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The Wigner solution of quark gap equation and chiral phase transition of QCD at finite temperature and nonzero chemical potential

  • Zhu-fang Cui
  • Chao Shi
  • Yong-hui Xia
  • Yu Jiang
  • Hong-shi ZongEmail author
Regular Article - Theoretical Physics

Abstract

By employing some modification to the normal NJL model, we discuss the Wigner solution of quark gap equation at finite temperature and chemical potential when the current quark mass m is nonzero. The discovery of the coexistence of the Nambu solution and the Wigner solution at finite temperature and chemical potential beyond the chiral limit is of great importance in the study of the chiral phase transition of QCD. Using the pressure difference between Nambu phase and Wigner phase (or in other words, the bag constant) as an order parameter for chiral phase transition, we draw a possible phase diagram based on our calculations.

Keywords

Chiral Limit Gluon Propagator Quark Condensate Quark Propagator Chiral Phase Transition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work is supported in part by the National Natural Science Foundation of China (under Grant 11275097, 10935001, 11274166 and 11075075), the National Basic Research Program of China (under Grant 2012CB921504) and the Research Fund for the Doctoral Program of Higher Education (under Grant No 2012009111002).

References

  1. 1.
    M.A. Stephanov, PoS(LAT2006)024. arXiv:hep-lat/0701002
  2. 2.
    Y. Aoki, G. Endrődi, Z. Fodor, S.D. Katz, K.K. Szabó, Nature 443, 675 (2006) ADSCrossRefGoogle Scholar
  3. 3.
    K. Fukushima, Phys. Rev. D 77, 114028 (2008) ADSCrossRefGoogle Scholar
  4. 4.
    G.S. Bali, F. Bruckmann, G. Endrődi, Z. Fodor, S.D. Katz, S. Krieg, A. Scha̋fer, K.K. Szabó, J. High Energy Phys. 02, 044 (2012) ADSCrossRefGoogle Scholar
  5. 5.
    M. Hanada, N. Yamamoto, J. High Energy Phys. 02, 0138 (2012) ADSCrossRefGoogle Scholar
  6. 6.
    Y. Jiang, H. Chen, W.-m. Sun, H.-s. Zong, J. High Energy Phys. 04, 014 (2013) MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    C.D. Roberts, A.G. Williams, Prog. Part. Nucl. Phys. 33, 477 (1994) ADSCrossRefGoogle Scholar
  8. 8.
    C.D. Roberts, S.M. Schmidt, Prog. Part. Nucl. Phys. 45, S1 (2000) ADSCrossRefGoogle Scholar
  9. 9.
    R.T. Cahill, C.D. Roberts, Phys. Rev. D 32, 2419 (1985) ADSCrossRefGoogle Scholar
  10. 10.
    P.C. Tandy, Prog. Part. Nucl. Phys. 39, 117 (1997) ADSCrossRefGoogle Scholar
  11. 11.
    H.-s. Zong, W.-m. Sun, J.-l. Ping, X.-f. Lü, F. Wang, Chin. Phys. Lett. 22, 3036 (2005) ADSCrossRefGoogle Scholar
  12. 12.
    L. Chang, Y.-x. Liu, M.S. Bhagwat, C.D. Roberts, S.V. Wright, Phys. Rev. C 75, 015201 (2007) ADSCrossRefGoogle Scholar
  13. 13.
    R. Williams, C.S. Fischer, M.R. Pennington, Phys. Lett. B 645, 167 (2007) ADSCrossRefGoogle Scholar
  14. 14.
    K.-l. Wang, S.-x. Qin, Y.-x. Liu, L. Chang, C.D. Roberts, S.M. Schmidt, Phys. Rev. D 86, 114001 (2012) ADSCrossRefGoogle Scholar
  15. 15.
    S. Borsányi, Z. Fodor, C. Hoelbling, S.D. Katz, S. Krieg, C. Ratti, K.K. Szabó, J. High Energy Phys. 09, 073 (2010) ADSCrossRefGoogle Scholar
  16. 16.
    A. Bazavov et al. (HotQCD Collaboration), Phys. Rev. D 85, 054503 (2012) ADSCrossRefGoogle Scholar
  17. 17.
    N. Bratovic, T. Hatsuda, W. Weise, Phys. Lett. B 719, 131 (2013) ADSCrossRefGoogle Scholar
  18. 18.
    S. Carignano, D. Nickel, M. Buballa, Phys. Rev. D 82, 054009 (2010) ADSCrossRefGoogle Scholar
  19. 19.
    M. Kitazawa, T. Koide, T. Kunihiro, Y. Nemoto, Prog. Theor. Phys. 108, 929 (2002) ADSCrossRefzbMATHGoogle Scholar
  20. 20.
    D. Blaschke, M.K. Volkov, V.L. Yudichev, Eur. Phys. J. A 17, 103 (2003) ADSCrossRefGoogle Scholar
  21. 21.
    T. Hatsuda, M. Tachibana, N. Yamamoto, G. Baym, Phys. Rev. Lett. 97, 122001 (2006) ADSCrossRefGoogle Scholar
  22. 22.
    D. Blaschke, H. Grigorian, A. Khalatyan, D.N. Voskresensky, Nucl. Phys. B, Proc. Suppl. 141, 137 (2005) ADSCrossRefGoogle Scholar
  23. 23.
    A. Andronic et al., Nucl. Phys. A 837, 65 (2010) ADSCrossRefGoogle Scholar
  24. 24.
    Y. Jiang, H. Gong, W.-m. Sun, H.-s. Zong, Phys. Rev. D 85, 034031 (2012) ADSCrossRefGoogle Scholar
  25. 25.
    S.P. Klevansky, Rev. Mod. Phys. 64, 649 (1992) MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    M. Buballa, Phys. Rep. 407, 205 (2005) ADSCrossRefGoogle Scholar
  27. 27.
    J.M. Cornwall, R. Jackiw, E. Tomboulis, Phys. Rev. D 10, 2428 (1974) ADSCrossRefzbMATHGoogle Scholar
  28. 28.
    Y. Jiang, L.-j. Luo, H.-s. Zong, J. High Energy Phys. 02, 066 (2011) ADSCrossRefGoogle Scholar
  29. 29.
    M. Asakawa, K. Yazaki, Nucl. Phys. A 504, 668 (1989) CrossRefGoogle Scholar
  30. 30.
    T. Hatsuda, T. Kunihiro, Phys. Rep. 247, 221 (1994) ADSCrossRefGoogle Scholar
  31. 31.
    T.G. Steele, Z. Phys. C 42, 499 (1989) MathSciNetCrossRefGoogle Scholar
  32. 32.
    P. Pascual, R. Tarrach, QCD: Renormalization for the Practitioner. Lecture Notes in Physics, vol. 194 (Springer, Berlin, 1984) CrossRefGoogle Scholar
  33. 33.
    H.-s. Zong, J.-l. Ping, H.-t. Yang, X.-f. Lü, F. Wang, Phys. Rev. D 67, 074004 (2003) ADSCrossRefGoogle Scholar
  34. 34.
    P. Maris, C.D. Roberts, P.C. Tandy, Phys. Lett. B 420, 267 (1998) ADSCrossRefGoogle Scholar
  35. 35.
    M. He, F. Hu, W.-m. Sun, H.-s. Zong, Phys. Lett. B 675, 32 (2009) ADSCrossRefGoogle Scholar
  36. 36.
    H.-s. Zong, W.-m. Sun, Int. J. Mod. Phys. A 23, 3591 (2008) MathSciNetADSCrossRefGoogle Scholar
  37. 37.
    A. Chodos, R.L. Jaffe, K. Johnson, C.B. Thorn, V.F. Weisskopf, Phys. Rev. D 9, 3471 (1974) MathSciNetADSCrossRefGoogle Scholar
  38. 38.
    A. Chodos, R.L. Jaffe, K. Johnson, C.B. Thorn, Phys. Rev. D 10, 2599 (1974) MathSciNetADSCrossRefGoogle Scholar
  39. 39.
    K. Kashiwa, H. Kouno, M. Matsuzaki, M. Yahiro, Phys. Lett. B 662, 26 (2008) ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  • Zhu-fang Cui
    • 1
    • 3
  • Chao Shi
    • 2
    • 3
  • Yong-hui Xia
    • 2
    • 3
  • Yu Jiang
    • 4
    • 5
  • Hong-shi Zong
    • 2
    • 3
    • 4
    Email author
  1. 1.Key Laboratory of Modern Acoustics, MOE, Institute of Acoustics, and Department of PhysicsNanjing UniversityNanjingChina
  2. 2.Department of PhysicsNanjing UniversityNanjingChina
  3. 3.State Key Laboratory of Theoretical PhysicsInstitute of Theoretical Physics, CASBeijingChina
  4. 4.Joint Center for ParticleNuclear Physics and CosmologyNanjingChina
  5. 5.Center for Statistical and Theoretical Condensed Matter PhysicsZhejiang Normal UniversityJinhua CityChina

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