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Advances in High Energy Physics
Volume 2015 (2015), Article ID 563428, 15 pages
http://dx.doi.org/10.1155/2015/563428
Research Article

On SU(3) Effective Models and Chiral Phase Transition

1Egyptian Center for Theoretical Physics (ECTP), Modern University for Technology and Information (MTI), Cairo 11571, Egypt
2World Laboratory for Cosmology And Particle Physics (WLCAPP), Cairo 11571, Egypt
3Department of Physics, Brookhaven National Laboratory (BNL), P.O. Box 5000, Upton, NY 11973-5000, USA

Received 29 April 2015; Revised 15 August 2015; Accepted 6 September 2015

Academic Editor: Enrico Lunghi

Copyright © 2015 Abdel Nasser Tawfik and Niseem Magdy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Linked References

  1. D. J. Gross and F. Wilczek, “Ultraviolet behavior of non-Abelian gauge theories,” Physical Review Letters, vol. 30, no. 26, pp. 1343–1346, 1973. View at Publisher · View at Google Scholar · View at Scopus
  2. H. D. Politzer, “Reliable perturbative results for strong interactions?” Physical Review Letters, vol. 30, no. 26, article 1346, 1973. View at Publisher · View at Google Scholar · View at Scopus
  3. N. Cabibbo and G. Parisi, “Exponential hadronic spectrum and quark liberation,” Physics Letters B, vol. 59, no. 1, pp. 67–69, 1975. View at Publisher · View at Google Scholar · View at Scopus
  4. J. C. Collins and M. J. Perry, “Superdense matter: neutrons or asymptotically free quarks?” Physical Review Letters, vol. 34, no. 21, pp. 1353–1356, 1975. View at Publisher · View at Google Scholar · View at Scopus
  5. D. H. Rischke, “The quark gluon plasma in equilibrium,” Nuclear Physics, vol. 52, pp. 197–296, 2004. View at Publisher · View at Google Scholar
  6. Y. Nambu and G. Jona-Lasinio, “Dynamical model of elementary particles based on an analogy with superconductivity. I,” Physical Review, vol. 122, no. 1, pp. 345–358, 1961. View at Publisher · View at Google Scholar · View at Scopus
  7. K. Fukushima, “Chiral effective model with the Polyakov loop,” Physics Letters B, vol. 591, no. 3-4, pp. 277–284, 2004. View at Publisher · View at Google Scholar
  8. C. Ratti, M. A. Thaler, and W. Weise, “Phases of QCD: lattice thermodynamics and a field theoretical model,” Physical Review D, vol. 73, Article ID 014019, 2006. View at Publisher · View at Google Scholar
  9. K. Fukushima, “Phase diagrams in the three-flavor Nambu-Jona-Lasinio model with the Polyakov loop,” Physical Review D, vol. 77, Article ID 114028, 2008. View at Publisher · View at Google Scholar
  10. T. Hatsuda and T. Kunihiro, “QCD phenomenology based on a chiral effective Lagrangian,” Physics Report, vol. 247, no. 5-6, pp. 221–367, 1994. View at Publisher · View at Google Scholar · View at Scopus
  11. A. Masayuki and Y. Koichi, “Chiral restoration at finite density and temperature,” Nuclear Physics A, vol. 504, no. 4, pp. 668–684, 1989. View at Publisher · View at Google Scholar · View at Scopus
  12. H. Fujii, “Scalar density fluctuation at the critical end point in the Nambu–Jona-Lasinio model,” Physical Review D, vol. 67, no. 9, Article ID 094018, 2003. View at Publisher · View at Google Scholar · View at Scopus
  13. M. Gell-Mann and M. Lévy, “The axial vector current in beta decay,” Il Nuovo Cimento, vol. 16, pp. 705–726, 1960. View at Publisher · View at Google Scholar · View at MathSciNet
  14. J. T. Lenaghan and D. H. Rischke, “The O(N) model at nonzero temperature: renormalization of the gap equations in Hartree and large-N approximations,” Journal of Physics G: Nuclear and Particle Physics, vol. 26, no. 4, pp. 431–450, 2000. View at Publisher · View at Google Scholar · View at Scopus
  15. N. Petropoulos, “Linear sigma model and chiral symmetry at finite temperature,” Journal of Physics G, vol. 25, no. 11, pp. 2225–2241, 1999. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Lévy, “Currents and symmetry breaking,” Il Nuovo Cimento A, vol. 52, no. 1, pp. 23–49, 1967. View at Publisher · View at Google Scholar
  17. B. Hu, “Chiral SU4×SU4 and scale invariance,” Physical Review D, vol. 9, no. 6, pp. 1825–1834, 1974. View at Publisher · View at Google Scholar
  18. J. Schechter and M. Singer, “SU(4) σ model,” Physical Review D, vol. 12, no. 9, pp. 2781–2790, 1975. View at Publisher · View at Google Scholar · View at Scopus
  19. H. B. Geddes, “Spin-zero mass spectrum in the one-loop approximation in a linear SU(4) sigma model,” Physical Review D, vol. 21, no. 1, pp. 278–289, 1980. View at Publisher · View at Google Scholar · View at Scopus
  20. A. M. Polyakov, “Thermal properties of gauge fields and quark liberation,” Physics Letters B, vol. 72, no. 4, pp. 477–480, 1978. View at Publisher · View at Google Scholar · View at Scopus
  21. L. Susskind, “Lattice models of quark confinement at high temperature,” Physical Review D, vol. 20, no. 10, pp. 2610–2618, 1979. View at Publisher · View at Google Scholar · View at Scopus
  22. B. Svetitsky and L. G. Yaffe, “Critical behavior at finite-temperature confinement transitions,” Nuclear Physics B, vol. 210, no. 4, pp. 423–447, 1982. View at Publisher · View at Google Scholar · View at Scopus
  23. B. Svetitsky, “Symmetry aspects of finite temperature confinement transitions,” Physics Reports, vol. 132, no. 1, pp. 1–53, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. B.-J. Schaefer, J. M. Pawlowski, and J. Wambach, “Phase structure of the Polyakov-quark-meson model,” Physical Review D, vol. 76, no. 7, Article ID 074023, 2007. View at Publisher · View at Google Scholar · View at Scopus
  25. T. Kahara and K. Tuominen, “Degrees of freedom and the phase transitions of two flavor QCD,” Physical Review D, vol. 78, Article ID 034015, 2008. View at Publisher · View at Google Scholar
  26. B.-J. Schaefer and M. Wagner, “On the QCD phase structure from effective models,” Nuclear Physics, vol. 62, no. 2, pp. 381–385, 2009. View at Publisher · View at Google Scholar
  27. M. Bluhm, B. Kämpfer, and G. Soff, “The QCD equation of state near Tc within a quasi-particle model,” Physics Letters B, vol. 620, no. 3-4, pp. 131–136, 2005. View at Publisher · View at Google Scholar · View at Scopus
  28. M. A. Thaler, R. A. Schneider, and W. Weise, “Quasiparticle description of hot QCD at finite quark chemical potential,” Physical Review C, vol. 69, no. 3, Article ID 035210, 2004. View at Publisher · View at Google Scholar · View at Scopus
  29. G. Boyd, J. Engels, F. Karsch et al., “Thermodynamics of SU(3) lattice gauge theory,” Nuclear Physics B, vol. 469, no. 3, pp. 419–444, 1996. View at Publisher · View at Google Scholar · View at Scopus
  30. M. Okamoto, A. A. Khan, S. Aoki et al., “Equation of state for pure SU(3) gauge theory with renormalization group improved action,” Physical Review D, vol. 60, Article ID 094510, 1999. View at Publisher · View at Google Scholar
  31. A. N. Tawfik and N. Magdy, “Thermodynamics and higher order moments in SU(3) linear σ-model with gluonic quasiparticles,” Journal of Physics G: Nuclear and Particle Physics, vol. 42, no. 1, Article ID 015004, 2015. View at Publisher · View at Google Scholar · View at Scopus
  32. S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, and K. K. Szabo, “Full result for the QCD equation of state with 2+1 flavors,” Physics Letters B, vol. 370, pp. 99–104, 2014. View at Publisher · View at Google Scholar
  33. E. Megías, E. R. Arriola, and L. L. Salcedo, “Polyakov loop in chiral quark models at finite temperature,” Physical Review D, vol. 74, Article ID 065005, 2006. View at Publisher · View at Google Scholar
  34. E. Ruiz Arriola, L. L. Salcedo, and E. Megías, “Quark properties from the Hadron resonance gas,” Acta Physica Polonica B Proceedings Suplement, vol. 8, no. 2, pp. 439–444, 2015. View at Publisher · View at Google Scholar
  35. F. Karsch, K. Redlich, and A. Tawfik, “Hadron resonance mass spectrum and lattice QCD thermodynamics,” European Physical Journal C, vol. 29, no. 4, pp. 549–556, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  36. F. Karsch, K. Redlich, and A. Tawfik, “Thermodynamics at non-zero baryon number density: a comparison of lattice and hadron resonance gas model calculations,” Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, vol. 571, no. 1-2, pp. 67–74, 2003. View at Publisher · View at Google Scholar · View at Scopus
  37. K. Redlich, F. Karsch, and A. Tawfik, “Heavy-ion collisions and lattice QCD at finite baryon density,” Journal of Physics G: Nuclear and Particle Physics, vol. 30, no. 8, pp. S1271–S1274, 2004. View at Publisher · View at Google Scholar · View at Scopus
  38. A. Tawfik, “QCD phase diagram: a comparison of lattice and hadron resonance gas model calculations,” Physical Review D, vol. 71, Article ID 054502, 2005. View at Publisher · View at Google Scholar
  39. A. Tawfik, “Influence of strange quarks on the QCD phase diagram and chemical freeze-out,” Journal of Physics G, vol. 31, no. 6, pp. S1105–S1110, 2005. View at Publisher · View at Google Scholar · View at Scopus
  40. A. Tawfik, “In-medium modifications of hadron properties,” Indian Journal of Physics, vol. 85, no. 5, pp. 755–766, 2011. View at Publisher · View at Google Scholar · View at Scopus
  41. A. Tawfik, “Phase space and dynamical fluctuations of kaon-to-pion ratios,” Progress of Theoretical Physics, vol. 126, no. 2, pp. 279–292, 2011. View at Publisher · View at Google Scholar
  42. A. Tawfik, “Antiproton-to-proton ratios for ALICE heavy-ion collisions,” Nuclear Physics A, vol. 859, no. 1, pp. 63–72, 2011. View at Publisher · View at Google Scholar · View at Scopus
  43. A. Tawfik, “Matter–antimatter asymmetry in heavy-ion collisions,” International Journal of Theoretical Physics, vol. 51, no. 5, pp. 1396–1407, 2012. View at Publisher · View at Google Scholar
  44. A. Tawfik, “On the higher moments of particle multiplicity, chemical freeze-out, and QCD critical endpoint,” Advances in High Energy Physics, vol. 2013, Article ID 574871, 22 pages, 2013. View at Publisher · View at Google Scholar
  45. A. Tawfik and D. Toublan, “Quark-antiquark condensates in the hadronic phase,” Physics Letters B, vol. 623, no. 1-2, pp. 48–54, 2005. View at Publisher · View at Google Scholar · View at Scopus
  46. R. Hagedorn, “Statistical thermodynamics of strong interactions at high energies,” Nuovo Cimento. Supplemento, vol. 3, pp. 147–186, 1965. View at Google Scholar
  47. A. Bazavov, T. Bhattacharya, M. Cheng et al., “Chiral and deconfinement aspects of the QCD transition,” Physical Review D, vol. 85, no. 5, Article ID 054503, 2012. View at Publisher · View at Google Scholar · View at Scopus
  48. C. Schmidt, “Universal critical behavior and the transition temperature in (2+1)flavor QCD,” AIP Conference Proceedings, vol. 1343, p. 513, 2011. View at Publisher · View at Google Scholar
  49. S. Borsanyi, Z. Fodor, C. Hoelbling et al., “QCD transition temperature: full staggered result,” in Proceedings of the 28th International Symposium on Lattice Field Theory (LATTICE '10), Villasimius, Italy, June 2010.
  50. A. Tawfik, N. Magdy, and A. Diab, “Polyakov linear SU(3) σ model: features of higher-order moments in a dense and thermal hadronic medium,” Physical Review C, vol. 89, no. 5, Article ID 055210, 2014. View at Publisher · View at Google Scholar · View at Scopus
  51. H. Mao, J. Jin, and M. Huang, “Phase diagram and thermodynamics of the polyakov linear sigma model with three quark flavors,” Journal of Physics G, vol. 37, no. 3, Article ID 035001, 2010. View at Publisher · View at Google Scholar · View at Scopus
  52. J. T. Lenaghan, D. H. Rischke, and J. Schaffner-Bielich, “Chiral symmetry restoration at nonzero temperature in the SU (3)r×SU (3)l linear sigma model,” Physical Review D, vol. 62, Article ID 085008, 2000. View at Publisher · View at Google Scholar
  53. B.-J. Schaefer and M. Wagner, “Three-flavor chiral phase structure in hot and dense QCD matter,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 79, no. 1, Article ID 014018, 2009. View at Publisher · View at Google Scholar · View at Scopus
  54. P. Kovács and Z. Szép, “Critical surface of the SU (3)L×SU (3)R chiral quark model at nonzero baryon density,” Physical Review D, vol. 75, Article ID 025015, 2007. View at Publisher · View at Google Scholar
  55. S. Rößner, C. Ratti, and W. Weise, “Polyakov loop, diquarks, and the two-flavor phase diagram,” Physical Review D, vol. 75, Article ID 034007, 2007. View at Publisher · View at Google Scholar
  56. B.-J. Schaefer, J. M. Pawlowski, and J. Wambach, “Phase structure of the Polyakov-quark-meson model,” Physical Review D, vol. 76, Article ID 074023, 2007. View at Publisher · View at Google Scholar
  57. O. Scavenius, Á. Mócsy, I. N. Mishustin, and D. H. Rischke, “Chiral phase transition within effective models with constituent quarks,” Physical Review C, vol. 64, no. 4, Article ID 045202, 2001. View at Google Scholar · View at Scopus
  58. J. I. Kapusta and C. Gale, Finite-Temperature Field Theory: Principles and Applications, Cambridge University Press, Cambridge, UK, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  59. P. Lévai and U. Heinz, “Massive gluons and quarks and the equation of state obtained from SU(3) lattice QCD,” Physical Review C: Nuclear Physics, vol. 57, no. 4, pp. 1879–1890, 1998. View at Publisher · View at Google Scholar · View at Scopus
  60. P. Romatschke, “Quasiparticle description of the hot and dense quark-gluon plasma,” http://arxiv.org/abs/hep-ph/0312152.
  61. M. Bluhm, B. Kämpfer, R. Schulze, D. Seipt, and U. Heinz, “A Family of equations of state based on lattice QCD: impact on flow in ultrarelativistic heavy-ion collisions,” Physical Review C, vol. 76, no. 3, Article ID 034901, 2007. View at Publisher · View at Google Scholar · View at Scopus
  62. J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, vol. 113 of International Series of Monographs on Physics, 2002.
  63. A. A. Osipov, B. Hiller, and J. da Providência, “Multi-quark interactions with a globally stable vacuum,” Physics Letters B, vol. 634, no. 1, pp. 48–54, 2006. View at Publisher · View at Google Scholar
  64. A. Bhattacharyya, P. Deb, S. K. Ghosh, and R. Ray, “Investigation of the phase diagram and bulk thermodynamic properties using the Polyakov-Nambu-Jona-Lasinio model with eight-quark interactions,” Physical Review D, vol. 82, no. 1, Article ID 014021, 2010. View at Publisher · View at Google Scholar · View at Scopus
  65. C. Ratti, M. A. Thaler, and W. Weise, “Phases of QCD: lattice thermodynamics and a field theoretical model,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 73, no. 1, 2006. View at Publisher · View at Google Scholar · View at Scopus
  66. C. A. Islam, R. Abir, M. G. Mustafa, R. Ray, and S. K. Ghosh, “The consequences of SU (3) colorsingletness, Polyakov Loop and Z (3) symmetry on a quark-gluon gas,” Journal of Physics G: Nuclear and Particle Physics, vol. 41, no. 2, Article ID 025001, 2014. View at Publisher · View at Google Scholar · View at Scopus
  67. J. Moreira, B. Hiller, A. A. Osipov, and A. H. Blin, “Thermodynamic potential with correct asymptotics for PNJL model,” International Journal of Modern Physics A, vol. 27, no. 11, Article ID 1250060, 2012. View at Publisher · View at Google Scholar
  68. R. Venugopalan and M. Prakash, “Thermal properties of interacting hadrons,” Nuclear Physics A, vol. 546, no. 4, pp. 718–760, 1992. View at Publisher · View at Google Scholar · View at Scopus
  69. A. Majumder and B. Müller, “Hadron mass spectrum from lattice QCD,” Physical Review Letters, vol. 105, no. 25, Article ID 252002, 4 pages, 2010. View at Publisher · View at Google Scholar
  70. R. Hagedorn, “Statistical thermodynamics of strong interactions at high energies,” Nuovo Cimento Supplemento, vol. 3, pp. 147–186, 1965. View at Google Scholar
  71. R. Hagedorn, “Large-angle cross-sections p+pA+B and π+pA+B at high energies predicted by the statistical model,” Il Nuovo Cimento, vol. 35, no. 1, pp. 216–226, 1965. View at Publisher · View at Google Scholar
  72. W. Broniowski, F. Giacosa, and V. Begun, “Why the sigma meson should not be included in thermal models,” http://arxiv.org/abs/1506.01260.
  73. M. A. Stankiewicz, “Entropy in the thermal model,” http://arxiv.org/abs/nucl-th/0509058.
  74. J. Cleymans, H. Oeschler, K. Redlich, and S. Wheaton, “Transition from baryonic to mesonic freeze-out,” Physics Letters B, vol. 615, no. 1-2, pp. 50–54, 2005. View at Publisher · View at Google Scholar · View at Scopus
  75. A. Tawfik, “A universal description for the freezeout parameters in heavy-ion collisions,” Nuclear Physics A, vol. 764, no. 1–4, pp. 387–392, 2006. View at Publisher · View at Google Scholar · View at Scopus
  76. A. Tawfik, “Condition driving chemical freeze-out,” Europhysics Letters, vol. 75, no. 3, pp. 420–426, 2006. View at Publisher · View at Google Scholar
  77. A. Tawfik, “Chemical freeze-out and higher order multiplicity moments,” Nuclear Physics A, vol. 922, pp. 225–236, 2014. View at Publisher · View at Google Scholar · View at Scopus
  78. A. Tawfik, “Constant-trace anomaly as a universal condition for the chemical freeze-out,” Physical Review C, vol. 88, no. 3, Article ID 035203, 2013. View at Publisher · View at Google Scholar · View at Scopus
  79. R. Dashen, S.-K. Ma, and H. J. Bernstein, “S-matrix formulation of statistical mechanics,” Physical Review, vol. 187, no. 1, pp. 345–370, 1969. View at Publisher · View at Google Scholar · View at Scopus
  80. A. Tawfik, M. Y. El-Bakry, D. M. Habashy, M. T. Mohamed, and E. Abbas, “Degree of chemical non-equilibrium in central Au-Au collisions at RHIC energies,” International Journal of Modern Physics E, vol. 25, no. 8, 2015. View at Publisher · View at Google Scholar
  81. C. Schmidt, “Universal critical behavior and the transition temperature in (2+1)-flavor QCD,” AIP Conference Proceedings, vol. 1343, pp. 513–515, 2011. View at Publisher · View at Google Scholar
  82. J. Gasser and H. Leutwyler, “Chiral perturbation theory: expansions in the mass of the strange quark,” Nuclear Physics B, vol. 250, no. 1–4, pp. 465–516, 1985. View at Publisher · View at Google Scholar · View at Scopus
  83. M. Cheng, S. Ejiri, P. Hegde et al., “Equation of state for physical quark masses,” Physical Review D, vol. 81, no. 5, Article ID 054504, 8 pages, 2010. View at Publisher · View at Google Scholar
  84. F. Karsch, “The last word(s) on CPOD 2013,” in Proceedings of the 8th International Workshop on Critical Point and Onset of Deconfinement (CPOD '13), p. 46, Napa, Calif, USA, March 2013.
  85. Y. Aoki, S. Borsányi, S. Dürr et al., “The QCD transition temperature: results with physical masses in the continuum limit II,” Journal of High Energy Physics, vol. 2009, no. 6, article 088, 2009. View at Publisher · View at Google Scholar
  86. A. Bazazov, T. Bhattacharya, M. Cheng et al., “Chiral and deconfinement aspects of the QCD transition,” Physical Review D, vol. 85, no. 5, Article ID 065503, 37 pages, 2012. View at Publisher · View at Google Scholar
  87. A. Tawfik and E. Abbas, “Thermal description of particle production in Au-Au collisions at RHIC energies (STAR),” Physics of Particles and Nuclei Letters, vol. 12, no. 4, pp. 521–531, 2015. View at Publisher · View at Google Scholar
  88. F. Becattini, M. Bleicher, T. Kollegger, T. Schuster, J. Steinheimer, and R. Stock, “Hadron formation in relativistic nuclear collisions and the QCD phase diagram,” Physical Review Letters, vol. 111, Article ID 082302, 2013. View at Publisher · View at Google Scholar
  89. R. Stock, F. Becattini, M. Bleicher, T. Kollegger, T. Schuster, and J. Steinheimer, “Hadronic freeze-out in A+A collisions meets the lattice QCD Parton-Hadron transition line,” in Proceedings of the 8th International Workshop on Critical Point and Onset of Deconfinement (CPOD '13), p. 11, Napa, Calif, USA, March 2013.