The spectral density of the QCD dirac operator and patterns of chiral symmetry breaking

Nuclear Physics B

Volumn 560, Issue 1-3, 1999, Pages 259-282

  Toublan, D ^a   Verbaarschot, J J M ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

Chiral random matrix theory; Microscopic spectral density; Partially quenched chiral perturbation theory; QCD dirac operator; Valence quark mass dependence

Indexed keywords

EID: 0033229159     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(99)00449-6     Document Type: Article

References (93)

1. [1] T. Banks and A. Casher, Nucl. Phys. B 169 (1980) 103.
2. [2] C. DeTar, Quark-gluon plasma in numerical simulations of QCD, in Quark Gluon Plasma 2, ed. R. Hwa (World Scientific, Singapore, 1995).
3. [3] A.V. Smilga, Phys. Rep. 291 (1997) 1.
4. [4] A. Smilga and J. Stern, Phys. Lett. B 318 (1993) 531.
5. [5] J.C. Osborn, D. Toublan and J.J.M. Verbaarschot, Nucl. Phys. B 540 (1999) 317.
6. [6] P.H. Damgaard, J.C. Osborn, D. Toublan and J.J.M. Verbaarschot, Nucl. Phys. B 547 (1999) 305.
7. [7] J.J.M. Verbaarschot, Phys. Lett. B 368 (1996) 137.
8. [8] A. Morel, J. Physique 48 (1987) 1111.
9. [9] C. Bernard and M. Golterman, Phys. Rev. D 49 (1994) 486; C. Bernard and M. Golterman, hep-lat/9311070.
10. [9] C. Bernard and M. Golterman, Phys. Rev. D 49 (1994) 486; C. Bernard and M. Golterman, hep-lat/9311070.
11. [10] M.F.L. Golterman and K.C. Leung, Phys. Rev. D 57 (1998) 703; M.F.L. Golterman, Acta Phys. Polon. B 25 (1994).
12. [10] M.F.L. Golterman and K.C. Leung, Phys. Rev. D 57 (1998) 703; M.F.L. Golterman, Acta Phys. Polon. B 25 (1994).
13. [11] S. Chandrasekharan, Nucl. Phys. Proc. Suppl. 42 (1995) 475; S. Chandrasekharan and N. Christ, Nucl. Phys. B (Proc. Suppl.) 42 (1996) 527; N. Christ, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 253.
14. [11] S. Chandrasekharan, Nucl. Phys. Proc. Suppl. 42 (1995) 475; S. Chandrasekharan and N. Christ, Nucl. Phys. B (Proc. Suppl.) 42 (1996) 527; N. Christ, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 253.
15. [11] S. Chandrasekharan, Nucl. Phys. Proc. Suppl. 42 (1995) 475; S. Chandrasekharan and N. Christ, Nucl. Phys. B (Proc. Suppl.) 42 (1996) 527; N. Christ, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 253.
16. [12] J.J.M. Verbaarschot, in Non-perturbative Approaches to Quantum Chromodynamics, ed. D. Diakonov (Gatchina, 1995).
17. [13] C. Bernard and M. Golterman, Phys. Rev. D 46 (1992) 853; M. Golterman, hep-lat/9411005, Chiral Perturbation Theory and the quenched approximation of QCD; S. Sharpe, Phys. Rev. D 46 (1992) 3146.
18. [13] C. Bernard and M. Golterman, Phys. Rev. D 46 (1992) 853; M. Golterman, hep-lat/9411005, Chiral Perturbation Theory and the quenched approximation of QCD; S. Sharpe, Phys. Rev. D 46 (1992) 3146.
19. [13] C. Bernard and M. Golterman, Phys. Rev. D 46 (1992) 853; M. Golterman, hep-lat/9411005, Chiral Perturbation Theory and the quenched approximation of QCD; S. Sharpe, Phys. Rev. D 46 (1992) 3146.
20. [14] S. Sharpe, Phys. Rev. D 56 (1997) 7052.
21. [15] E.V. Shuryak and J.J.M. Verbaarschot, Nucl. Phys. A 560 (1993) 306.
22. [16] J. Verbaarschot, Phys. Rev. Lett. 72 (1994) 2531; Phys. Lett. B 329 (1994) 351.
23. [16] J. Verbaarschot, Phys. Rev. Lett. 72 (1994) 2531; Phys. Lett. B 329 (1994) 351.
24. [17] E. Brézin, S. Hikami and A. Zee, Nucl. Phys. B 464 (1996) 411.
25. [18] G. Akemann, P. Damgaard, U. Magnea and S. Nishigaki, Nucl. Phys. B 487[FS] (1997) 721. (1994)487.
26. [18] G. Akemann, P. Damgaard, U. Magnea and S. Nishigaki, Nucl. Phys. B 487[FS] (1997) 721. (1994) 487.
27. [19] A.D. Jackson, M.K. Sener and J.J.M. Verbaarschot, Nucl. Phys. B 479 (1996) 707.
28. [20] T. Guhr and T. Wettig, Nucl. Phys. B 506 (1997) 589.
29. [21] A.D. Jackson, M.K. Sener and J.J.M. Verbaarschot, Nucl. Phys. B 506 (1997) 612.
30. [22] P.H. Damgaard, Phys. Lett. B 424 (1998) 322; B 425 (1998) 151; G. Akemann and P.H. Damgaard, Phys. Lett. B 432 (1998) 390; Nucl. Phys. B 528 (1998) 411.
31. [22] P.H. Damgaard, Phys. Lett. B 424 (1998) 322; B 425 (1998) 151; G. Akemann and P.H. Damgaard, Phys. Lett. B 432 (1998) 390; Nucl. Phys. B 528 (1998) 411.
32. [22] P.H. Damgaard, Phys. Lett. B 424 (1998) 322; B 425 (1998) 151; G. Akemann and P.H. Damgaard, Phys. Lett. B 432 (1998) 390; Nucl. Phys. B 528 (1998) 411.
33. [22] P.H. Damgaard, Phys. Lett. B 424 (1998) 322; B 425 (1998) 151; G. Akemann and P.H. Damgaard, Phys. Lett. B 432 (1998) 390; Nucl. Phys. B 528 (1998) 411.
34. [23] P.H. Damgaard and S.M. Nishigaki, Phys. Rev. D 57 (1998) 5299.
35. [24] J. Christiansen, Nucl. Phys. B 547 (1999) 329.
36. [25] J.C. Osborn and J.J.M. Verbaarschot, Phys. Rev. Lett. 81 (1998) 268.
37. [26] M.A. Halasz and J.J.M. Verbaarschot, Phys. Rev. Lett. 74 (1995) 3920; M.A. Halasz, T. Kalkreuter and J.J.M. Verbaarschot, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 266.
38. [26] M.A. Halasz and J.J.M. Verbaarschot, Phys. Rev. Lett. 74 (1995) 3920; M.A. Halasz, T. Kalkreuter and J.J.M. Verbaarschot, Nucl. Phys. B (Proc. Suppl.) 53 (1997) 266.
39. [27] M.E. Berbenni-Bitsch, S. Meyer, A. Schäfer, J.J.M. Verbaarschot and T. Wettig, Phys. Rev. Lett. 80 (1998) 1146.
40. [28] M.E. Berbenni-Bitsch, M. Göckeler, T. Guhr, A.D. Jackson, J.Z. Ma, S. Meyer, A. Schäfer, H.A. Weidenmüller, T. Wettig and T. Wilke, Phys. Lett. B 438 (1998) 14.
41. [29] J.Z. Ma, T. Guhr and T. Wettig, Eur. Phys. J. A 2 (1998) 87.
42. [30] T. Guhr, J.Z. Ma, S. Meyer and T. Wilke, Phys. Rev. D 59 (1999) 054501.
43. [31] M.E. Berbenni-Bitsch, S. Meyer and T. Wettig, Phys. Rev. D 58 (1998) 071502.
44. [32] K. Splittorff and A.D. Jackson, hep-lat/9805018; K. Splittorf, Nucl. Phys. B 548 (1999) 613.
45. [32] K. Splittorff and A.D. Jackson, hep-lat/9805018; K. Splittorf, Nucl. Phys. B 548 (1999) 613.
46. [33] R. Pullirsch, K. Rabitsch, T. Wettig and H. Markum, Phys. Lett. B 427 (1998) 119.
47. [34] P.H. Damgaard, U.M. Heller, A. Krasnitz and T. Madsen, Phys. Lett. B 440 (1998) 129.
48. [35] P.H. Damgaard, U.M. Heller and A. Krasnitz, hep-lat/981006.
49. [36] M. Göckeler, H. Hehl, P.E.L. Rakow, A. Schäfer and T. Wettig, Phys. Rev. D 59 (1999) 094503.
50. [37] B.A. Berg, H. Markum and R. Pullirsch, Phys. Rev. D 59 (1999) 097504.
51. [38] F. Farchioni, I. Hip, C.B. Lang and M. Wohlgenannt, Nucl. Phys. B 549 (1999) 364.
52. [39] R.G. Edwards, U.M. Heller and R. Narayanan, hep-lat/9902021.
53. [40] R.G. Edwards, U.M. Heller, J. Kiskis and R. Narayanan, Phys. Rev. Lett. 82 (1999) 4188.
54. [41] J.J.M. Verbaarschot, Nucl. Phys. B 427 (1994) 534.
55. [42] J.C. Osborn and J.J.M. Verbaarschot, Nucl. Phys. B 525 (1998) 738.
56. [43] A. Altland and B.D. Simons, J. Phys. A 32 (1999) L353.
57. [44] K. Takahashi and S. Iida, hep-th/9903119.
58. [45] B.L. Altshuler, I.Kh. Zharekeshev, S.A. Kotochigova and B.I. Shklovskii, Zh. Eksp. Teor. Fiz. 94 (1988) 343.
59. [46] H.A. Weidenmüller, Nucl. Phys. A 518 (1990) 1.
60. [47] K. Johnson, L. Lellouch and J. Polonyi, Nucl. Phys. B 367 (1991) 675.
61. [48] R. Janik, G. Papp, M. Nowak and I. Zahed, Phys. Rev. Lett. 81 (1999) 264.
62. [49] K.B. Efetov, Adv. Phys. 32 (1983) 53; K.B. Efetov, Supersymmetry in Disorder and Chaos (Cambridge Univ. Press, Cambridge, 1997).
63. [49] K.B. Efetov, Adv. Phys. 32 (1983) 53; K.B. Efetov, Supersymmetry in Disorder and Chaos (Cambridge Univ. Press, Cambridge, 1997).
64. [50] T. Guhr, A. Müller-Groeling and H.A. Weidenmüller, Phys. Rep. 299 (1998) 189.
65. [51] G. Montambaux, in Quantum Fluctuations, Les Houches, Session LXIII, ed. E. Giacobino, S. Reynaud and J. Zinn-Justin (Elsevier Science, Amsterdam, 1995), cond-mat/9602071.
66. [52] F. Wegner, Z. Phys. B 49 (1983) 297.
67. [53] J. Verbaarschot, H. Weidenmüller and M. Zirnbauer, Phys. Rep. 129 (1985) 367.
68. [54] M.E. Peskin, Nucl. Phys. B 175 (1980) 197.
69. [55] S. Dimopoulos, Nucl. Phys. B 168 (1980) 69; M. Vysotskii, Y. Kogan and M. Shifman, Sov. J. Nucl. Phys. 42 (1985) 318; D.I. Diakonov and V.Yu. Petrov, Lecture Notes in Physics 417 (Springer, Berlin, 1993).
70. [55] S. Dimopoulos, Nucl. Phys. B 168 (1980) 69; M. Vysotskii, Y. Kogan and M. Shifman, Sov. J. Nucl. Phys. 42 (1985) 318; D.I. Diakonov and V.Yu. Petrov, Lecture Notes in Physics 417 (Springer, Berlin, 1993).
71. [55] S. Dimopoulos, Nucl. Phys. B 168 (1980) 69; M. Vysotskii, Y. Kogan and M. Shifman, Sov. J. Nucl. Phys. 42 (1985) 318; D.I. Diakonov and V.Yu. Petrov, Lecture Notes in Physics 417 (Springer, Berlin, 1993).
72. [56] A. Smilga and J.J.M. Verbaarschot, Phys. Rev. D 51 (1995) 829.
73. [57] M. Zirnbauer, J. Math. Phys. 37 (1996) 4986.
74. [58] J.J.M. Verbaarschot, Lectures given at APCTP - RCNP Joint International School on Physics of Hadrons and QCD, Osaka, Japan, 1998 and the 1998 YITP Workshop on QCD and Hadron Physics, Kyoto, Japan, 1998, hep-ph/9902394.
75. [59] C. Vafa and E. Witten, Nucl. Phys. B 234 (1984) 173.
76. [60] M.A. Halasz and J.J.M. Verbaarschot, Phys. Rev. D 52 (1995) 2563.
77. [61] J. Gasser and H. Leutwyler, Ann. Phys. 158 (1984) 142; Nucl. Phys. B 250 (1985) 465.
78. [61] J. Gasser and H. Leutwyler, Ann. Phys. 158 (1984) 142; Nucl. Phys. B 250 (1985) 465.
79. [62] H. Leutwyler, Ann. Phys. 235 (1994) 165.
80. [63] J. Gasser and H. Leutwyler, Phys. Lett. B 188(1987) 477; Nucl. Phys. B 307 (1988) 763.
81. [63] J. Gasser and H. Leutwyler, Phys. Lett. B 188(1987) 477; Nucl. Phys. B 307 (1988) 763.
82. [64] H. Leutwyler and A. Smilga, Phys. Rev. D 46 (1992) 5607.
83. [65] P. Hasenfratz and H. Leutwyler, Nucl. Phys. B 343 (1990) 241.
84. [66] M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B 166 (1980) 493.
85. [67] M.E. Berbenni-Bitsch, M. Göckeler, H. Hehl, S. Meyer, P.E.L. Rakow, A. Schäfer and T. Wettig, hep-lat/9901013.
86. [68] P.E.L. Rakow, private communication.
87. [69] J.J.M. Verbaarschot, Nucl. Phys. B 426 [FS] (1994) 559.
88. [70] T. Wettig, Habilitationsschrift Universität Heidelberg (1998).
89. [71] T. Nagao and P.J. Forrester, Nucl. Phys. B 435 (1995) 401.
90. [72] J. Verbaarschot and I. Zahed, Phys. Rev. Lett. 70 (1993) 3852.
91. [73] P.H. Damgaard, hep-th/9903096.
92. [74] U. Sharan and M. Teper, Nucl. Phys. B (Proc. Suppl.) 73 (1999) 617; Phys. Rev. D 60 (1999) 054501.
93. [74] U. Sharan and M. Teper, Nucl. Phys. B (Proc. Suppl.) 73 (1999) 617; Phys. Rev. D 60 (1999) 054501.