Wigner function of produced particles in string fragmentation

Physical Review C - Nuclear Physics

Volumn 80, Issue 5, 2009, Pages

  Wong, Cheuk Yin ^a  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 73649105163     PISSN: 05562813     EISSN: 1089490X     Source Type: Journal    
DOI: 10.1103/PhysRevC.80.054917     Document Type: Article

References (128)

1. S. Wolfram, in Proceedings of the 15th Recontre de Moriond, edited by, Tran Thanh Van, (Editions Frontieres, Gif-sur-Yvette, France, 1980);
2. G. C. Fox and S. Wolfram, Nucl. Phys. NUPBBO 0550-3213 10.1016/0550-3213(84)90333-X 238, 492 (1984).
3. L. Van Hove and A. Giovannini, Acta Phys. Pol. B 19, 931 (1988);
4. M. Garetto, A. Giovannini, T. Sjostrand, and L.van Hove, CERN Report CERN-TH-5252/88, Presented at Perugia Workshop on Multiparticle Dynamics, Perugia, Italy, 21-28 June 1988;
5. Y. L. Dokshizer, V. A. Khoze, and S. I. Troyan, in Perturbative Quantum Chromodynamics, edited by, A. H. Mueller, (World Publishing, Singapore 1989), p. 241.
6. R. O'dorico, Nucl. Phys. NUPBBO 0550-3213 10.1016/0550-3213(80)90165-0 B172, 157 (1980);
7. R. O'dorico, Comput. Phys. Commun. CPHCBZ 0010-4655 10.1016/0010-4655(84) 90067-5 32, 139 (1984);
8. G. Marchesini and B. R. Webber, Nucl. Phys. NUPBBO 0550-3213 10.1016/0550-3213(84)90463-2 B238, 1 (1984);
9. B. R. Webber, Nucl. Phys. 0550-3213 10.1016/0550-3213(84)90333-X B238, 492 (1984);
10. T. D. Gottschalk, Nucl. Phys. 0550-3213 10.1016/0550-3213(84)90252-9 B239, 325 (1984).
11. B. Andersson, G. Gustafson, and T. Sjöstrand, Zeit. Phys. C ZPCFD2 0170-9739 10.1007/BF01407824 20, 317 (1983);
12. B. Andersson, G. Gustafson, G. Ingelman, and T. Sjöstrand, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(83)90080-7 97, 31 (1983);
13. T. Sjöstrand and M. Bengtsson, Comput. Phys. Commun. CPHCBZ 0010-4655 10.1016/0010-4655(87)90054-3 43, 367 (1987);
14. B. Andersson, G. Gustavson, and B. Nilsson-Alqvist, Nucl. Phys. NUPBBO 0550-3213 10.1016/0550-3213(87)90257-4 B281, 289 (1987).
15. A. Capella and A. Krzywicki, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.18.3357 18, 3357 (1978);
16. A. Capella and J. Tran Thanh Van, Zeit. Phys. C ZPCFD2 0170-9739 10.1007/BF01549733 10, 249 (1981);
17. A. Capella, Zeit. Phys. C ZPCFD2 0170-9739 10.1007/BF01548267 33, 541 (1987);
18. A. Capella and J. Tran Thanh Van, Z. Phys. C ZPCFD2 0170-9739 10.1007/BF01574534 38, 177 (1988);
19. N. Armesto and C. Pajares, Int. J. Mod. Phys. A 15, 2019 (2000).
20. K. Werner, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.39.780 39, 780 (1989).
21. H. Sorge, H. Stöcker, and W. Greiner, Nucl. Phys. NUPABL 0375-9474 10.1016/0375-9474(89)90641-6 A498, 567 c (1989).
22. C. Y. Wong and Z. D. Lu, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.39.2606 39, 2606 (1989).
23. X. N. Wang and M. Gyulassy, Comput. Phys. Commun. CPHCBZ 0010-4655 10.1016/0010-4655(94)90057-4 83, 307 (1994).
24. K. Geiger and B. Müller, Nucl. Phys. NUPABL 0375-9474 10.1016/0375-9474(92)90599-F A544, 467 c (1992).
25. L. D. McLerran and R. Venugopalan, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.49.2233 49, 2233 (1994);
26. L. D. McLerran and R. Venugopalan, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.49.3352 49, 3352 (1994);
27. L. D. McLerran and R. Venugopalan, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.50.2225 50, 2225 (1994);
28. A. Kovner, L. McLerran, and H. Weigert, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.52.6231 52, 6231 (1995).
29. Z.-W. Lin, C. M. Ko, B.-A. Li, B. Zhang, and S. Pal, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.72.064901 72, 064901 (2005).
30. S. Jeon and J. Kapusta, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.56.468 56, 468 (1997).
31. J. Schwinger, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.128.2425 128, 2425 (1962);
32. J. Schwinger, in Theoretical Physics, Trieste Lectures, 1962 (IAEA, Vienna, 1963), p. 89.
33. J. H. Lowenstein and J. A. Swieca, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/0003-4916(71)90246-6 68, 172 (1971).
34. S. Coleman, R. Jackiw, and L. Susskind, Ann. Phys. APNYA6 0003-4916 10.1016/0003-4916(75)90212-2 93, 267 (1975).
35. S. Coleman, Ann. Phys. APNYA6 0003-4916 10.1016/0003-4916(76)90280-3 101, 239 (1976).
36. A. Casher, J. Kogut, and L. Susskind, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.10.732 10, 732 (1974).
37. J. D. Bjorken, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.27.140 27, 140 (1983).
38. N. P. Ilieva and V. N. Pervushin, Sov. J. Nucl. Phys. 39, 638 (1984).
39. T. Eller, H.-C. Pauli, and S. J. Brodsky, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.35.1493 35, 1493 (1987);
40. T. Eller and H.-C. Pauli, Zeit. Phys. ZPCFD2 0170-9739 10.1007/BF01565128 42, 59 (1989).
41. T. Fujita and J. Hüfner, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.40.604 40, 604 (1989).
42. C. Y. Wong, R. C. Wang, and C. C. Shih, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.44.257 44, 257 (1991).
43. C. Y. Wong, Introduction to High-Energy Heavy-Ion Collisions (World Scientific, Singapore, 1994).
44. H. Aihara (TPC/Two-Gamma Collaboration), Lawrence Berkeley Laboratory Report No. LBL-23737, 1988.
45. W. Hofmann, Annu. Rev. Nucl. Sci. ARNUA8 0066-4243 10.1146/annurev.ns.38. 120188.001431 38, 279 (1988).
46. Please note that in Ref. [25], the experimental data of the rapidity distribution are presented as dNch/d|y|, which includes both positive and negative y contributions, and Nch is Nπ++π-. On the other hand, the experimental data of the rapidity distribution are given as dNch/dy for positive y in Ref. [26]. They are related by a factor of two as dNch/d|y|=2dNch/dy.
47. A. Petersen (Mark II Collaboration), Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.37.1 37, 1 (1988).
48. K. Abe (SLD Collaboration), Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.59.052001 59, 052001 (1999).
49. K. Abreu (DELPHI Collaboration), Phys. Lett. PYLBAJ 0370-2693 10.1016/S0370-2693(99)00601-2 B459, 397 (1999).
50. H. Yang (BRAHMS Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/35/10/104129 35, 104129 (2008);
51. K. Hagel (BRAHMS Collaboration), Annual Fall Meeting of the Division of Nuclear Physics of the American Physical Society 2008, Oakland, California, USA, 23-27 October 2008.
52. J. Adams (for the STAR Collaboration), Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.152301 95, 152301 (2005).
53. J. Adams (STAR Collaboration), Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.73.064907 73, 064907 (2006).
54. J. Putschke (STAR Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/34/8/S72 34, S679 (2007).
55. J. Bielcikova (STAR Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/34/8/S128 34, S929 (2007).
56. F. Wang (STAR Collaboration), Invited talk at the XIth International Workshop on Correlation and Fluctuation in Multiparticle Production, Hangzhou, China, November 2007, arXiv: 0707.0815.
57. J. Bielcikova (STAR Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/34/8/S128 34, S929 (2007);
58. J. Bielcikova (STAR Collaboration), Talk presented at 23rd Winter Workshop on Nuclear Dynamics, Big Sky, Montana, USA, 11-18 February 2007, arXiv: 0707.3100;
59. J. Bielcikova (STAR Collaboration), Talk presented at XLIII Rencontres de Moriond, QCD and High Energy Interactions, La Thuile, 8-15 March 2008, arXiv: 0806.2261.
60. B. Abelev (STAR Collaboration), Talk presented at 23rd Winter Workshop on Nuclear Dynamics, Big Sky, Montana, USA, 11-18 February 2007, arXiv: 0705.3371.
61. L. Molnar (STAR Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/34/8/S51 34, S593 (2007).
62. R. S. Longacre (STAR Collaboration), Int. J. Mod. Phys. E IMPEER 0218-3013 10.1142/S021830130700760X 16, 2149 (2007).
63. C. Nattrass (STAR Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/35/10/104110 35, 104110 (2008).
64. A. Feng (STAR Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/35/10/104082 35, 104082 (2008).
65. P. K. Netrakanti (STAR Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/35/10/104010 35, 104010 (2008).
66. O. Barannikova (STAR Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/35/10/104086 35, 104086 (2008).
67. M. Daugherity (STAR Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/35/10/104090 35, 104090 (2008).
68. A. Adare (PHENIX Collaboration), Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.78.014901 78, 014901 (2008).
69. M. P. McCumber (PHENIX Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/35/10/104081 35, 104081 (2008).
70. C.-H. Chen (PHENIX Collaboration), in Studying the Medium Response by Two Particle Correlations, Hard Probes 2008 International Conference on Hard Probes of High Energy Nuclear Collisions, A Toxa, Galicia, Spain, 8-14 June 2008.
71. E. Wenger (PHOBOS Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/35/10/104080 35, 104080 (2008).
72. M. J. Tannenbaum, Eur. Phys. J. C 1434-6044 10.1140/epjc/s10052-009-0877- 6 61, 747 (2009).
73. J. Jia (PHENIX Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/35/10/104033 35, 104033 (2008).
74. M. van Leeuwen (STAR Collaboration), Eur. Phys. J. C 1434-6044 10.1140/epjc/s10052-009-1007-1 61, 569 (2009).
75. C. Y. Wong, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.76.054908 76, 054908 (2007).
76. C. Y. Wong, Chin. Phys. Lett. CPLEEU 0256-307X 10.1088/0256-307X/25/11/ 027 25, 3936 (2008).
77. C. Y. Wong, J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/35/10/104085 35, 104085 (2008).
78. C. Y. Wong, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.78.064905 78, 064905 (2008).
79. C. Y. Wong, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.80.034908 80, 034908 (2009).
80. L. D. Landau, Izv. Akad. Nauk SSSR 17, 51 (1953);
81. S. Z. Belenkij and L. D. Landau, Usp. Fiz. Nauk 56, 309 (1955);
82. S. Z. Belenkij and L. D. Landau, Nuovo Cimento Suppl. NUCIAD 0029-6341 10.1007/BF02745507 3, 15 (1956);
83. I. M. Khalatnikov, Pis'ma Zh. Eksp. Teor. Fiz. 27, 529 (1954).
84. C. Y. Wong, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.78.054902 78, 054902 (2008).
85. C. Y. Wong, Lectures presented at the Helmholtz International Summer School, Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, 14-26 July 2008, arXiv: 0809.0517.
86. R. P. Feynman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.23. 1415 23, 1415 (1969).
87. S. D. Drell and T. M. Yan, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/0003-4916(71)90071-6 66, 578 (1971).
88. G. F. Chew and A. Pignotti, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.176.2112 176, 2112 (1968);
89. J. Finkelstein and K. Kajantie, Nuovo Cimento A NCIAAT 0369-3546 10.1007/BF02819826 56, 659 (1968);
90. I. M. Dremin and A. M. Dunaevskii, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(75)90024-1 18, 159 (1975).
91. J. Hüfner, Y. P. Ivanov, B. Z. Kepeliovich, and A. V. Tarasov, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.62.094022 62, 094022 (2000);
92. B. Z. Kepeliovich, A. V. Tarasov, and J. Hüfner, Nucl. Phys. NUPABL 0375-9474 10.1016/S0375-9474(01)01220-9 A696, 669 (2001);
93. Y. P. Ivanov, B. Z. Kepeliovich, A. V. Tarasov, and J. Hüfner, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.66.024903 66, 024903 (2002);
94. B. Z. Kepeliovich and J. Raufeisen, Lecuture Notes in Phys. 647, 305 (2004)
95. hep-ph/0305094.
96. P. Jordon, Z. Phys. EPJAFV 1434-6001 10.1007/BF01330373 93, 464 (1935);
97. P. Jordon, Z. Phys. EPJAFV 1434-6001 10.1007/BF01343669 98, 759 (1936);
98. P. Jordon, Z. Phys. EPJAFV 1434-6001 10.1007/BF01847817 99, 109 (1936);
99. P. Jordon, Z. Phys. EPJAFV 1434-6001 10.1007/BF01336689 102, 243 (1936);
100. P. Jordon, Z. Phys. EPJAFV 1434-6001 10.1007/BF01330148 105, 229 (1937).
101. G. t'Hooft, Nucl. Phys. NUPBBO 0550-3213 10.1016/0550-3213(74)90154-0 B72, 461 (1974).
102. G. t'Hooft, Nucl. Phys. NUPBBO 0550-3213 10.1016/0550-3213(74)90088-1 B75, 461 (1974).
103. Y. Frishman and J. Sonnenschein, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(93)90145-4 223, 309 (1993).
104. S. Dalley and I. R. Klebanov, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.47.2517 47, 2517 (1993).
105. Y. Frishmann, A. Hanany, and J. Sonnenschein, Nucl. Phys. NUPBBO 0550-3213 10.1016/S0550-3213(94)80042-1 B429, 75 (1994).
106. A. Armonic and J. Sonnenschein, Nucl. Phys. NUPBBO 0550-3213 10.1016/0550-3213(95)00505-6 B457, 81 (1995).
107. D. Kutasov and A. Schwimmer, Nucl. Phys. NUPBBO 0550-3213 10.1016/0550-3213(95)00106-3 B442, 447 (1995).
108. D. Gross, I. R. Klebanov, A. Matysin, and A. V. Smilga, Nucl. Phys. NUPBBO 0550-3213 10.1016/0550-3213(95)00655-9 B461, 109 (1996).
109. E. Abdalla and M. C. B. Abdalla, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(95)00019-4 265, 253 (1996).
110. S. Dalley, Phys. Lett. PYLBAJ 0370-2693 10.1016/S0370-2693(97)01474-3 B418, 160 (1998).
111. A. Armonic, Y. Frishmann, J. Sonnenschein, and U. Trittmann, Nucl. Phys. NUPBBO 0550-3213 10.1016/S0550-3213(98)00664-6 537, 503 (1999).
112. M. Engelhardt, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.64.065004 64, 065004 (2001).
113. U. Trittmann, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.66.025001 66, 025001 (2002).
114. A. Abrashikin, Y. Frishmann, and J. Sonnenschein, Nucl. Phys. NUPBBO 0550-3213 10.1016/j.nuclphysb.2004.10.019 B703, 320 (2004).
115. M. Li, L. Wilets, and M. C. Birse, J. Phys. G JPHGBM 0305-4616 10.1088/0305-4616/13/7/005 13, 915 (1987).
116. E. Witten, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01215276 92, 455 (1984).
117. N. Isgur and J. Paton, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.31. 2910 31, 2910 (1985).
118. G. Gatoff and C. Y. Wong, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.46.997 46, 997 (1992);
119. C. Y. Wong and G. Gatoff, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(94)90182-1 242, 489 (1994).
120. The signs on the right-hand sides of Eqs. (40) and (41) in Ref. [56] should be reversed as in Eqs. (20a) and (20b) here.
121. C. Adam, Phys. Lett. PYLBAJ 0370-2693 10.1016/S0370-2693(03)00051-0 B555, 132 (2003).
122. The boson mass in the large Nf limit of massless multiflavor QCD2 is given as M2=e2Nf/2π in Ref. [76], but as M2=e2Nf/π in Refs. [78,79], using apparently different definitions of the coupling constant e. I shall follow the convention of Refs. [78,79] with the boson mass of M2=e2Nf/π.
123. C. Y. Wong and W.-N. Zhang, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.70.064904 70, 064904 (2004).
124. C. Y. Wong, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.25.1460 25, 1460 (1982).
125. C. Y. Wong and K. T. R. Davies, Phys. Rev. C PRVCAN 0556-2813 10.1103/PhysRevC.26.1502 26, 1502 (1982).
126. M. Murray (Brahms Collaboration), J. Phys. G JPGPED 0954-3899 10.1088/0954-3899/30/8/004 30, S667 (2004).
127. P. Steinberg, Nucl. Phys. NUPABL 0375-9474 10.1016/j.nuclphysa.2005.02. 139 A752, 423 (2005).
128. P. Steinberg, in Proceedings of 3rd International Workshop on Critical Point and Onset of Deconfinement, Florence, Italy, 3-6 July 2006, p. 36, arXiv: nucl-ex/0702019.