Transport properties of the quark-gluon plasma

A lattice QCD perspective
  • Harvey B. Meyer
Review

Abstract

Transport properties of a thermal medium determine how its conserved charge densities (for instance the electric charge, energy or momentum) evolve as a function of time and eventually relax back to their equilibrium values. Here the transport properties of the quark-gluon plasma are reviewed from a theoretical perspective. The latter play a key role in the description of heavy-ion collisions, and are an important ingredient in constraining particle production processes in the early universe. We place particular emphasis on lattice QCD calculations of conserved current correlators. These Euclidean correlators are related by an integral transform to spectral functions, whose small-frequency form determines the transport properties via Kubo formulae. The universal hydrodynamic predictions for the small-frequency pole structure of spectral functions are summarized. The viability of a quasiparticle description implies the presence of additional characteristic features in the spectral functions. These features are in stark contrast with the functional form that is found in strongly coupled plasmas via the gauge/gravity duality. A central goal is therefore to determine which of these dynamical regimes the quark-gluon plasma is qualitatively closer to as a function of temperature. We review the analysis of lattice correlators in relation to transport properties, and tentatively estimate what computational effort is required to make decisive progress in this field.

References

  1. 1.
    C. DeTar, U.M. Heller, Eur. Phys. J. A 41, 405 (2009) arXiv:0905.2949 ADSCrossRefGoogle Scholar
  2. 2.
    Y. Bai, Anisotropic Flow Measurements in STAR at the Relativistic Heavy Ion Collider, Ph.D. thesis (2007)Google Scholar
  3. 3.
    D.A. Teaney, Viscous Hydrodynamics and the Quark Gluon Plasma, arXiv:0905.2433
  4. 4.
    PHENIX Collaboration (K. Adcox et al.), Nucl. Phys. A 757, 184 (2005) arXiv:nucl-ex/0410003 ADSCrossRefGoogle Scholar
  5. 5.
    STAR Collaboration (J. Adams et al.), Nucl. Phys. A 757, 102 (2005) arXiv:nucl-ex/0501009 ADSCrossRefGoogle Scholar
  6. 6.
    B.B. Back et al., Nucl. Phys. A 757, 28 (2005) arXiv:nucl-ex/0410022 ADSCrossRefGoogle Scholar
  7. 7.
    BRAHMS Collaboration (I. Arsene et al., Nucl. Phys. A 757, 1 (2005) arXiv:nucl-ex/0410020 ADSCrossRefGoogle Scholar
  8. 8.
    T. Schafer, D. Teaney, Rept. Prog. Phys. 72, 126001 (2009) arXiv:0904.3107 ADSCrossRefGoogle Scholar
  9. 9.
    The ALICE Collaboration (K. Aamodt), arXiv:1011.3914
  10. 10.
    P. Romatschke, U. Romatschke, Phys. Rev. Lett. 99, 172301 (2007) arXiv:0706.1522 ADSCrossRefGoogle Scholar
  11. 11.
    K. Dusling, D. Teaney, Phys. Rev. C 77, 034905 (2008) arXiv:0710.5932 ADSCrossRefGoogle Scholar
  12. 12.
    H. Song, U.W. Heinz, Phys. Lett. B 658, 279 (2008) arXiv:0709.0742 ADSCrossRefGoogle Scholar
  13. 13.
    D. Teaney, L. Yan, arXiv:1010.1876
  14. 14.
    P. Arnold, G.D. Moore, L.G. Yaffe, JHEP 11, 001 (2000) arXiv: hep-ph/0010177 ADSCrossRefGoogle Scholar
  15. 15.
    P. Arnold, G.D. Moore, L.G. Yaffe, JHEP 05, 051 (2003) arXiv:hep-ph/0302165 ADSCrossRefGoogle Scholar
  16. 16.
    G. Policastro, D.T. Son, A.O. Starinets, Phys. Rev. Lett. 87, 081601 (2001) arXiv:hep-th/0104066 ADSCrossRefGoogle Scholar
  17. 17.
    P. Kovtun, D.T. Son, A.O. Starinets, Phys. Rev. Lett. 94, 111601 (2005) hep-th/0405231ADSCrossRefGoogle Scholar
  18. 18.
    M. Luzum, P. Romatschke, Phys. Rev. C 78, 034915 (2008) arXiv:0804.4015 ADSCrossRefGoogle Scholar
  19. 19.
    B. Mueller, Prog. Theor. Phys. Suppl. 174, 103 (2008)ADSCrossRefGoogle Scholar
  20. 20.
    STAR Collaboration (B.I. Abelev et al.), Phys. Rev. Lett. 98, 192301 (2007) arXiv:nucl-ex/0607012 ADSCrossRefGoogle Scholar
  21. 21.
    PHENIX Collaboration (A. Adare et al.), Phys. Rev. Lett. 98, 172301 (2007) arXiv:nucl-ex/0611018 ADSCrossRefGoogle Scholar
  22. 22.
    G.D. Moore, D. Teaney, Phys. Rev. C 71, 064904 (2005) arXiv:hep-ph/0412346 ADSCrossRefGoogle Scholar
  23. 23.
    PHENIX Collaboration (K. Adcox et al.), Phys. Rev. Lett. 88, 022301 (2002) arXiv:nucl-ex/0109003 ADSCrossRefGoogle Scholar
  24. 24.
    STAR Collaboration (C. Adler et al.), Phys. Rev. Lett. 89, 202301 (2002) arXiv:nucl-ex/0206011 ADSCrossRefGoogle Scholar
  25. 25.
    U.A. Wiedemann, arXiv:0908.2306
  26. 26.
    F. Iocco, G. Mangano, G. Miele, O. Pisanti, P.D. Serpico, Phys. Rep. 472, 1 (2009) arXiv:0809.0631 ADSCrossRefGoogle Scholar
  27. 27.
    Y. Aoki, G. Endrodi, Z. Fodor, S. Katz, K. Szabo, Nature 443, 675 (2006) arXiv:hep-lat/0611014 ADSCrossRefGoogle Scholar
  28. 28.
    R. Durrer, J. Phys. Conf. Ser. 222, 012021 (2010) arXiv:1002.1389 ADSCrossRefGoogle Scholar
  29. 29.
    L.P. Csernai, J.I. Kapusta, Phys. Rev. D 46, 1379 (1992)ADSCrossRefGoogle Scholar
  30. 30.
    T. Asaka, S. Blanchet, M. Shaposhnikov, Phys. Lett. B 631, 151 (2005) arXiv:hep-ph/0503065 ADSCrossRefGoogle Scholar
  31. 31.
    T. Asaka, M. Laine, M. Shaposhnikov, JHEP 06, 053 (2006) arXiv:hep-ph/0605209 ADSCrossRefGoogle Scholar
  32. 32.
    T. Asaka, M. Laine, M. Shaposhnikov, JHEP 01, 091 (2007) arXiv:hep-ph/0612182 ADSCrossRefGoogle Scholar
  33. 33.
    S. Borsanyi, G. Endrodi, Z. Fodor, A. Jakovac, S.D. Katz, JHEP 1011, 077 (2010) arXiv:1007.2580 ADSCrossRefGoogle Scholar
  34. 34.
    P. Arnold, L.G. Yaffe, Phys. Rev. D 52, 7208 (1995) arXiv:hep-ph/9508280 ADSCrossRefGoogle Scholar
  35. 35.
    P.B. Arnold, L.G. Yaffe, Phys. Rev. D 57, 1178 (1998) arXiv:hep-ph/9709449 ADSCrossRefGoogle Scholar
  36. 36.
    M. Laine, M. Vepsalainen, JHEP 09, 023 (2009) arXiv:0906.4450 ADSCrossRefGoogle Scholar
  37. 37.
    M. Cheng, S. Datta, A. Francis, J. van der Heide, C. Jung et al., Eur. Phys. J. C 71, 1564 (2011) arXiv:1010.1216 ADSCrossRefGoogle Scholar
  38. 38.
    S. Caron-Huot, G.D. Moore, Phys. Rev. Lett. 100, 052301 (2008) arXiv:0708.4232 ADSCrossRefGoogle Scholar
  39. 39.
    F. Jegerlehner, A. Nyffeler, Phys.Rep. 477, 1 (2009) arXiv:0902.3360 ADSCrossRefGoogle Scholar
  40. 40.
    D. Bernecker, H. B. Meyer, unpublished (2011)Google Scholar
  41. 41.
    Y. Aoki, Z. Fodor, S.D. Katz, K.K. Szabo, Phys. Lett. B 643, 46 (2006) hep-lat/0609068ADSCrossRefGoogle Scholar
  42. 42.
    Y. Aoki et al., JHEP 06, 088 (2009) arXiv:0903.4155 ADSCrossRefGoogle Scholar
  43. 43.
    Wuppertal-Budapest Collaboration (S. Borsanyi et al.), JHEP 09, 073 (2010) arXiv:1005.3508 ADSCrossRefGoogle Scholar
  44. 44.
    A. Bazavov et al., Phys. Rev. D 80, 014504 (2009) arXiv:0903.4379 ADSCrossRefGoogle Scholar
  45. 45.
    M. Cheng et al., Phys. Rev. D 81, 054504 (2010) arXiv:0911.2215 ADSCrossRefGoogle Scholar
  46. 46.
    E. Laermann, O. Philipsen, Ann. Rev. Nucl. Part. Sci. 53, 163 (2003) arXiv:hep-ph/0303042 ADSCrossRefGoogle Scholar
  47. 47.
    P. Romatschke, Int. J. Mod. Phys. E 19, 1 (2010) arXiv:0902.3663 ADSCrossRefGoogle Scholar
  48. 48.
    D.T. Son, Acta Phys. Polon. B 39, 3173 (2008)ADSGoogle Scholar
  49. 49.
    S.S. Gubser, A. Karch, Ann. Rev. Nucl. Part. Sci. 59, 145 (2009) arXiv:0901.0935 ADSCrossRefGoogle Scholar
  50. 50.
    J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal, U.A. Wiedemann, Gauge/String Duality, Hot QCD and Heavy Ion Collisions, arXiv:1101.0618
  51. 51.
    G.D. Moore, Transport coefficients in hot QCD, arXiv:hep-ph/0408347
  52. 52.
    P.K. Kovtun, A.O. Starinets, Phys. Rev. D 72, 086009 (2005) arXiv:hep-th/0506184 ADSCrossRefGoogle Scholar
  53. 53.
    J.I. Kapusta, C. Gale, Finite-temperature field theory: Principles and applications, (Cambridge University Press, UK, 2006) p. 428Google Scholar
  54. 54.
    J. Hong, D. Teaney, Phys. Rev. C 82, 044908 (2010) arXiv:1003.0699 ADSCrossRefGoogle Scholar
  55. 55.
    P.B. Arnold, G.D. Moore, L.G. Yaffe, JHEP 0111, 057 (2001) arXiv:hep-ph/0109064 ADSCrossRefGoogle Scholar
  56. 56.
    D. Teaney, Phys. Rev. D 74, 045025 (2006) arXiv:hep-ph/0602044 ADSCrossRefGoogle Scholar
  57. 57.
    P. Romatschke, D.T. Son, Phys. Rev. D 80, 065021 (2009) arXiv:0903.3946 ADSCrossRefGoogle Scholar
  58. 58.
    H.B. Meyer, JHEP 04, 099 (2010) arXiv:1002.3343 ADSCrossRefGoogle Scholar
  59. 59.
    R. Baier, P. Romatschke, D.T. Son, A.O. Starinets, M.A. Stephanov, JHEP 04, 100 (2008) arXiv:0712.2451 MathSciNetADSCrossRefGoogle Scholar
  60. 60.
    G.D. Moore, K.A. Sohrabi, Kubo Formulae for Second-Order Hydrodynamic Coefficients, arXiv:1007.5333
  61. 61.
    P. Romatschke, Class. Quantum. Grav. 27, 025006 (2010) arXiv:0906.4787 MathSciNetADSCrossRefGoogle Scholar
  62. 62.
    G.S. Denicol, J. Noronha, H. Niemi, D.H. Rischke, Phys. Rev. D 83, 074019 (2011) arXiv:1102.4780 ADSCrossRefGoogle Scholar
  63. 63.
    P. Petreczky, D. Teaney, Phys. Rev. D 73, 014508 (2006) arXiv:hep-ph/0507318 ADSCrossRefGoogle Scholar
  64. 64.
    S. Caron-Huot, M. Laine, G.D. Moore, JHEP 04, 053 (2009) arXiv:0901.1195 ADSCrossRefGoogle Scholar
  65. 65.
    Y. Burnier, M. Laine, J. Langelage, L. Mether, JHEP 08, 094 (2010) arXiv:1006.0867 ADSCrossRefGoogle Scholar
  66. 66.
    G. Aarts, J.M. Martinez Resco, Nucl. Phys. B 726, 93 (2005) arXiv:hep-lat/0507004 ADSMATHCrossRefGoogle Scholar
  67. 67.
    H.B. Meyer, JHEP 08, 031 (2008) arXiv:0806.3914 CrossRefGoogle Scholar
  68. 68.
    P. Arnold, C. Dogan, G.D. Moore, Phys. Rev. D 74, 085021 (2006) arXiv:hep-ph/0608012 ADSCrossRefGoogle Scholar
  69. 69.
    G. Baym, H. Monien, C. Pethick, D. Ravenhall, Phys. Rev. Lett. 64, 1867 (1990)ADSCrossRefGoogle Scholar
  70. 70.
    Z. Xu, C. Greiner, Phys. Rev. Lett. 100, 172301 (2008) arXiv:0710.5719 ADSCrossRefGoogle Scholar
  71. 71.
    J.-W. Chen, J. Deng, H. Dong, Q. Wang, Phys. Rev. D 83, 034031 (2011) arXiv:1011.4123 ADSCrossRefGoogle Scholar
  72. 72.
    M. Laine, M. Vepsalainen, A. Vuorinen, JHEP 1010, 010 (2010) arXiv:1008.3263 ADSCrossRefGoogle Scholar
  73. 73.
    A.L. Kataev, N.V. Krasnikov, A.A. Pivovarov, Nucl. Phys. B 198, 508 (1982) arXiv:hep-ph/9612326 ADSCrossRefGoogle Scholar
  74. 74.
    A.A. Pivovarov, Phys. Atom. Nucl. 63, 1646 (2000) arXiv:hep-ph/9905485 ADSCrossRefGoogle Scholar
  75. 75.
    F. Karsch, M. Mustafa, M. Thoma, Phys. Lett. B 497, 249 (2001) arXiv:hep-ph/0007093 ADSMATHCrossRefGoogle Scholar
  76. 76.
    A. Vuorinen, Phys. Rev. D 67, 074032 (2003) arXiv:hep-ph/0212283 ADSCrossRefGoogle Scholar
  77. 77.
    D.T. Son, A.O. Starinets, JHEP 09, 042 (2002) arXiv:hep-th/0205051 MathSciNetADSCrossRefGoogle Scholar
  78. 78.
    G. Policastro, D.T. Son, A.O. Starinets, JHEP 09, 043 (2002) arXiv:hep-th/0205052 MathSciNetADSCrossRefGoogle Scholar
  79. 79.
    G. Policastro, D.T. Son, A.O. Starinets, JHEP 12, 054 (2002) arXiv:hep-th/0210220 MathSciNetADSCrossRefGoogle Scholar
  80. 80.
    P. Kovtun, A. Starinets, Phys. Rev. Lett. 96, 131601 (2006) arXiv:hep-th/0602059 ADSCrossRefGoogle Scholar
  81. 81.
    D.T. Son, A.O. Starinets, Ann. Rev. Nucl. Part. Sci. 57, 95 (2007) arXiv:0704.0240 ADSCrossRefGoogle Scholar
  82. 82.
    R.C. Myers, A.O. Starinets, R.M. Thomson, JHEP 11, 091 (2007) arXiv:0706.0162 MathSciNetADSCrossRefGoogle Scholar
  83. 83.
    D.Z. Freedman, S.D. Mathur, A. Matusis, L. Rastelli, Nucl. Phys. B 546, 96 (1999) arXiv:hep-th/9804058 MathSciNetADSMATHCrossRefGoogle Scholar
  84. 84.
    G. Chalmers, H. Nastase, K. Schalm, R. Siebelink, Nucl. Phys. B 540, 247 (1999) arXiv:hep-th/9805105 MathSciNetADSMATHCrossRefGoogle Scholar
  85. 85.
    M. Natsuume, T. Okamura, Phys. Rev. D 77, 066014 (2008) arXiv:0712.2916 MathSciNetADSCrossRefGoogle Scholar
  86. 86.
    U. Gursoy, E. Kiritsis, JHEP 0802, 032 (2008) arXiv:0707.1324 MathSciNetADSCrossRefGoogle Scholar
  87. 87.
    S.S. Gubser, A. Nellore, S.S. Pufu, F.D. Rocha, Phys. Rev. Lett. 101, 131601 (2008) arXiv:0804.1950 MathSciNetADSCrossRefGoogle Scholar
  88. 88.
    U. Gursoy, E. Kiritsis, L. Mazzanti, G. Michalogiorgakis, F. Nitti, Lect. Notes Phys. 828, 79 (2011) arXiv:1006.5461 CrossRefGoogle Scholar
  89. 89.
    A. Buchel, Phys. Lett. B 663, 286 (2008) arXiv:0708.3459 ADSCrossRefGoogle Scholar
  90. 90.
    S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations (Cambridge University Press, UK, 1995) p. 609Google Scholar
  91. 91.
    S.-z. Huang, M. Lissia, Phys. Rev. D 52, 1134 (1995) arXiv:hep-ph/9412246 ADSCrossRefGoogle Scholar
  92. 92.
    S. Caron-Huot, Phys. Rev. D 79, 125009 (2009) arXiv:0903.3958 ADSCrossRefGoogle Scholar
  93. 93.
    M. Laine, M. Vepsalainen, A. Vuorinen, JHEP 1012, 078 (2010) arXiv:1011.4439 MathSciNetADSCrossRefGoogle Scholar
  94. 94.
    P.J. Ellis, J.I. Kapusta, H.-B. Tang, Phys. Lett. B 443, 63 (1998) nucl-th/9807071ADSCrossRefGoogle Scholar
  95. 95.
    D. Kharzeev, K. Tuchin, JHEP 09, 093 (2008) arXiv:0705.4280 ADSCrossRefGoogle Scholar
  96. 96.
    H.B. Meyer, Phys. Rev. D 82, 054504 (2010) arXiv:1005.2686 ADSCrossRefGoogle Scholar
  97. 97.
    J.I. Kapusta, E.V. Shuryak, Phys. Rev. D 49, 4694 (1994) arXiv:hep-ph/9312245 ADSCrossRefGoogle Scholar
  98. 98.
    L. Giusti, M. Luscher, JHEP 03, 013 (2009) arXiv:0812.3638 ADSCrossRefGoogle Scholar
  99. 99.
    G. Ford, M. Kac, P. Mazur, J. Math. Phys. 6, 604 (1965)MathSciNetCrossRefGoogle Scholar
  100. 100.
    C. Gardiner, P. Zoller, Quantum Noise (Springer-Verlag, Berlin)Google Scholar
  101. 101.
    P. Kovtun, L.G. Yaffe, Phys. Rev. D 68, 025007 (2003) hep-th/0303010ADSCrossRefGoogle Scholar
  102. 102.
    D. Scalapino, H.-B. Schuttler, Phys. Rev. Lett. 55, 1204 (1985)ADSCrossRefGoogle Scholar
  103. 103.
    M. Luscher, Commun. Math. Phys. 54, 283 (1977)MathSciNetADSCrossRefGoogle Scholar
  104. 104.
    K.G. Wilson, Phys. Rev. D 10, 2445 (1974)ADSCrossRefGoogle Scholar
  105. 105.
    K. Symanzik, Nucl. Phys. B 226, 187 (1983)MathSciNetADSCrossRefGoogle Scholar
  106. 106.
    M. Luescher, S. Sint, R. Sommer, P. Weisz, Nucl. Phys. B 478, 365 (1996) arXiv:hep-lat/9605038 ADSCrossRefGoogle Scholar
  107. 107.
    M. Luscher, S. Sint, R. Sommer, P. Weisz, U. Wolff, Nucl. Phys. B 491, 323 (1997) arXiv:hep-lat/9609035 ADSCrossRefGoogle Scholar
  108. 108.
    ALPHA Collaboration (K. Jansen, R. Sommer), Nucl. Phys. B 530, 185 (1998) arXiv:hep-lat/9803017 ADSCrossRefGoogle Scholar
  109. 109.
    CP-PACS Collaboration, JLQCD Collaboration (S. Aoki et al.), Phys. Rev. D 73, 034501 (2006) arXiv:hep-lat/0508031 ADSCrossRefGoogle Scholar
  110. 110.
    J.B. Kogut, L. Susskind, Phys. Rev. D 11, 395 (1975)ADSCrossRefGoogle Scholar
  111. 111.
    M. Golterman, Applications of chiral perturbation theory to lattice QCD, arXiv:0912.4042
  112. 112.
    D.B. Kaplan, Phys. Lett. B 288, 342 (1992) arXiv:hep-lat/9206013 MathSciNetADSCrossRefGoogle Scholar
  113. 113.
    Y. Shamir, Nucl. Phys. B 406, 90 (1993) arXiv:hep-lat/9303005 MathSciNetADSCrossRefGoogle Scholar
  114. 114.
    H. Neuberger Phys. Lett. B4171411998, arXiv:hep-lat/9707022
  115. 115.
    S. Chandrasekharan, U. Wiese, Prog. Part. Nucl. Phys. 53, 373 (2004) arXiv:hep-lat/0405024 ADSCrossRefGoogle Scholar
  116. 116.
    S. Duane, A. Kennedy, B. Pendleton, D. Roweth, Phys. Lett. B 195, 216 (1987)ADSCrossRefGoogle Scholar
  117. 117.
    M. Hasenbusch, Phys. Lett. B 519, 177 (2001) arXiv:hep-lat/0107019 ADSMATHCrossRefGoogle Scholar
  118. 118.
    M. Luscher, Comput. Phys. Commun. 165, 199 (2005) arXiv:hep-lat/0409106 ADSCrossRefGoogle Scholar
  119. 119.
    M. Clark, A. Kennedy, Phys. Rev. Lett. 98, 051601 (2007) arXiv:hep-lat/0608015 ADSCrossRefGoogle Scholar
  120. 120.
    M. Luscher, JHEP 0305, 052 (2003) arXiv:hep-lat/0304007 ADSCrossRefGoogle Scholar
  121. 121.
    M. Luscher, JHEP 0707, 081 (2007) arXiv:0706.2298 ADSCrossRefGoogle Scholar
  122. 122.
    R. Babich, J. Brannick, R. Brower, M. Clark, T. Manteuffel et al., Phys. Rev. Lett. 105, 201602 (2010) arXiv:1005.3043 ADSCrossRefGoogle Scholar
  123. 123.
    M. Luscher, P. Weisz, JHEP 09, 010 (2001) arXiv:hep-lat/0108014 ADSCrossRefGoogle Scholar
  124. 124.
    H.B. Meyer, JHEP 01, 048 (2003) arXiv:hep-lat/0209145 ADSCrossRefGoogle Scholar
  125. 125.
    M. Luscher, Computational Strategies in Lattice QCD, arXiv:1002.4232
  126. 126.
    M. Della Morte, R. Hoffmann, F. Knechtli, R. Sommer, U. Wolff, JHEP 0507, 007 (2005) arXiv:hep-lat/0505026 ADSCrossRefGoogle Scholar
  127. 127.
    M. Della Morte, R. Sommer, S. Takeda, Phys. Lett. B 672, 407 (2009) arXiv:0807.1120 ADSCrossRefGoogle Scholar
  128. 128.
    S.L. Adler, J.C. Collins, A. Duncan, Phys. Rev. D 15, 1712 (1977) Revised versionADSCrossRefGoogle Scholar
  129. 129.
    K. Fujikawa, Phys. Rev. D 23, 2262 (1981)MathSciNetADSCrossRefGoogle Scholar
  130. 130.
    H.B. Meyer, J.W. Negele, Phys. Rev. D 77, 037501 (2008) arXiv:0707.3225 ADSCrossRefGoogle Scholar
  131. 131.
    M. Goeckeler et al., Phys. Rev. D 54, 5705 (1996) arXiv:hep-lat/9602029 ADSCrossRefGoogle Scholar
  132. 132.
    J. Engels, F. Karsch, H. Satz, I. Montvay, Nucl. Phys. B 205, 545 (1982)ADSCrossRefGoogle Scholar
  133. 133.
    H.B. Meyer, Nucl. Phys. B 795, 230 (2008) arXiv:0711.0738 ADSMATHCrossRefGoogle Scholar
  134. 134.
    D.T. Son, M.A. Stephanov, Phys. Rev. D 66, 076011 (2002) arXiv:hep-ph/0204226 ADSCrossRefGoogle Scholar
  135. 135.
    P. Hasenfratz, S. Hauswirth, T. Jorg, F. Niedermayer, K. Holland, Nucl. Phys. B 643, 280 (2002) arXiv:hep-lat/0205010 ADSCrossRefGoogle Scholar
  136. 136.
    QCDSF Collaboration (M. Gockeler et al.), Nucl. Phys. B 688, 135 (2004) arXiv:hep-lat/0312032 ADSCrossRefGoogle Scholar
  137. 137.
    H.B. Meyer, JHEP 06, 077 (2009) arXiv:0904.1806 ADSCrossRefGoogle Scholar
  138. 138.
    S. Capitani, Phys. Rept. 382, 113 (2003) arXiv:hep-lat/0211036 MathSciNetADSMATHCrossRefGoogle Scholar
  139. 139.
    CP-PACS Collaboration (Y. Namekawa et al.), Phys. Rev. D 64, 074507 (2001) hep-lat/0105012ADSCrossRefGoogle Scholar
  140. 140.
    A. Jakovac, P. Petreczky, K. Petrov, A. Velytsky, Phys. Rev. D 75, 014506 (2007) arXiv:hep-lat/0611017 ADSCrossRefGoogle Scholar
  141. 141.
    T.R. Klassen, Nucl. Phys. B 533, 557 (1998) arXiv:hep-lat/9803010 ADSCrossRefGoogle Scholar
  142. 142.
    J. Engels, F. Karsch, T. Scheideler, Nucl. Phys. B 564, 303 (2000) arXiv:hep-lat/9905002 ADSCrossRefGoogle Scholar
  143. 143.
    R. Morrin, A.O. Cais, M. Peardon, S.M. Ryan, J.-I. Skullerud, Phys. Rev. D 74, 014505 (2006) arXiv:hep-lat/0604021 ADSCrossRefGoogle Scholar
  144. 144.
    H.B. Meyer, Phys. Rev. Lett. 100, 162001 (2008) arXiv:0710.3717 ADSCrossRefGoogle Scholar
  145. 145.
    H.-T. Ding, A. Francis, O. Kaczmarek, F. Karsch, E. Laermann, Phys. Rev. D 83, 034504 (2011) arXiv:1012.4963 ADSCrossRefGoogle Scholar
  146. 146.
    S. Gupta, Phys. Lett. B 597, 57 (2004) arXiv:hep-lat/0301006 ADSCrossRefGoogle Scholar
  147. 147.
    G. Aarts, C. Allton, J. Foley, S. Hands, and S. Kim, PoS LAT2006, 134 (2006) arXiv:hep-lat/0610061 Google Scholar
  148. 148.
    H.T. Ding, O. Kaczmarek, F. Karsch, H. Satz, W. Soldner, Charmonium correlators and spectral functions at finite temperature, arXiv:0910.3098
  149. 149.
    A. Bazavov, P. Petreczky, A. Velytsky, Quarkonium at Finite Temperature, arXiv:0904.1748
  150. 150.
    T. Matsui, H. Satz, Phys. Lett. B 178, 416 (1986)ADSCrossRefGoogle Scholar
  151. 151.
    M. Laine, Nucl. Phys. A 820, 25C (2009) arXiv:0810.1112 ADSCrossRefGoogle Scholar
  152. 152.
    Y. Burnier, M. Laine, M. Vepsalainen, JHEP 0801, 043 (2008) arXiv:0711.1743 ADSCrossRefGoogle Scholar
  153. 153.
    T. Umeda, Phys. Rev. D 75, 094502 (2007) arXiv:hep-lat/0701005 ADSCrossRefGoogle Scholar
  154. 154.
    A. Mocsy, P. Petreczky, Phys. Rev. D 73, 074007 (2006) arXiv:hep-ph/0512156 ADSCrossRefGoogle Scholar
  155. 155.
    S. Datta, P. Petreczky, J. Phys. G 35, 104114 (2008) arXiv:0805.1174 ADSCrossRefGoogle Scholar
  156. 156.
    S. Datta, F. Karsch, P. Petreczky, I. Wetzorke, Phys. Rev. D 69, 094507 (2004) arXiv:hep-lat/0312037 ADSCrossRefGoogle Scholar
  157. 157.
    H.B. Meyer, New J. Phys. 13, 035008 (2011) arXiv:1012.0234 ADSCrossRefGoogle Scholar
  158. 158.
    J. Casalderrey-Solana, D. Teaney, Phys. Rev. D 74, 085012 (2006) arXiv:hep-ph/0605199 ADSCrossRefGoogle Scholar
  159. 159.
    H.B. Meyer, Phys. Rev. D 76, 101701 (2007) arXiv:0704.1801 ADSCrossRefGoogle Scholar
  160. 160.
    K. Huebner, F. Karsch, C. Pica, Phys. Rev. D 78, 094501 (2008) arXiv:0808.1127 ADSCrossRefGoogle Scholar
  161. 161.
    H.B. Meyer, JHEP 01, 030 (2004) arXiv:hep-lat/0312034 ADSCrossRefGoogle Scholar
  162. 162.
    H.B. Meyer, Prog. Theor. Phys. Suppl. 174, 220 (2008) arXiv:0805.4567 ADSMATHCrossRefGoogle Scholar
  163. 163.
    G. Aarts, J.M. Martinez Resco, JHEP 04, 053 (2002) arXiv:hep-ph/0203177 ADSCrossRefGoogle Scholar
  164. 164.
    H.B. Meyer, Nucl. Phys. A 830, 641C (2009) arXiv:0907.4095 ADSCrossRefGoogle Scholar
  165. 165.
    G. Boyd et al., Nucl. Phys. B 469, 419 (1996) arXiv:hep-lat/9602007 ADSCrossRefGoogle Scholar
  166. 166.
    T. Kunihiro, Y. Minami, PoS CPOD2009, 014 (2009) arXiv:0908.2710 Google Scholar
  167. 167.
    WHOT-QCD Collaboration (H. Ohno et al.), PoS LATTICE2010, 209 (2010) arXiv:1011.1728 Google Scholar
  168. 168.
    F. Karsch, H.W. Wyld, Phys. Rev. D 35, 2518 (1987)ADSCrossRefGoogle Scholar
  169. 169.
    J. Serene, H. Vidberg, J. Low Temp. Phys. 29, 179 (1977)ADSCrossRefGoogle Scholar
  170. 170.
    D. Thirumalai, B.J. Berne, J. Chem. Phys. 79, 5029 (1983)ADSCrossRefGoogle Scholar
  171. 171.
    M. Jarrell, O. Biham, Phys. Rev. Lett. 63, 2504 (1989)ADSCrossRefGoogle Scholar
  172. 172.
    J. Gubernatis, M. Jarrell, R. Silver, D. Sivia, Phys. Rev. B 44, 6011 (1991)ADSCrossRefGoogle Scholar
  173. 173.
    J. Gubernatis, M. Jarrell, Phys. Rep. 269, 133 (1996)MathSciNetADSCrossRefGoogle Scholar
  174. 174.
    S. Koonin, D. Dean, K. Langanke, Phys. Rep. 278, 1 (1997) arXiv:nucl-th/9602006 ADSCrossRefGoogle Scholar
  175. 175.
    O. Gunnarsson, M. W. Haverkort, G. Sangiovanni, Phys. Rev. B 82, 165125 (2010)ADSCrossRefGoogle Scholar
  176. 176.
    A.S. Mishchenko, N.V. Prokof’ev, A. Sakamoto, B.V. Svistunov, Phys. Rev. B 62, 6317 (2000)ADSCrossRefGoogle Scholar
  177. 177.
    I. Krivenko, A. Rubtsov, Analytical Continuation of Quantum Monte Carlo Data: Optimal Stochastic Regularization Approach, arXiv:cond-mat/0612233
  178. 178.
    M. Laine, O. Philipsen, P. Romatschke, M. Tassler, JHEP 03, 054 (2007) arXiv:hep-ph/0611300 ADSCrossRefGoogle Scholar
  179. 179.
    G. Cuniberti, E. De Micheli, G.A. Viano, Commun. Math. Phys. 216, 59 (2001)MathSciNetADSMATHCrossRefGoogle Scholar
  180. 180.
    M. Bertero, P. Boccacci, E. Pike, Proc. R. Soc. London 383, 15 (1982)ADSMATHCrossRefGoogle Scholar
  181. 181.
    W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, (Cambridge University Press, UK, 2007)Google Scholar
  182. 182.
    Y. Burnier, M. Laine, L. Mether, A Test on analytic continuation of thermal imaginary-time data, arXiv:1101.5534
  183. 183.
    Y. Nakahara, M. Asakawa, T. Hatsuda, Phys. Rev. D 60, 091503 (1999) arXiv:hep-lat/9905034 ADSCrossRefGoogle Scholar
  184. 184.
    M. Asakawa, T. Hatsuda, Y. Nakahara, Prog. Part. Nucl. Phys. 46, 459 (2001) arXiv:hep-lat/0011040 ADSCrossRefGoogle Scholar
  185. 185.
    G. Aarts, C. Allton, J. Foley, S. Hands, S. Kim, Phys. Rev. Lett. 99, 022002 (2007) arXiv:hep-lat/0703008 ADSCrossRefGoogle Scholar
  186. 186.
    J. Engels, O. Vogt, Nucl. Phys. B 832, 538 (2010) arXiv:0911.1939 ADSMATHCrossRefGoogle Scholar
  187. 187.
    O. Gunnarsson, M. W. Haverkort, G. Sangiovanni, Phys. Rev. B 81, 155107 (2010)ADSCrossRefGoogle Scholar
  188. 188.
    M.A. York, G.D. Moore, Phys. Rev. D 79, 054011 (2009) arXiv:0811.0729 ADSCrossRefGoogle Scholar
  189. 189.
    S. Pu, T. Koide, D.H. Rischke, Phys. Rev. D 81, 114039 (2010) arXiv:0907.3906 ADSCrossRefGoogle Scholar
  190. 190.
    H.B. Meyer, JHEP 01, 071 (2009) arXiv:0808.3151 ADSCrossRefGoogle Scholar
  191. 191.
    Y. Chen et al., Phys. Rev. D 73, 014516 (2006) arXiv:hep-lat/0510074 ADSCrossRefGoogle Scholar
  192. 192.
    G.D. Moore, O. Saremi, JHEP 09, 015 (2008) arXiv:0805.4201 ADSCrossRefGoogle Scholar
  193. 193.
    N. Iqbal, H.B. Meyer, JHEP 11, 029 (2009) arXiv:0909.0582 ADSCrossRefGoogle Scholar
  194. 194.
    C. Sachrajda, G. Villadoro, Phys. Lett. B 609, 73 (2005) arXiv:hep-lat/0411033 ADSCrossRefGoogle Scholar
  195. 195.
    P.F. Bedaque, Phys. Lett. B 593, 82 (2004) arXiv:nucl-th/0402051 ADSCrossRefGoogle Scholar
  196. 196.
    J. Chao, M. Braby, T. Schafer, New J. Phys. 13, 035014 (2001) arXiv:1012.0219 Google Scholar
  197. 197.
    E. Taylor, M. Randeria, Phys. Rev. A 81, 053610 (2010) arXiv:1012.0219 ADSCrossRefGoogle Scholar
  198. 198.
    D.T. Son, E.G. Thompson, Phys. Rev. A 81, 063634 (2010) arXiv:1002.0922 ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Harvey B. Meyer
    • 1
  1. 1.Institut für KernphysikJohannes Gutenberg Universität MainzMainzGermany

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