He Liu, Jun Xu, Lie-Wen Chen, and Kai-Jia Sun, “Isospin properties of quark matter from a 3-flavor NJL model,” Phys. Rev. D 94, 065032 (2016), arXiv:1602.01579 [nucl-th] .
- Lu-Meng Liu, Wen-Hao Zhou, Jun Xu, and Guang-Xiong Peng, “Isospin effect on quark matter instabilities,” Phys. Lett. B 822, 136694 (2021b), arXiv:2104.12971 [nucl-th] .
- G. Sarma, “On the influence of a uniform exchange field acting on the spins of the conduction electrons in a superconductor,” Journal of Physics and Chemistry of Solids 24, 1029–1032 (1963).
- Wojciech Florkowski and Bengt L. Friman, “Spatial dependence of the finite temperature meson correlation function,” Z. Phys. A 347, 271–276 (1994).
- Chengfu Mu and Pengfei Zhuang, “Quark Potential in a Quark-Meson Plasma,” Eur. Phys. J. C 58, 271–279 (2008), arXiv:0803.0581 [nucl-th] .
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.