About this Journal Submit a Manuscript Table of Contents
Advances in High Energy Physics
Volume 2013 (2013), Article ID 627137, 15 pages
http://dx.doi.org/10.1155/2013/627137
Research Article

Viscous Coefficients of a Hot Pion Gas

Theoretical Physics Division, Variable Energy Cyclotron Centre, 1/AF, Bidhannagar, Kolkata 700064, India

Received 26 March 2013; Accepted 20 May 2013

Academic Editor: Edward Sarkisyan-Grinbaum

Copyright © 2013 Sourav Sarkar. 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.

Linked References

  1. P. Kovtun, D. T. Son, and A. O. Starinets, “Viscosity in strongly interacting quantum field theories from black hole physics,” Physical Review Letters, vol. 94, no. 11, Article ID 111601, 4 pages, 2005. View at Publisher · View at Google Scholar
  2. L. P. Csernai, J. I. Kapusta, and L. D. McLerran, “Strongly interacting low-viscosity matter created in relativistic nuclear collisions,” Physical Review Letters, vol. 97, no. 15, Article ID 152303, 4 pages, 2006. View at Publisher · View at Google Scholar
  3. H. B. Meyer, “Transport properties of the quark-gluon plasma,” The European Physical Journal A, vol. 47, p. 86, 2011. View at Publisher · View at Google Scholar
  4. N. Demir and S. A. Bass, “Shear-viscosity to entropy-density ratio of a relativistic hadron gas,” Physical Review Letters, vol. 102, no. 17, Article ID 172302, 4 pages, 2009. View at Publisher · View at Google Scholar
  5. T. Matsubara, “A new approach to quantum-statistical mechanics,” Progress of Theoretical Physics, vol. 14, pp. 351–378, 1955. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. R. Mills, Propagators for Many Particle Systems, Gordon and Breach, New York, NY, USA, 1969.
  7. H. Matsumoto, Y. Nakano, and H. Umezawa, “An equivalence class of quantum field theories at finite temperature,” Journal of Mathematical Physics, vol. 25, no. 10, pp. 3076–3085, 1984. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. A. J. Niemi and G. W. Semenoff, “Finite-temperature quantum field theory in Minkowski space,” Annals of Physics, vol. 152, no. 1, pp. 105–129, 1984. View at Scopus
  9. R. L. Kobes and G. W. Semenoff, “Discontinuities of green functions in field theory at finite temperature and density,” Nuclear Physics B, vol. 260, no. 3-4, pp. 714–746, 1985. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. A. Hosoya, M. Sakagami, and M. Takao, “Nonequilibrium thermo field dynamics in field theory: transport coefficients,” Annals of Physics, vol. 154, p. 229, 1982.
  11. R. Lang, N. Kaiser, and W. Weise, “Shear viscosity of a hot pion gas,” The European Physical Journal A, vol. 48, article 109, 2012. View at Publisher · View at Google Scholar
  12. S. Jeon, “Computing spectral densities in finite temperature field theory,” Physical Review D, vol. 47, no. 10, pp. 4586–4607, 1993. View at Publisher · View at Google Scholar
  13. G. K. Källen, “On the definition of the renormalization constants in quantum electrodynamics,” Helvetica Physica Acta, vol. 25, p. 417, 1952.
  14. H. Lehmann, “Über Eigenschaften von Ausbreitungsfunktionen und Renormierungskonstanten quantisierter Felder,” Il Nuovo Cimento, vol. 11, no. 4, pp. 342–357, 1954. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Dystems, Dover Publications, New York, NY, USA, 2003.
  16. S. Mallik and S. Sarkar, “Real-time propagators at finite temperature and chemical potential,” The European Physical Journal C, vol. 61, no. 3, pp. 489–494, 2009. View at Publisher · View at Google Scholar
  17. S. Weinberg, “Phenomenological lagrangians,” Physica A, vol. 96, no. 1-2, pp. 327–340, 1979. View at Scopus
  18. J. Gasser and H. Leutwyler, “Chiral perturbation theory to one loop,” Annals of Physics, vol. 158, no. 1, pp. 142–210, 1984. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. A. Dobado and S. N. Santalla, “Pion gas viscosity at low temperature and density,” Physical Review D, vol. 65, no. 9, Article ID 096011, 13 pages, 2002. View at Publisher · View at Google Scholar
  20. J. W. Chen, Y. H. Li, Y. F. Liu, and E. Nakano, “QCD viscosity to entropy density ratio in the hadronic phase,” Physical Review D, vol. 76, no. 11, Article ID 114011, 8 pages, 2007.
  21. A. Dobado and F. J. Llanes-Estrada, “Viscosity of meson matter,” Physical Review D, vol. 69, no. 11, Article ID 116004, 2004. View at Publisher · View at Google Scholar · View at Scopus
  22. D. Davesne, “Transport coefficients of a hot pion gas,” Physical Review C, vol. 53, no. 6, pp. 3069–3084, 1996. View at Publisher · View at Google Scholar · View at Scopus
  23. M. Prakash, M. Prakash, R. Venugopalan, and G. Welke, “Non-equilibrium properties of hadronic mixtures,” Physics Report, vol. 227, no. 6, pp. 321–366, 1993. View at Scopus
  24. K. Itakura, O. Morimatsu, and H. Otomo, “Shear viscosity of a hadronic gas mixture,” Physical Review D, vol. 77, no. 1, Article ID 014014, 19 pages, 2008. View at Publisher · View at Google Scholar
  25. S. Mitra, S. Ghosh, and S. Sarkar, “Effect of a spectral modification of the ρ meson on the shear viscosity of a pion gas,” Physical Review C, vol. 85, no. 6, Article ID 064917, 8 pages, 2012. View at Publisher · View at Google Scholar
  26. R. Kubo, “Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems,” Journal of the Physical Society of Japan, vol. 12, pp. 570–586, 1957. View at MathSciNet
  27. P. C. Martin and J. Schwinger, “Theory of many-particle systems. I,” Physical Review, vol. 115, no. 6, pp. 1342–1373, 1959. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  28. D. N. Zubarev, Nonequilibrium Statistical Thermodynamics, Plenum, New York, NY, USA, 1974. View at MathSciNet
  29. M. Gell-Mann and M. L. Golberger, “The formal theory of scattering,” Physical Review, vol. 91, no. 2, pp. 398–408, 1953. View at Publisher · View at Google Scholar
  30. J. L. Goity and H. Leutwyler, “On the mean free path of pions in hot matter,” Physics Letters B, vol. 228, no. 4, pp. 517–522, 1989. View at Scopus
  31. S. Mitra and S. Sarkar, “Medium effects on the viscosities of a pion gas,” Physical Review D, vol. 87, no. 9, Article ID 094026, 12 pages, 2013.
  32. P. Chakraborty and J. I. Kapusta, “Quasiparticle theory of shear and bulk viscosities of hadronic matter,” Physical Review C, vol. 83, no. 1, Article ID 014906, 17 pages, 2011.
  33. P. H. Polak, W. A. van Leeuwen, and S. R. de Groot, “On relativistic kinetic gas theory. X. Transport coefficients in the intermediate relativistic regime. Values for special models,” Physica, vol. 66, no. 3, pp. 455–473, 1973. View at Scopus
  34. G. Bertsch, M. Gong, L. McLerran, P. V. Ruuskanen, and E. Sarkkinen, “Cascade simulation of ultrarelativistic collisions,” Physical Review D, vol. 37, no. 5, pp. 1202–1209, 1988. View at Publisher · View at Google Scholar · View at Scopus
  35. M. Le Bellac, Thermal Field Theory, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, Mass, USA, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  36. S. Sarkar, B. K. Patra, V. J. Menon, and S. Mallik, “Spectral representation at finite temperature,” Indian Journal of Physics, vol. 76A, pp. 385–391, 2002.
  37. S. Ghosh, S. Sarkar, and S. Mallik, “Analytic structure of ρ meson propagator at finite temperature,” The European Physical Journal C, vol. 70, no. 1-2, pp. 251–262, 2010. View at Publisher · View at Google Scholar
  38. H. A. Weldon, “Simple rules for discontinuities in finite-temperature field theory,” Physical Review D, vol. 28, no. 8, pp. 2007–2015, 1983. View at Publisher · View at Google Scholar
  39. K. Nakamura, K. Hagiwara, K. Hikasa, et al., “Review of particle physics,” Journal of Physics G, vol. 37, Article ID 075021, 2010. View at Publisher · View at Google Scholar
  40. S. Ghosh and S. Sarkar, “ρ self-energy at finite temperature and density in the real-time formalism,” Nuclear Physics A, vol. 870-871, pp. 94–111, 2011. View at Publisher · View at Google Scholar
  41. H. W. Barz, G. Bertsch, P. Danielewicz, and H. Schulz, “Pion-pion cross section in a dense and hot pionic gas,” Physics Letters B, vol. 275, no. 1-2, pp. 19–23, 1992. View at Scopus
  42. S. Gavin, “Transport coefficients in ultra-relativistic heavy-ion collisions,” Nuclear Physics A, vol. 435, no. 3-4, pp. 826–843, 1985. View at Publisher · View at Google Scholar
  43. A. Wiranata and M. Prakash, “Shear viscosities from the Chapman-Enskog and the relaxation time approaches,” Physical Review C, vol. 85, no. 5, Article ID 054908, 14 pages, 2012. View at Publisher · View at Google Scholar
  44. T. Hirano and K. Tsuda, “Collective flow and two-pion correlations from a relativistic hydrodynamic model with early chemical freeze-out,” Physical Review C, vol. 66, no. 5, Article ID 054905, 14 pages, 2002.
  45. E. Lu and G. D. Moore, “Bulk viscosity of a pion gas,” Physical Review C, vol. 83, no. 4, Article ID 044901, 7 pages, 2011. View at Publisher · View at Google Scholar
  46. M. E. Carrington, H. Defu, and R. Kobes, “Nonlinear response from transport theory and quantum field theory at finite temperature,” Physical Review D, vol. 64, no. 2, Article ID 025001, 15 pages, 2001. View at Publisher · View at Google Scholar
  47. K. Dusling and T. Schafer, “Bulk viscosity, particle spectra, and flow in heavy-ion collisions,” Physical Review C, vol. 85, no. 4, Article ID 044909, 19 pages, 2012. View at Publisher · View at Google Scholar