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Shear viscosity of a hot pion gas

  • Regular Article - Theoretical Physics
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Abstract

The shear viscosity of an interacting pion gas is studied using the Kubo formalism as a microscopic description of thermal systems close to global equilibrium. We implement the skeleton expansion in order to approximate the retarded correlator of the viscous part of the energy-momentum tensor. After exploring this in gφ 4 theory we show how the skeleton expansion can be consistently applied to pions in chiral perturbation theory. The shear viscosity η is determined by the spectral width, or equivalently, the mean free path of pions in the heat bath. We derive a new analytical result for the mean free path which is well conditioned for numerical evaluation and discuss the temperature and pion-mass dependence of the mean free path and the shear viscosity. The ratio η/s of the interacting pion gas exceeds the lower bound 1/4π from AdS/CFT correspondence.

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References

  1. BRAHMS Collaboration (I. Arsene et al.), Nucl. Phys. A 757, 1 (2005).

    Article  ADS  Google Scholar 

  2. PHENIX Collaboration (K. Adcox et al.), Nucl. Phys. A 757, 184 (2005).

    Article  ADS  Google Scholar 

  3. PHOBOS Collaboration (B.B. Back et al.), Nucl. Phys. A 757, 28 (2005).

    Article  ADS  Google Scholar 

  4. STAR Collaboration (J. Adams et al.), Nucl. Phys. A 757, 102 (2005).

    Article  ADS  Google Scholar 

  5. U.W. Heinz, J. Phys. Conf. Ser. 50, 230 (2005).

    Article  ADS  Google Scholar 

  6. P. Romatschke, U. Romatschke, Phys. Rev. Lett. 99, 172301 (2007).

    Article  ADS  Google Scholar 

  7. M. Luzum, P. Romatschke, Phys. Rev. C 78, 034915 (2008).

    Article  ADS  Google Scholar 

  8. N. Armesto et al., J. Phys. G: Nucl. Part. Phys. Conf. Ser. 35, 054001 (2008).

    Article  Google Scholar 

  9. G. Kestin. U.W. Heinz, Eur. Phys. J. C 61, 545 (2008).

    Article  ADS  Google Scholar 

  10. ALICE Collaboration (K. Aamodt et al.), Phys. Rev. Lett. 108, 252302 (2010).

    Article  ADS  Google Scholar 

  11. ALICE Collaboration (K. Aamodt et al.), Phys. Lett. B 696, 30 (2011).

    Article  ADS  Google Scholar 

  12. ALICE Collaboration (K. Aamodt et al.), Phys. Lett. B 708, 249 (2012).

    Article  ADS  Google Scholar 

  13. E. Nakano, J.-W. Chen, Phys. Lett. B 347, 371 (2007).

    Google Scholar 

  14. E. Wang, U.W. Heinz, Phys. Rev. D 53, 5978 (1996).

    Article  ADS  Google Scholar 

  15. A.B. Larionov, O. Buss, K. Gallmeister, U. Mosel, Phys. Rev. C 76, 044909 (2007).

    Article  ADS  Google Scholar 

  16. H. Liu, D.-F. Hou, J.-R. Li, Commun. Theor. Phys. 50, 429 (2006).

    ADS  Google Scholar 

  17. M. Iwasaki, H. Ohnishi, T. Fukutome, J. Phys. G: Nucl. Part. Phys. 35, 035003 (2008).

    Article  ADS  Google Scholar 

  18. K. Haglin, S. Pratt, Phys. Lett. B 328, 255 (1994).

    Article  ADS  Google Scholar 

  19. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).

    Article  MathSciNet  ADS  Google Scholar 

  20. K. Yagi, T. Hatsuda, Y. Miake, Quark-Gluon Plasma (Cambridge, 2008).

  21. S. Weinberg, Gravitation and Cosmology (John Wiley & Sons, 1972).

  22. A. Muronga, Heavy Ion Phys. 15, 337 (2002).

    Article  Google Scholar 

  23. J.D. Bjorken, Phys. Rev. D 27, 140 (1983).

    Article  ADS  Google Scholar 

  24. A. Hosoya, M.A. Sakagami, M. Takao, Ann. Phys. 154, 229 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  25. D.N. Zubarev, Nonequilibrium Statistical Thermodynamics (Plenum, NY, 1974).

  26. P. Danielewicz, M. Gyulassy, Phys. Rev. D 31, 53 (1985).

    Article  ADS  Google Scholar 

  27. J.L. Hung, Phys. Rev. D 45, 1217 (1992).

    Article  MathSciNet  Google Scholar 

  28. S. Jeon, Phys. Rev. D 52, 3591 (1995).

    Article  ADS  Google Scholar 

  29. S. Jeon, L.G. Yaffe, Phys. Rev. D 53, 5799 (1996).

    Article  ADS  Google Scholar 

  30. W.J. Moore, Physical Chemistry (Longmans, London, 1958).

  31. Masaharu Iwasaki, Hiromasa Ohnishi, Takahiko Fukutome, J. Phys. G: Nucl. Part. Phys. 35, 035003 (2008).

    Article  ADS  Google Scholar 

  32. J. Gasser, H. Leutwyler, Phys. Lett. B 188, 477 (1987).

    Article  ADS  Google Scholar 

  33. P. Gerber, H. Leutwyler, Nucl. Phys. B 321, 387 (1989).

    Article  ADS  Google Scholar 

  34. Y. Aoki, Z. Fodor, S.D. Katz, K.K. Szabo, Phys. Lett. B 643, 46 (2006).

    Article  ADS  Google Scholar 

  35. A. Bazavov et al., Phys. Rev. D 80, 014504 (2009).

    Article  ADS  Google Scholar 

  36. M. Cheng et al., Phys. Rev. D 81, 054510 (2010).

    Article  ADS  Google Scholar 

  37. J.L. Goity, H. Leutwyler, Phys. Lett. B 228, 517 (1989).

    Article  ADS  Google Scholar 

  38. J. Maldacena, Int. J. Theor. Phys. 38, 1113 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  39. P.K. Kovtun, D.T. Son, A.O. Starinets, Phys. Lett. 94, 111601 (2005).

    Article  Google Scholar 

  40. R.A. Lacey et al., Phys. Rev. Lett. 98, 092301 (2007).

    Article  ADS  Google Scholar 

  41. T.D. Cohen, Phys. Rev. Lett. 99, 021602 (2007).

    Article  MathSciNet  ADS  Google Scholar 

  42. A. Rebhan, D. Steineder, Phys. Rev. Lett. 108, 021601 (2012).

    Article  ADS  Google Scholar 

  43. D. Fernández-Fraile, A. Gómez Nicola, Eur. Phys. J. A 31, 848 (2006).

    Article  ADS  Google Scholar 

  44. D. Fernández-Fraile, A. Gómez Nicola, Eur. Phys. J. C 62, 37 (2008).

    Article  Google Scholar 

  45. G. Aarts, J.M.M. Resco, Phys. Rev. D 68, 085009 (2003).

    Article  ADS  Google Scholar 

  46. G. Aarts, J.M.M. Resco, JHEP 02, 061 (2004).

    Article  ADS  Google Scholar 

  47. D. Toublan, Phys. Rev. D 56, 5629 (1997).

    Article  ADS  Google Scholar 

  48. N. Kaiser, Phys. Rev. C 59, 2945 (1999).

    Article  ADS  Google Scholar 

  49. J.I. Kapusta, Ch. Gale, Finite-Temperature Field Theory (Cambridge, 2006).

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Authors and Affiliations

  1. Physik Department, Technische Universität München, D-85747, Garching, Germany

    R. Lang, N. Kaiser & W. Weise

Authors
  1. R. Lang
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  2. N. Kaiser
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  3. W. Weise
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Correspondence to R. Lang.

Additional information

Communicated by Bo-Qiang Ma

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Lang, R., Kaiser, N. & Weise, W. Shear viscosity of a hot pion gas. Eur. Phys. J. A 48, 109 (2012). https://doi.org/10.1140/epja/i2012-12109-3

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  • DOI: https://doi.org/10.1140/epja/i2012-12109-3

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