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Transport coefficients and resonances for a meson gas in chiral perturbation theory

  • Regular Article - Theoretical Physics
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Abstract

We present recent results on a systematic method to calculate transport coefficients for a meson gas (in particular, we analyze a pion gas) at low temperatures in the context of Chiral Perturbation Theory (ChPT). Our method is based on the study of Feynman diagrams taking into account collisions in the plasma by means of the non-zero particle width. This implies a modification of the standard ChPT power counting scheme. We discuss the importance of unitarity, which allows for an accurate high-energy description of scattering amplitudes, generating dynamically the ρ(770) and f 0(600) mesons. Our results are compatible with analyses of kinetic theory, both in the non-relativistic very low-T regime and near the transition. We show the behavior with temperature of the electrical and thermal conductivities as well as of the shear and bulk viscosities. We obtain the result that the bulk viscosity is negligible against the shear viscosity, except near the chiral phase transition where the conformal anomaly might induce larger bulk effects. Various asymptotic limits for transport coefficients, large-N c scaling and some applications to heavy-ion collisions are studied.

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References

  1. J. Adams (STAR Collaboration), Phys. Rev. Lett. 92, 052302 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. H. Song, U.W. Heinz, Phys. Lett. B 658, 279 (2008)

    Article  ADS  Google Scholar 

  4. K. Dusling, D. Teaney, Phys. Rev. C 77, 034905 (2008)

    Article  ADS  Google Scholar 

  5. D. Kharzeev, K. Tuchin, J. High Energy Phys. 0809, 093 (2008)

    Article  ADS  Google Scholar 

  6. F. Karsch, D. Kharzeev, K. Tuchin, Phys. Lett. B 663, 217 (2008)

    Article  ADS  Google Scholar 

  7. G. Torrieri, B. Tomasik, I. Mishustin, Phys. Rev. C 77, 034903 (2008)

    Article  ADS  Google Scholar 

  8. G. Aarts, J.M. Martinez Resco, J. High Energy Phys. 0204, 053 (2002)

    Article  ADS  Google Scholar 

  9. H.B. Meyer, arXiv:0805.4567 [hep-lat]

  10. H.B. Meyer, J. High Energy Phys. 0808, 031 (2008)

    Article  Google Scholar 

  11. K. Huebner, F. Karsch, C. Pica, Phys. Rev. D 78, 094501 (2008)

    Article  ADS  Google Scholar 

  12. S. Gupta, Phys. Lett. B 597, 57 (2004)

    Article  ADS  Google Scholar 

  13. P. Arnold, G.D. Moore, L.G. Yaffe, J. High Energy Phys. 0011, 001 (2000)

    Article  ADS  Google Scholar 

  14. M. Prakash, M. Prakash, R. Venugopalan, G. Welke, Phys. Rep. 227, 321 (1993)

    Article  ADS  Google Scholar 

  15. A. Dobado, F.J. Llanes-Estrada, Phys. Rev. D 69, 116004 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. M.A. Valle Basagoiti, Phys. Rev. D 66, 045005 (2002)

    Article  ADS  Google Scholar 

  18. D. Fernandez-Fraile, A. Gomez Nicola, Phys. Rev. D 73, 045025 (2006)

    Article  ADS  Google Scholar 

  19. D. Fernandez-Fraile, A. Gomez Nicola, Eur. Phys. J. A 31, 848 (2007)

    Article  ADS  Google Scholar 

  20. D. Fernández-Fraile, A. Gómez Nicola, Int. J. Mod. Phys. E 16, 3010 (2007)

    Article  ADS  Google Scholar 

  21. D. Fernandez-Fraile, A. Gomez Nicola, arXiv:0809.4663 [hep-ph]. Phys. Rev. Lett., accepted

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

    Article  ADS  Google Scholar 

  23. S. Scherer, Adv. Nucl. Phys. 27, 277 (2003)

    Article  Google Scholar 

  24. H. Georgi, Weak Interactions and Modern Particle Theory (Benjamin-Cummings, Redwood City, 1984)

    Google Scholar 

  25. S.R. de Groot, W.A. van Leeuwen, Ch.G. van Weert, Relativistic Kinetic Theory (North-Holland, Amsterdam, 1980)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  27. M. Le Bellac, Thermal Field Theory (Cambridge, 1996)

  28. D.N. Zubarev, Non-equilibrium Statistical Thermodynamics (Consultants Bureau, New York, 1974)

    Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  30. R. Horsley, W. Schoenmaker, Nucl. Phys. B 280, 716 (1987)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  32. A. Gomez Nicola, J.R. Pelaez, Phys. Rev. D 65, 054009 (2002)

    Article  ADS  Google Scholar 

  33. A. Dobado, M.J. Herrero, T.N. Truong, Phys. Lett. B 235, 134 (1990)

    Article  ADS  Google Scholar 

  34. A. Dobado, J.R. Peláez, Phys. Rev. D 47, 4883 (1993)

    Article  ADS  Google Scholar 

  35. A. Dobado, J.R. Peláez, Phys. Rev. D 56, 3057 (1997)

    Article  ADS  Google Scholar 

  36. A. Gomez Nicola, J.R. Pelaez, G. Rios, Phys. Rev. D 77, 056006 (2008)

    Article  ADS  Google Scholar 

  37. A. Gomez Nicola, F.J. Llanes-Estrada, J.R. Pelaez, Phys. Lett. B 550, 55 (2002)

    Article  ADS  Google Scholar 

  38. D. Fernandez-Fraile, A. Gomez Nicola, E.T. Herruzo, Phys. Rev. D 76, 085020 (2007)

    Article  ADS  Google Scholar 

  39. D. Cabrera, D. Fernandez-Fraile, A.G. Nicola, Eur. Phys. J. C (2009). doi:10.1140/epjc/s10052-008-0831-z. arXiv:0809.5237 [hep-ph]

    Google Scholar 

  40. M.M. Aggarwal (WA98 Collaboration), Phys. Rev. Lett. 93, 022301 (2004)

    Article  ADS  Google Scholar 

  41. W. Liu, R. Rapp, Nucl. Phys. A 796, 101 (2007)

    Article  ADS  Google Scholar 

  42. D. Fernández-Fraile, A. Gómez Nicola, arXiv:0903.0982 [hep-ph]

  43. S. Gavin, Nucl. Phys. A 435, 826 (1985)

    Article  ADS  Google Scholar 

  44. L.D. Landau, E.M. Lifshitz, L.P. Pitaevskiĭ, Physical Kinetics (Pergamon, Oxford, 1981)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  46. A. Nakamura, S. Sakai, Phys. Rev. Lett. 94, 072305 (2005)

    Article  ADS  Google Scholar 

  47. L.P. Csernai, J.I. Kapusta, L.D. McLerran, Phys. Rev. Lett. 97, 152303 (2006)

    Article  ADS  Google Scholar 

  48. Y. Hidaka, R.D. Pisarski, Phys. Rev. D 78, 071501 (2008)

    Article  ADS  Google Scholar 

  49. D. Teaney, Phys. Rev. C 68, 034913 (2003)

    Article  ADS  Google Scholar 

  50. J.-W. Chen, E. Nakano, Phys. Lett. B 647, 371 (2007)

    Article  ADS  Google Scholar 

  51. P. Arnold, C. Dogan, G.D. Moore, Phys. Rev. D 74, 085021 (2006)

    Article  ADS  Google Scholar 

  52. J.C. Collins, A. Duncan, S.D. Joglekar, Phys. Rev. D 16, 438 (1977)

    Article  ADS  Google Scholar 

  53. G. Boyd, J. Engels, F. Karsch, E. Laermann, C. Legeland, M. Lutgemeier, B. Petersson, Nucl. Phys. B 469, 419 (1996)

    Article  ADS  Google Scholar 

  54. M. Cheng , Phys. Rev. D 77, 014511 (2008)

    Article  ADS  Google Scholar 

  55. F. Karsch, K. Redlich, A. Tawfik, Eur. Phys. J. C 29, 549 (2003)

    Article  MATH  ADS  Google Scholar 

  56. B.C. Li, M. Huang, Phys. Rev. D 78, 117503 (2008)

    Article  ADS  Google Scholar 

  57. H. Leutwyler, Nucl. Phys. Proc. Suppl. 4, 248 (1988)

    Article  ADS  Google Scholar 

  58. R. Garcia Martin, J.R. Pelaez, Phys. Rev. D 74, 096003 (2006)

    Article  ADS  Google Scholar 

  59. K. Paech, S. Pratt, Phys. Rev. C 74, 014901 (2006)

    Article  ADS  Google Scholar 

  60. A.V. Manohar, arXiv:hep-ph/9802419

  61. J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 465 (1985)

    Article  ADS  Google Scholar 

  62. J.W. Chen, J. Wang, arXiv:0711.4824 [hep-ph]

Download references

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Authors and Affiliations

  1. Departamento de Física Teórica II, Universidad Complutense, 28040, Madrid, Spain

    D. Fernández-Fraile & A. Gómez Nicola

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  1. D. Fernández-Fraile
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  2. A. Gómez Nicola
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Correspondence to D. Fernández-Fraile.

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Fernández-Fraile, D., Gómez Nicola, A. Transport coefficients and resonances for a meson gas in chiral perturbation theory. Eur. Phys. J. C 62, 37–54 (2009). https://doi.org/10.1140/epjc/s10052-009-0935-0

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  • DOI: https://doi.org/10.1140/epjc/s10052-009-0935-0

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