Advertisement

The European Physical Journal C

, Volume 56, Issue 4, pp 483–492 | Cite as

Chiral susceptibility and chiral phase transition in Nambu–Jona-Lasinio model

  • Yue Zhao
  • Lei Chang
  • Wei Yuan
  • Yu-xin LiuEmail author
Regular Article - Theoretical Physics

Abstract

We give a general relation between the chiral susceptibility and the thermodynamical potential and a relation between the chiral susceptibility and the condition for furcations to appear in the Wigner solution(s) in the Nambu–Jona-Lasinio (NJL) model. We find that the chiral susceptibility is a quantity able to represent the appearance of furcation in the solution(s) of the gap equation and the concavo–convexity of the thermodynamical potential in the NJL model. It indicates that the chiral susceptibility can identify the stability of the states and the chiral phase transition in NJL model. We propose that analyzing the chiral susceptibility may play an important role in studying the chiral phase transition in approaches superior to the NJL model.

PACS

12.38.Aw 05.70.Fh 11.30.Rd 12.40.-y 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. ’t Hooft, Nucl. Phys. B 33, 173 (1971) ADSMathSciNetGoogle Scholar
  2. 2.
    D.J. Gross, F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973) ADSGoogle Scholar
  3. 3.
    H.D. Politzer, Phys. Rev. Lett. 30, 1346 (1973) ADSGoogle Scholar
  4. 4.
    C.D. Roberts, A.G. Williams, Prog. Part. Nucl. Phys. 33, 477 (1994) ADSGoogle Scholar
  5. 5.
    M. Harada, A. Shibata, Phys. Rev. D 59, 014010 (1999) ADSGoogle Scholar
  6. 6.
    C.D. Roberts, S.M. Schmidt, Prog. Part. Nucl. Phys. 45(S1), 1 (2000) ADSGoogle Scholar
  7. 7.
    C.D. Roberts, M.S. Bhagwat, A. Hoell, S.V. Wright, Eur. Phys. J. Special Topics 140, 53 (2007) Google Scholar
  8. 8.
    R. Alkofer, L. von Smekal, Phys. Rep. 353, 281 (2001) zbMATHADSMathSciNetGoogle Scholar
  9. 9.
    R. Alkofer, Braz. J. Phys. 37, 144 (2007) Google Scholar
  10. 10.
    P. Maris, C.D. Roberts, Int. J. Mod. Phys. E 12, 297 (2003) ADSGoogle Scholar
  11. 11.
    P. Maris, P.C. Tandy, Nucl. Phys. B (Proc. Suppl.) 161, 136 (2006) ADSGoogle Scholar
  12. 12.
    R. Alkofer, P. Watson, H. Weigel, Phys. Rev. D 65, 094026 (2002) ADSGoogle Scholar
  13. 13.
    C.S. Fischer, R. Alkofer, Phys. Rev. D 67, 094020 (2003) ADSGoogle Scholar
  14. 14.
    R. Alkofer, W. Detmold, C.S. Fischer, P. Maris, Phys. Rev. D 70, 014014 (2004) ADSGoogle Scholar
  15. 15.
    R. Alkofer, M. Kloker, A. Krassnigg, R.F. Wagenbrunn, Phys. Rev. Lett. 96, 022001 (2006) ADSGoogle Scholar
  16. 16.
    M.S. Bhagwat, M.A. Pichowsky, C.D. Roberts, P.C. Tandy, Phys. Rev. C 68, 015203 (2003) ADSGoogle Scholar
  17. 17.
    M.R. Pennington, arXiv:hep-ph/0409156
  18. 18.
    C.S. Fischer, J. Phys. G 32, R253 (2006) ADSGoogle Scholar
  19. 19.
    C.S. Fischer, B. Gruter, R. Alkofer, Ann. Phys. (N.Y.) 321, 1918 (2006) zbMATHADSMathSciNetGoogle Scholar
  20. 20.
    L. Chang, Y.X. Liu, H. Guo, Phys. Rev. D 72, 094023 (2005) ADSGoogle Scholar
  21. 21.
    L. Chang, H. Chen, B. Wang, W. Yuan, Y.X. Liu, Phys. Lett. B 644, 315 (2007) ADSGoogle Scholar
  22. 22.
    Z. Zhang, Y.X. Liu, Phys. Rev. C 75, 035201 (2007) ADSGoogle Scholar
  23. 23.
    W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006) ADSGoogle Scholar
  24. 24.
    M. He, D.K. He, H.T. Feng, W.M. Sun, H.S. Zong, Phys. Rev. D 76, 076005 (2007) ADSGoogle Scholar
  25. 25.
    M. He, W.M. Sun, H.T. Feng, H.S. Zong, J. Phys. G 34, 2655 (2007) ADSGoogle Scholar
  26. 26.
    Y. Nambu, G. Jona-Lasinio, Phys. Rev. 112, 345 (1961) ADSGoogle Scholar
  27. 27.
    Y. Nambu, G. Jona-Lasinio, Phys. Rev. 124, 246 (1961) ADSGoogle Scholar
  28. 28.
    M.K. Volkov, Ann. Phys. (N.Y. ) 157, 282 (1984) ADSGoogle Scholar
  29. 29.
    T. Hatsuda, T. Kunihiro, Phys. Lett. B 145, 7 (1984) ADSGoogle Scholar
  30. 30.
    T. Hatsuda, T. Kunihiro, Phys. Rep. 247, 221 (1994) ADSGoogle Scholar
  31. 31.
    S.P. Klevansky, Rev. Mod. Phys. 64, 649 (1992) ADSMathSciNetGoogle Scholar
  32. 32.
    R. Alkofer, H. Reinhardt, H. Weigel, Phys. Rep. 265, 139 (1996) ADSMathSciNetGoogle Scholar
  33. 33.
    M. Buballa, Phys. Rep. 407, 205 (2005) ADSGoogle Scholar
  34. 34.
    P.N. Meisinger, M.C. Ogilvie, Phys. Lett. B 379, 163 (1996) ADSGoogle Scholar
  35. 35.
    C. Ratti, M.A. Thaler, W. Weise, Phys. Rev. D 73, 014019 (2006) ADSGoogle Scholar
  36. 36.
    K. Fukushima, Phys. Lett. B 591, 277 (2004) ADSGoogle Scholar
  37. 37.
    K. Fukushima, arXiv:0803.3318 [hep-ph]
  38. 38.
    C. Sasaki, B. Friman, K. Redlich, Phys. Rev. D 75, 074013 (2007) ADSGoogle Scholar
  39. 39.
    Z. Zhang, Y.X. Liu, Phys. Rev. C 75, 064910 (2007) ADSGoogle Scholar
  40. 40.
    W.J. Fu, Z. Zhang, Y.X. Liu, Phys. Rev. D 77, 014006 (2008) ADSGoogle Scholar
  41. 41.
    M. Ciminale, R. Gatto, N.D. Ippolito, G. Nardulli, M. Ruggieri, arXiv:0711.3397 [hep-ph]
  42. 42.
    A. Faessler, F. Fernandez, G. Lübeck, K. Shimizu, Phys. Lett. B 112, 201 (1982) ADSGoogle Scholar
  43. 43.
    A. Faessler, F. Fernandez, G. Lübeck, K. Shimizu, Nucl. Phys. A 402, 555 (1983) ADSGoogle Scholar
  44. 44.
    Th. Gutsche, D. Robson, Phys. Lett. B 229, 333 (1989) ADSGoogle Scholar
  45. 45.
    V.E. Lyubovitskij, Th. Gutsche, A. Faessler, E.G. Drukarev, Phys. Rev. D 63, 054026 (2001) ADSGoogle Scholar
  46. 46.
    V.E. Lyubovitskij, Th. Gutsche, A. Faessler, R. Vinh Mau, Phys. Lett. B 520, 204 (2001) ADSGoogle Scholar
  47. 47.
    V.E. Lyubovitskij, Th. Gutsche, A. Faessler, Phys. Rev. C 64, 065203 (2001) ADSGoogle Scholar
  48. 48.
    V.E. Lyubovitskij, Th. Gutsche, A. Faessler, R. Vinh Mau, Phys. Rev. C 65, 025202 (2002) ADSGoogle Scholar
  49. 49.
    A. Manohar, H. Georgi, Nucl. Phys. B 234, 189 (1984) ADSGoogle Scholar
  50. 50.
    C.V. Christov, A. Blotz, H.C. Kim, P. Pobylitsa, T. Watabe, T. Meissner, E.R. Arriola, K. Goeke, Prog. Part. Nucl. Phys. 37, 91 (1996) ADSGoogle Scholar
  51. 51.
    L.Ya. Glozman, D.O. Riska, Phys. Rep. 268, 263 (1996) ADSGoogle Scholar
  52. 52.
    D.O. Riska, G.E. Brown, Nucl. Phys. A 653, 251 (1999) ADSGoogle Scholar
  53. 53.
    Y.W. Yu, Z.Y. Zhang, P.N. Shen, L.R. Dai, Phys. Rev. C 52, 3393 (1995) ADSGoogle Scholar
  54. 54.
    Z.Y. Zhang, Y.W. Yu, P.N. Shen, L.R. Dai, Nucl. Phys. A 625, 59 (1997) ADSGoogle Scholar
  55. 55.
    R.T. Cahill, C.D. Roberts, Phys. Rev. D 32, 2419 (1985) ADSGoogle Scholar
  56. 56.
    J. Praschifka, C.D. Roberts, R.T. Cahill, Phys. Rev. D 36, 209 (1987) ADSGoogle Scholar
  57. 57.
    C.D. Roberts, R.T. Cahill, J. Praschifka, Ann. Phys. (N.Y.) 188, 20 (1988) ADSGoogle Scholar
  58. 58.
    C.D. Roberts, R.T. Cahill, M.E. Sevior, N. Iannella, Phys. Rev. D 49, 125 (1994) ADSGoogle Scholar
  59. 59.
    M.R. Frank, P.C. Tandy, G. Fai, Phys. Rev. C 43, 2808 (1991) ADSGoogle Scholar
  60. 60.
    M.R. Frank, P.C. Tandy, Phys. Rev. C 46, 338 (1992) ADSGoogle Scholar
  61. 61.
    C.W. Johnson, G. Fai, Phys. Rev. C 56, 3353 (1997) ADSGoogle Scholar
  62. 62.
    P.C. Tandy, Prog. Part. Nucl. Phys. 39, 117 (1997) ADSGoogle Scholar
  63. 63.
    X.F. Lü, Y.X. Liu, H.S. Zong, E.G. Zhao, Phys. Rev. C 58, 1195 (1998) ADSGoogle Scholar
  64. 64.
    Y.X. Liu, D.F. Gao, H. Guo, Phys. Rev. C 68, 035204 (2003) ADSGoogle Scholar
  65. 65.
    B. Wang, H.C. Song, L. Chang, H. Chen, Y.X. Liu, Phys. Rev. C 73, 015206 (2006) ADSGoogle Scholar
  66. 66.
    B. Wang, H. Chen, L. Chang, Y.X. Liu, Phys. Rev. C 76, 025201 (2007) ADSGoogle Scholar
  67. 67.
    P.A.M. Guichon, Phys. Lett. B 200, 235 (1998) ADSGoogle Scholar
  68. 68.
    K. Saito, K. Tsushima, A.W. Thomas, Prog. Part. Nucl. Phys. 58, 1 (2007) ADSGoogle Scholar
  69. 69.
    A.W. Thomas, Nucl. Phys. A 787, 396 (2007) ADSGoogle Scholar
  70. 70.
    J.R. Stone, P.A.M. Guichon, H.H. Matevosyan, A.W. Thomas, Nucl. Phys. A 792, 341 (2007) ADSGoogle Scholar
  71. 71.
    B.-J. Schaefer, J.M. Pawlowski, J. Wambach, Phys. Rev. D 76, 074023 (2007) ADSGoogle Scholar
  72. 72.
    H. Toki, U. Meyer, A. Faessler, R. Brockmann, Phys. Rev. C 58, 3749 (1998) ADSGoogle Scholar
  73. 73.
    M.M. Islam, H. Weigel, Found. Phys. 30, 577 (2000) Google Scholar
  74. 74.
    M. Huang, P.F. Zhuang, W.Q. Chao, Phys. Rev. D 65, 076012 (2002) ADSGoogle Scholar
  75. 75.
    M. Huang, P.F. Zhuang, W.Q. Chao, Phys. Rev. D 67, 065015 (2003) ADSGoogle Scholar
  76. 76.
    M. Baldo, M. Buballa, G.F. Burgio, F. Neumann, M. Oertel, H.J. Schulze, Phys. Lett. B 562, 153 (2003) ADSGoogle Scholar
  77. 77.
    D. Blaschke, K.K. Volkov, V.L. Yudichev, Eur. Phys. J. A 17, 103 (2003) ADSGoogle Scholar
  78. 78.
    D. Blaschke, D. Ebert, K.G. Klimenko, M.K. Volkov, V.L. Yudichev, Phys. Rev. D 70, 014006 (2004) ADSGoogle Scholar
  79. 79.
    D. Ebert, K.G. Klimenko, V.L. Yudichev, Phys. Rev. D 72, 056007 (2005) ADSGoogle Scholar
  80. 80.
    D. Blaschke, S. Fredriksson, H. Grigorian, A.M. Oztas, F. Sandin, Phys. Rev. D 72, 065020 (2005) ADSGoogle Scholar
  81. 81.
    W. Bentz, T. Horikawa, N. Ishii, A.W. Thomas, Nucl. Phys. A 720, 95 (2003) zbMATHADSGoogle Scholar
  82. 82.
    I.C. Cloet, W. Bentz, A.W. Thomas, Phys. Rev. Lett. 95, 052302 (2005) ADSGoogle Scholar
  83. 83.
    S. Lawley, W. Bentz, A.W. Thomas, Phys. Lett. B 632, 495 (2006) ADSGoogle Scholar
  84. 84.
    S. Lawley, W. Bentz, A.W. Thomas, J. Phys. G 32, 667 (2006) ADSGoogle Scholar
  85. 85.
    S.B. Ruster, D.H. Rischke, Phys. Rev. D 69, 045011 (2004) ADSGoogle Scholar
  86. 86.
    S.B. Ruster, V. Werth, M. Buballa, I.A. Shovkovy, D.H. Rischke, Phys. Rev. D 72, 034004 (2005) ADSGoogle Scholar
  87. 87.
    A. Barducci, R. Casalbuoni, G. Pettini, L. Ravagli, Phys. Rev. D 69, 096004 (2004) ADSGoogle Scholar
  88. 88.
    A. Barducci, R. Casalbuoni, G. Pettini, L. Ravagli, Phys. Rev. D 71, 016011 (2005) ADSGoogle Scholar
  89. 89.
    A. Barducci, R. Casalbuoni, G. Pettini, L. Ravagli, Phys. Rev. D 72, 056002 (2005) ADSGoogle Scholar
  90. 90.
    D.N. Aguilera, D. Blaschke, M. Buballa, V.L. Yudichev, Phys. Rev. D 72, 034008 (2005) ADSGoogle Scholar
  91. 91.
    L.Y. He, P.F. Zhuang, Phys. Lett. B 615, 93 (2005) ADSGoogle Scholar
  92. 92.
    L.Y. He, M. Jin, P.F. Zhuang, Phys. Rev. D 71, 116001 (2005) ADSGoogle Scholar
  93. 93.
    L.Y. He, M. Jin, P.F. Zhuang, Phys. Rev. D 74, 036005 (2006) ADSGoogle Scholar
  94. 94.
    L.Y. He, M. Jin, P.F. Zhuang, Phys. Rev. D 75, 036003 (2007) ADSGoogle Scholar
  95. 95.
    G.F. Sun, L.Y. He, P.F. Zhuang, Phys. Rev. D 75, 096004 (2007) ADSGoogle Scholar
  96. 96.
    X.W. Hao, P.F. Zhuang, Phys. Lett. B 652, 275 (2007) ADSGoogle Scholar
  97. 97.
    X.G. Huang, X.W. Hao, P.F. Zhuang, Astropart. Phys. 28, 472 (2007) ADSGoogle Scholar
  98. 98.
    P. Castorina, G. Nardulli, D. Zappala, Phys. Rev. D 72, 076006 (2005) ADSGoogle Scholar
  99. 99.
    M.M. Forbes, Phys. Rev. D 72, 094032 (2005) ADSGoogle Scholar
  100. 100.
    G.Y. Shao, L. Chang, Y.X. Liu, X.L. Wang, Phys. Rev. D 73, 076003 (2006) ADSGoogle Scholar
  101. 101.
    S.K. Ghosh, T.K. Mukherjee, M.G. Mustafa, R. Ray, Phys. Rev. D 73, 114007 (2006) ADSGoogle Scholar
  102. 102.
    T. Ohsaku, Phys. Lett. B 634, 285 (2006) ADSGoogle Scholar
  103. 103.
    S. Hands, A.S. Sehra, Phys. Lett. B 637, 229 (2006) ADSGoogle Scholar
  104. 104.
    Q. Wang, Z.G. Wang, J. Wu, Phys. Rev. D 74, 014021 (2006) ADSGoogle Scholar
  105. 105.
    D. Atkinson, J. Math. Phys. 28, 2494 (1987) zbMATHADSMathSciNetGoogle Scholar
  106. 106.
    D. Atkinson, V.P. Gusynin, P. Maris, Phys. Lett. B 303, 157 (1993) ADSGoogle Scholar
  107. 107.
    A.C. Aguilar, A.A. Natale, R. Rosenfeld, Phys. Rev. D 62, 094014 (2000) ADSGoogle Scholar
  108. 108.
    L. Chang, Y.X. Liu, M.S. Bhagwat, C.D. Roberts, S.V. Wright, Phys. Rev. C 75, 015201 (2007) ADSGoogle Scholar
  109. 109.
    R. Williams, C.S. Fischer, M.R. Pennington, Phys. Lett. B 645, 167 (2007) ADSGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2008

Authors and Affiliations

  1. 1.Department of Physics and State Key Laboratory of Nuclear Physics and TechnologyPeking UniversityBeijingChina
  2. 2.Center of Theoretical Nuclear PhysicsNational Laboratory of Heavy Ion AcceleratorLanzhouChina

Personalised recommendations