Skip to main content
SpringerLink
Log in

QCD phase diagram with the improved Polyakov loop effective potential

  • Published:
Nuclear Science and Techniques Aims and scope Submit manuscript

Abstract

We report our recent progress on the QCD phase structure. We explore the properties of quark–gluon matter in the improved Polyakov–Nambu–Jona–Lasinio (PNJL) model by introducing a chemical potential-dependent Polyakov loop potential. This treatment effectively reflects the quantum backreaction of matter sector to glue sector at nonzero chemical potential. Compared with the original PNJL model, a superiority of the improved PNJL model is that it can effectively describe the confinement–deconfinement transition at low temperature and high density. And the QCD phase diagram will be modified to a certain degree if the strength of the quantum backreaction of matter sector to glue sector is strong. One evident variation is that the region of quarkyonic phase will be greatly reduced in the improved PNJL model. This means that the modification to the Polyakov loop potential with the chemical potential dependence is possibly a significant improvement in exploring the full QCD phase structure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. S. Gupta, X. F. Luo, B. Mohanty et al., Scale for the phase diagram of quantum chromodynamics. Science 332, 1525 (2011), doi:10.1126/science.1204621

  2. P. Braun-Munzinger, J. Wambach, Phase diagram of strongly interacting matter. Rev. Mod. Phys. 81, 1031 (2009). doi:10.1103/RevModPhys.81.1031

    Article  Google Scholar 

  3. K. Fukushima, T. Hatsuda, The phase diagram of dense QCD. Rept. Prog. Phys. 74, 014001 (2011). doi:10.1088/0034-4885/74/1/014001

    Article  Google Scholar 

  4. O. Kaczmarek, F. Zantow, Static quark-antiquark interactions in zero and finite temperature QCD: I. Heavy quark free energies, running coupling, and quarkonium binding. Phys. Rev. D 71, 114510 (2005). doi:10.1103/PhysRevD.71.114510

    Article  Google Scholar 

  5. C.R. Allton, S. Ejiri, S.J. Hands et al., QCD thermal phase transition in the presence of a small chemical potential. Phys. Rev. D 66, 074507 (2002). doi:10.1103/PhysRevD.66.074507

    Article  Google Scholar 

  6. M. Cheng, N.H. Christ, S. Datta et al., Transition temperature in QCD. Phys. Rev. D 74, 054507 (2006). doi:10.1103/PhysRevD.74.054507

    Article  Google Scholar 

  7. Y. Aoki, S. Borsányi, S. Dürr et al., The QCD transition temperature: results with physical masses in the continuum limit II. J. High Energy Phys. 06, 088 (2009). doi:10.1088/1126-6708/2009/06/088

    Article  Google Scholar 

  8. Y. Aokia, Z. Fodora, S.D. Katza et al., The QCD transition temperature: Results with physical masses in the continuum limit. Phys. Lett. B 643, 46 (2006). doi:10.1016/j.physletb.2006.10.021

    Article  Google Scholar 

  9. S. Borsányi, Z. Fodor, C. Hoelbling et al., Is there still any \(T_c\) mystery in lattice QCD? Results with physical masses in the continuum limit III. J. High Energy Phys. 09, 073 (2010). doi:10.1007/JHEP09(2010)073

    Article  MATH  Google Scholar 

  10. M. D’Elia, F. Sanfilippo, Thermodynamics of two flavor QCD from imaginary chemical potentials. Phys. Rev. D 80, 014502 (2009). doi:10.1103/PhysRevD.80.014502

    Article  Google Scholar 

  11. S. Ejiri, Canonical partition function and finite density phase transition in lattice QCD. Phys. Rev. D 78, 074507 (2008). doi:10.1103/PhysRevD.78.074507

    Article  Google Scholar 

  12. M.A. Clark, A.D. Kennedy, Accelerating dynamical-fermion computations using the rational hybrid Monte Carlo algorithm with multiple pseudofermion fields. Phys. Rev. Lett. 98, 051601 (2007). doi:10.1103/PhysRevLett.98.051601

    Article  Google Scholar 

  13. I.C. Clöt, C.D. Roberts, Explanation and prediction of observables using continuum strong QCD. Prog. Part. Nucl. Phys. 77, 1 (2014). doi:10.1016/j.ppnp.2014.02.001

    Article  Google Scholar 

  14. S.S. Xu, Z.F. Cui, B. Wang et al., Chiral phase transition with a chiral chemical potential in the framework of Dyson–Schwinger equations. Phys. Rev. D 91, 056003 (2015). doi:10.1103/PhysRevD.91.056003

    Article  Google Scholar 

  15. M. Buballa, NJL-model analysis of dense quark matter. Phys. Rep. 407, 205 (2005). doi:10.1016/j.physrep.2004.11.004

    Article  Google Scholar 

  16. P.C. Chu, X. Wang, L.W. Chen et al., Quark magnetar in the three-flavor Nambu–Jona–Lasinio model with vector interactions and a magnetized gluon potential. Phys. Rev. D 91, 023003 (2015). doi:10.1103/PhysRevD.91.023003

    Article  Google Scholar 

  17. G.Q. Cao, L.Y. He, P.F. Zhuang, Collective modes and Kosterlitz–Thouless transition in a magnetic field in the planar Nambu–Jona–Lasinio model. Phys. Rev. D 90, 056005 (2014). doi:10.1103/PhysRevD.90.056005

    Article  Google Scholar 

  18. D.P. Menezes, M.B. Pinto, L.B. Castro et al., Repulsive vector interaction in three-flavor magnetized quark and stellar matter. Phys. Rev. C 89, 055207 (2014). doi:10.1103/PhysRevC.89.055207

    Article  Google Scholar 

  19. J. Xu, T. Song, C.M. Ko et al., Phys. Rev. Lett. 112, 012301 (2014). doi:10.1103/PhysRevLett.112.012301

    Article  Google Scholar 

  20. K. Fukushima, Phase diagrams in the three-flavor Nambu–Jona–Lasinio model with the Polyakov loop. Phys. Rev. D 77, 114028 (2008). doi:10.1103/PhysRevD.77.114028

    Article  Google Scholar 

  21. C. Ratti, M.A. Thaler, W. Weise, Phases of QCD: lattice thermodynamics and a field theoretical model. Phys. Rev. D 73, 014019 (2006). doi:10.1103/PhysRevD.73.014019

    Article  Google Scholar 

  22. P. Costa, M.C. Ruivo, C.A. de Sousa et al., Phase diagram and critical properties within an effective model of QCD: the Nambu–Jona–Lasinio model coupled to the Polyakov loop. Symmetry 2, 1338 (2010). doi:10.3390/sym2031338

    Article  Google Scholar 

  23. Y. Sakai, T. Sasaki, H. Kouno et al., Entanglement between deconfinement transition and chiral symmetry restoration. Phys. Rev. D 82, 076003 (2010). doi:10.1103/PhysRevD.82.076003

    Article  Google Scholar 

  24. B.-J. Schaefer, M. Wagner, J. Wambach, Thermodynamics of (2+1)-flavor QCD: confronting models with lattice studies. Phys. Rev. D 81, 074013 (2010). doi:10.1103/PhysRevD.81.074013

    Article  Google Scholar 

  25. V. Skokov, B. Friman, K. Redlich, Quark number fluctuations in the Polyakov loop-extended quark–meson model at finite baryon density. Phys. Rev. C 83, 054904 (2011). doi:10.1103/PhysRevC.83.054904

    Article  Google Scholar 

  26. S. Chatterjee, K.A. Mohan, Including the fermion vacuum fluctuations in the (2+1) flavor Polyakov quark–meson model. Phys. Rev. D 85, 074018 (2012). doi:10.1103/PhysRevD.85.074018

    Article  Google Scholar 

  27. J.F. Xu, G.X. Peng, F. Liu et al., Strange matter and strange stars in a thermodynamically self-consistent perturbation model with running coupling and running strange quark mass. Phys. Rev. D 92, 025025 (2015). doi:10.1103/PhysRevD.92.025025

    Article  Google Scholar 

  28. C.J. Xia, G.X. Peng, S.W. Chen et al., Thermodynamic consistency, quark mass scaling, and properties of strange matter. Phys. Rev. D 89, 105027 (2014). doi:10.1103/PhysRevD.89.105027

    Article  Google Scholar 

  29. G.X. Peng, A. Li, U. Lombardo, Deconfinement phase transition in hybrid neutron stars from the Brueckner theory with three-body forces and a quark model with chiral mass scaling. Phys. Rev. C 77, 065807 (2008). doi:10.1103/PhysRevC.77.065807

    Article  Google Scholar 

  30. L. McLarren, R.D. Pisarski, Phases of dense quarks at large \(N_c\). Nucl. Phys. A 796, 83 (2007). doi:10.1016/j.nuclphysa.2007.08.013

    Article  Google Scholar 

  31. Y. Hidaka, L. McLarren, R.D. Pisarski, Baryons and the phase diagram for a large number of colors and flavors. Nucl. Phys. A 808, 117 (2008). doi:10.1016/j.nuclphysa.2008.05.009

    Article  Google Scholar 

  32. B.-J. Schaefer, J.M. Pawlowski, J. Wambach, Phase structure of the Polyakov–quark–meson model. Phys. Rev. D 76, 074023 (2007). doi:10.1103/PhysRevD.76.074023

    Article  Google Scholar 

  33. T.K. Herbst, J.M. Pawlowski, B.-J. Schaefer, The phase structure of the Polyakov–quark–meson model beyond mean field. Phys. Lett. B 696, 58 (2011). doi:10.1016/j.physletb.2010.12.003

    Article  Google Scholar 

  34. T.K. Herbst, J.M. Pawlowski, B.-J. Schaefer, Phase structure and thermodynamics of QCD. Phys. Rev. D 88, 014007 (2013). doi:10.1103/PhysRevD.88.014007

    Article  Google Scholar 

  35. H. Abuki, R. Anglani, R. Gatto et al., Chiral crossover, deconfinement, and quarkyonic matter within a Nambu–Jona–Lasinio model with the Polyakov loop. Phys. Rev. D 78, 034034 (2008). doi:10.1103/PhysRevD.78.034034

    Article  Google Scholar 

  36. X.Y. Xin, S.X. Qin, Y.X. Liu, Improvement on the Polyakov–Nambu–Jona–Lasinio model and the QCD phase transitions. Phys. Rev. D 89, 094012 (2014). doi:10.1103/PhysRevD.89.094012

    Article  Google Scholar 

  37. G.Y. Shao, Z.D. Tang, M. Di Toro et al., Phase transition of strongly interacting matter with a chemical potential dependent Polyakov loop potential. Phys. Rev. D 94, 014008 (2016). doi:10.1103/PhysRevD.94.014008

    Article  Google Scholar 

  38. V.A. Dexheimer, S. Schramm, Novel approach to modeling hybrid stars. Phys. Rev. C 81, 045201 (2010). doi:10.1103/PhysRevC.81.045201

    Article  MATH  Google Scholar 

  39. S. Rößner, C. Ratti, W. Weise, Polyakov loop, diquarks, and the two-flavor phase diagram. Phys. Rev. D 75, 034007 (2007). doi:10.1103/PhysRevD.75.034007

    Article  Google Scholar 

  40. M. Fukugita, M. Okawa, A. Ukava, Finite-size scaling study of the deconfining phase transition in pure SU(3) lattice gauge theory. Nucl. Phys. B 337, 181 (1990). doi:10.1016/0550-3213(90)90256-D

    Article  Google Scholar 

  41. G.Y. Shao, Z.D. Tang, M. Di Toro et al., Entanglement interaction and the phase diagram of strongly interacting matter. Phys. Rev. D 92, 114027 (2015). doi:10.1103/PhysRevD.92.114027

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Physics, Xi’an Jiaotong University, Xi’an, 710049, China

    Guo-Yun Shao, Xue-Yan Gao, Zhan-Duo Tang & Ning Gao

Authors
  1. Guo-Yun Shao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xue-Yan Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhan-Duo Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ning Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guo-Yun Shao.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11305121), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20130201120046), the Natural Science Basic Research Plan in Shanxi Province of China (No. 2014JQ1012) and the Fundamental Research Funds for the Central Universities.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shao, GY., Gao, XY., Tang, ZD. et al. QCD phase diagram with the improved Polyakov loop effective potential . NUCL SCI TECH 27, 151 (2016). https://doi.org/10.1007/s41365-016-0152-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s41365-016-0152-0

Keywords

Search

Navigation