Skip to main content

Three-loop HTLpt thermodynamics at finite temperature and chemical potential

A preprint version of the article is available at arXiv.

Abstract

We calculate the three-loop thermodynamic potential of QCD at finite temperature and chemical potential(s) using the hard-thermal-loop perturbation theory (HTLpt) reorganization of finite temperature and density QCD. The resulting analytic thermodynamic potential allows us to compute the pressure, energy density, and entropy density of the quark-gluon plasma. Using these we calculate the trace anomaly, speed of sound, and second-, fourth-, and sixth-order quark number susceptibilities. For all observables considered we find good agreement between our three-loop HTLpt calculations and available lattice data for temperatures above approximately 300 MeV.

References

  1. [1]

    S. Borsányi et al., The QCD equation of state with dynamical quarks, JHEP 11 (2010) 077 [arXiv:1007.2580] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  2. [2]

    S. Borsányi et al., Fluctuations of conserved charges at finite temperature from lattice QCD, JHEP 01 (2012) 138 [arXiv:1112.4416] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  3. [3]

    S. Borsányi et al., QCD thermodynamics with continuum extrapolated Wilson fermions I, JHEP 08 (2012) 126 [arXiv:1205.0440] [INSPIRE].

    ADS  Article  Google Scholar 

  4. [4]

    S. Borsányi et al., QCD equation of state at nonzero chemical potential: continuum results with physical quark masses at order mu 2, JHEP 08 (2012) 053 [arXiv:1204.6710] [INSPIRE].

    ADS  Article  Google Scholar 

  5. [5]

    S. Borsányi, Thermodynamics of the QCD transition from lattice, Nucl. Phys. A 904-905 (2013) 270c [arXiv:1210.6901].

    ADS  Article  Google Scholar 

  6. [6]

    S. Borsányi et al., Freeze-out parameters: lattice meets experiment, Phys. Rev. Lett. 111 (2013) 062005 [arXiv:1305.5161] [INSPIRE].

    ADS  Article  Google Scholar 

  7. [7]

    S. Sharma, QCD Thermodynamics on the Lattice, Adv. High Energy Phys. 2013 (2013) 452978 [arXiv:1403.2102].

    MathSciNet  Google Scholar 

  8. [8]

    F. Karsch, B.-J. Schaefer, M. Wagner and J. Wambach, Towards finite density QCD with Taylor expansions, Phys. Lett. B 698 (2011) 256 [arXiv:1009.5211] [INSPIRE].

    ADS  Article  Google Scholar 

  9. [9]

    A. Bazavov et al., Strangeness at high temperatures: from hadrons to quarks, Phys. Rev. Lett. 111, 082301 (2013) 082301 [arXiv:1304.7220] [INSPIRE].

    ADS  Article  Google Scholar 

  10. [10]

    A. Bazavov et al., Quark number susceptibilities at high temperatures, arXiv:1309.2317 [INSPIRE].

  11. [11]

    A. Bazavov et al., Freeze-out Conditions in Heavy Ion Collisions from QCD Thermodynamics, Phys. Rev. Lett. 109 (2012) 192302 [arXiv:1208.1220] [INSPIRE].

    ADS  Article  Google Scholar 

  12. [12]

    MILC collaboration, C. Bernard et al., QCD thermodynamics with three flavors of improved staggered quarks, Phys. Rev. D 71 (2005) 034504 [hep-lat/0405029] [INSPIRE].

    ADS  Google Scholar 

  13. [13]

    A. Bazavov et al., Equation of state and QCD transition at finite temperature, Phys. Rev. D 80 (2009) 014504 [arXiv:0903.4379] [INSPIRE].

    ADS  Google Scholar 

  14. [14]

    HotQCD collaboration, A. Bazavov et al., Fluctuations and Correlations of net baryon number, electric charge and strangeness: A comparison of lattice QCD results with the hadron resonance gas model, Phys. Rev. D 86 (2012) 034509 [arXiv:1203.0784] [INSPIRE].

    ADS  Google Scholar 

  15. [15]

    P. Petreczky, Lattice QCD at non-zero temperature, J. Phys. G 39 (2012) 093002 [arXiv:1203.5320] [INSPIRE].

    ADS  Article  Google Scholar 

  16. [16]

    E.V. Shuryak, Theory of Hadronic Plasma, Sov. Phys. JETP 47 (1978) 212 [INSPIRE].

    ADS  Google Scholar 

  17. [17]

    S.A. Chin, Transition to Hot Quark Matter in Relativistic Heavy Ion Collision, Phys. Lett. B 78 (1978) 552 [INSPIRE].

    ADS  Article  Google Scholar 

  18. [18]

    J.I. Kapusta, Quantum Chromodynamics at High Temperature, Nucl. Phys. B 148 (1979) 461 [INSPIRE].

    ADS  Article  Google Scholar 

  19. [19]

    T. Toimela, The Next Term in the Thermodynamic Potential of QCD, Phys. Lett. B 124 (1983) 407 [INSPIRE].

    ADS  Article  Google Scholar 

  20. [20]

    P.B. Arnold and C.-X. Zhai, The Three loop free energy for pure gauge QCD, Phys. Rev. D 50 (1994) 7603 [hep-ph/9408276] [INSPIRE].

    ADS  Google Scholar 

  21. [21]

    P.B. Arnold and C.-x. Zhai, The Three loop free energy for high temperature QED and QCD with fermions, Phys. Rev. D 51 (1995) 1906 [hep-ph/9410360] [INSPIRE].

    ADS  Google Scholar 

  22. [22]

    C.-x. Zhai and B.M. Kastening, The Free energy of hot gauge theories with fermions through g 5, Phys. Rev. D 52 (1995) 7232 [hep-ph/9507380] [INSPIRE].

    ADS  Google Scholar 

  23. [23]

    E. Braaten and A. Nieto, Effective field theory approach to high temperature thermodynamics, Phys. Rev. D 51 (1995) 6990 [hep-ph/9501375] [INSPIRE].

    ADS  Google Scholar 

  24. [24]

    E. Braaten and A. Nieto, Free energy of QCD at high temperature, Phys. Rev. D 53 (1996) 3421 [hep-ph/9510408] [INSPIRE].

    ADS  Google Scholar 

  25. [25]

    K. Kajantie, M. Laine, K. Rummukainen and Y. Schröder, The Pressure of hot QCD up to g 6ln(1/g), Phys. Rev. D 67 (2003) 105008 [hep-ph/0211321] [INSPIRE].

    ADS  Google Scholar 

  26. [26]

    A. Vuorinen, Quark number susceptibilities of hot QCD up to g 6lng, Phys. Rev. D 67 (2003) 074032 [hep-ph/0212283] [INSPIRE].

    ADS  Google Scholar 

  27. [27]

    A. Vuorinen, The pressure of QCD at finite temperatures and chemical potentials, Phys. Rev. D 68 (2003) 054017 [hep-ph/0305183] [INSPIRE].

    ADS  Google Scholar 

  28. [28]

    A. Ipp, K. Kajantie, A. Rebhan and A. Vuorinen, The pressure of deconfined QCD for all temperatures and quark chemical potentials, Phys. Rev. D 74 (2006) 045016 [hep-ph/0604060] [INSPIRE].

    ADS  Google Scholar 

  29. [29]

    F. Karsch, A. Patkos and P. Petreczky, Screened perturbation theory, Phys. Lett. B 401 (1997) 69 [hep-ph/9702376] [INSPIRE].

    ADS  Article  Google Scholar 

  30. [30]

    S. Chiku and T. Hatsuda, Optimized perturbation theory at finite temperature, Phys. Rev. D 58 (1998) 076001 [hep-ph/9803226] [INSPIRE].

    ADS  Google Scholar 

  31. [31]

    J.O. Andersen, E. Braaten and M. Strickland, Screened perturbation theory to three loops, Phys. Rev. D 63 (2001) 105008 [hep-ph/0007159] [INSPIRE].

    ADS  Google Scholar 

  32. [32]

    J.O. Andersen and L. Kyllingstad, Four-loop screened perturbation theory, Phys. Rev. D 78 (2008) 076008 [arXiv:0805.4478] [INSPIRE].

    ADS  Google Scholar 

  33. [33]

    J.O. Andersen and M. Strickland, Mass expansions of screened perturbation theory, Phys. Rev. D 64 (2001) 105012 [hep-ph/0105214] [INSPIRE].

    ADS  Google Scholar 

  34. [34]

    V.I. Yukalov, Several remarks on quasiaverages, Teor. Mat. Fiz. 26 (1976) 403 [INSPIRE].

    MathSciNet  Article  Google Scholar 

  35. [35]

    P.M. Stevenson, Optimized perturbation theory, Phys. Rev. D 23 (1981) 2916 [INSPIRE].

    ADS  Google Scholar 

  36. [36]

    A. Duncan and M. Moshe, Nonperturbative physics from interpolating actions, Phys. Lett. B 215 (1988) 352 [INSPIRE].

    ADS  Article  Google Scholar 

  37. [37]

    A. Duncan and H.F. Jones, Convergence proof for optimized δ expansion: the anharmonic oscillator, Phys. Rev. D 47 (1993) 2560 [INSPIRE].

    ADS  Google Scholar 

  38. [38]

    A.N. Sisakian, I.L. Solovtsov and O. Shevchenko, Variational perturbation theory, Int. J. Mod. Phys. A 9 (1994) 1929 [INSPIRE].

    ADS  Article  Google Scholar 

  39. [39]

    W. Janke and H. Kleinert, Convergent strong-coupling expansions from divergent weak-coupling perturbation theory, Phys. Rev. Lett. 75 (1995) 2787 [INSPIRE].

    ADS  Article  Google Scholar 

  40. [40]

    J.O. Andersen, E. Braaten and M. Strickland, Hard thermal loop resummation of the free energy of a hot gluon plasma, Phys. Rev. Lett. 83 (1999) 2139 [hep-ph/9902327] [INSPIRE].

    ADS  Article  Google Scholar 

  41. [41]

    J.O. Andersen, E. Braaten and M. Strickland, Hard thermal loop resummation of the thermodynamics of a hot gluon plasma, Phys. Rev. D 61 (2000) 014017 [hep-ph/9905337] [INSPIRE].

    ADS  Google Scholar 

  42. [42]

    J.O. Andersen, E. Braaten and M. Strickland, Hard thermal loop resummation of the free energy of a hot quark-gluon plasma, Phys. Rev. D 61 (2000) 074016 [hep-ph/9908323] [INSPIRE].

    ADS  Google Scholar 

  43. [43]

    J.O. Andersen, S. Mogliacci, N. Su and A. Vuorinen, Quark number susceptibilities from resummed perturbation theory, Phys. Rev. D 87 (2013) 074003 [arXiv:1210.0912] [INSPIRE].

    ADS  Google Scholar 

  44. [44]

    S. Mogliacci, J.O. Andersen, M. Strickland, N. Su and A. Vuorinen, Equation of State of hot and dense QCD: Resummed perturbation theory confronts lattice data, JHEP 12 (2013) 055 [arXiv:1307.8098] [INSPIRE].

    ADS  Article  Google Scholar 

  45. [45]

    J.O. Andersen, E. Braaten, E. Petitgirard and M. Strickland, HTL perturbation theory to two loops, Phys. Rev. D 66 (2002) 085016 [hep-ph/0205085] [INSPIRE].

    ADS  Google Scholar 

  46. [46]

    J.O. Andersen, E. Petitgirard and M. Strickland, Two loop HTL thermodynamics with quarks, Phys. Rev. D 70 (2004) 045001 [hep-ph/0302069] [INSPIRE].

    ADS  Google Scholar 

  47. [47]

    N. Haque, M.G. Mustafa and M. Strickland, Two-loop HTL pressure at finite temperature and chemical potential, Phys. Rev. D 87 (2013) 105007 [arXiv:1212.1797] [INSPIRE].

    ADS  Google Scholar 

  48. [48]

    N. Haque, M.G. Mustafa and M. Strickland, Quark Number Susceptibilities from Two-Loop Hard Thermal Loop Perturbation Theory, JHEP 07 (2013) 184 [arXiv:1302.3228] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  49. [49]

    J.O. Andersen, M. Strickland and N. Su, Gluon Thermodynamics at Intermediate Coupling, Phys. Rev. Lett. 104 (2010) 122003 [arXiv:0911.0676] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  50. [50]

    J.O. Andersen, M. Strickland and N. Su, Three-loop HTL gluon thermodynamics at intermediate coupling, JHEP 08 (2010) 113 [arXiv:1005.1603] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  51. [51]

    J.O. Andersen, M. Strickland and N. Su, Three-loop HTL Free Energy for QED, Phys. Rev. D 80 (2009) 085015 [arXiv:0906.2936] [INSPIRE].

    ADS  Google Scholar 

  52. [52]

    J.O. Andersen, L.E. Leganger, M. Strickland and N. Su, NNLO hard-thermal-loop thermodynamics for QCD, Phys. Lett. B 696 (2011) 468 [arXiv:1009.4644] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  53. [53]

    J.O. Andersen, L.E. Leganger, M. Strickland and N. Su, Three-loop HTL QCD thermodynamics, JHEP 08 (2011) 053 [arXiv:1103.2528] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  54. [54]

    J.O. Andersen, L.E. Leganger, M. Strickland and N. Su, The QCD trace anomaly, Phys. Rev. D 84 (2011) 087703 [arXiv:1106.0514] [INSPIRE].

    ADS  Google Scholar 

  55. [55]

    N. Haque, J.O. Andersen, M.G. Mustafa, M. Strickland and N. Su, Three-loop HTLpt Pressure and Susceptibilities at Finite Temperature and Density, Phys. Rev. D 89 (2014) 061701 [arXiv:1309.3968] [INSPIRE].

    ADS  Google Scholar 

  56. [56]

    P. Chakraborty, M.G. Mustafa and M.H. Thoma, Quark number susceptibility in hard thermal loop approximation, Eur. Phys. J. C 23 (2002) 591 [hep-ph/0111022] [INSPIRE].

    ADS  Article  Google Scholar 

  57. [57]

    P. Chakraborty, M.G. Mustafa and M.H. Thoma, Chiral susceptibility in hard thermal loop approximation, Phys. Rev. D 67 (2003) 114004 [hep-ph/0210159] [INSPIRE].

    ADS  Google Scholar 

  58. [58]

    P. Chakraborty, M.G. Mustafa and M.H. Thoma, Quark number susceptibility, thermodynamic sum rule and hard thermal loop approximation, Phys. Rev. D 68 (2003) 085012 [hep-ph/0303009] [INSPIRE].

    ADS  Google Scholar 

  59. [59]

    N. Haque, M.G. Mustafa and M.H. Thoma, Conserved Density Fluctuation and Temporal Correlation Function in HTL Perturbation Theory, Phys. Rev. D 84 (2011) 054009 [arXiv:1103.3394] [INSPIRE].

    ADS  Google Scholar 

  60. [60]

    N. Haque and M.G. Mustafa, Quark Number Susceptibility and Thermodynamics in HTL approximation, Nucl. Phys. A 862-863 (2011) 271 [arXiv:1109.0799].

    Article  Google Scholar 

  61. [61]

    N. Haque and M.G. Mustafa, A Modified Hard Thermal Loop Perturbation Theory, arXiv:1007.2076 [INSPIRE].

  62. [62]

    J.P. Blaizot, E. Iancu and A. Rebhan, Comparing different hard thermal loop approaches to quark number susceptibilities, Eur. Phys. J. C 27 (2003) 433 [hep-ph/0206280] [INSPIRE].

    ADS  Article  Google Scholar 

  63. [63]

    J.P. Blaizot, E. Iancu and A. Rebhan, Quark number susceptibilities from HTL resummed thermodynamics, Phys. Lett. B 523 (2001) 143 [hep-ph/0110369] [INSPIRE].

    ADS  Article  Google Scholar 

  64. [64]

    J.P. Blaizot, E. Iancu and A. Rebhan, The thermodynamics of the quark gluon plasma: Selfconsistent resummations versus lattice data, Nucl. Phys. A 698 (2002) 404 [hep-ph/0104033] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  65. [65]

    J.P. Blaizot, E. Iancu and A. Rebhan, The entropy of the QCD plasma, Phys. Rev. Lett. 83 (1999) 2906 [hep-ph/9906340] [INSPIRE].

    ADS  Article  Google Scholar 

  66. [66]

    J.P. Blaizot, E. Iancu and A. Rebhan, Selfconsistent hard thermal loop thermodynamics for the quark gluon plasma, Phys. Lett. B 470 (1999) 181 [hep-ph/9910309] [INSPIRE].

    ADS  Article  Google Scholar 

  67. [67]

    J.P. Blaizot, E. Iancu and A. Rebhan, Approximately selfconsistent resummations for the thermodynamics of the quark gluon plasma. 1. Entropy and density, Phys. Rev. D 63 (2001) 065003 [hep-ph/0005003] [INSPIRE].

    ADS  Google Scholar 

  68. [68]

    T. Hatsuda and T. Kunihiro, QCD phenomenology based on a chiral effective Lagrangian, Phys. Rept. 247 (1994) 221 [hep-ph/9401310] [INSPIRE].

    ADS  Article  Google Scholar 

  69. [69]

    T. Kunihiro, Quark number susceptibility and fluctuations in the vector channel at high temperatures, Phys. Lett. B 271 (1991) 395 [INSPIRE].

    ADS  Article  Google Scholar 

  70. [70]

    K. Fukushima, Relation between the Polyakov loop and the chiral order parameter at strong coupling, Phys. Rev. D 68 (2003) 045004 [hep-ph/0303225] [INSPIRE].

    ADS  Google Scholar 

  71. [71]

    K. Fukushima, Chiral effective model with the Polyakov loop, Phys. Lett. B 591 (2004) 277 [hep-ph/0310121] [INSPIRE].

    ADS  Article  Google Scholar 

  72. [72]

    C. Ratti, M.A. Thaler and W. Weise, Phases of QCD: lattice thermodynamics and a field theoretical model, Phys. Rev. D 73 (2006) 014019 [hep-ph/0506234] [INSPIRE].

    ADS  Google Scholar 

  73. [73]

    S.K. Ghosh, T.K. Mukherjee, M.G. Mustafa and R. Ray, Susceptibilities and speed of sound from PNJL model, Phys. Rev. D 73 (2006) 114007 [hep-ph/0603050] [INSPIRE].

    ADS  Google Scholar 

  74. [74]

    S.K. Ghosh, T.K. Mukherjee, M.G. Mustafa and R. Ray, PNJL model with a Van der Monde term, Phys. Rev. D 77 (2008) 094024 [arXiv:0710.2790] [INSPIRE].

    ADS  Google Scholar 

  75. [75]

    S. Mukherjee, M.G. Mustafa and R. Ray, Thermodynamics of the PNJL model with nonzero baryon and isospin chemical potentials, Phys. Rev. D 75 (2007) 094015 [hep-ph/0609249] [INSPIRE].

    ADS  Google Scholar 

  76. [76]

    S. Roessner, C. Ratti and W. Weise, Polyakov loop, diquarks and the two-flavour phase diagram, Phys. Rev. D 75 (2007) 034007 [hep-ph/0609281] [INSPIRE].

    ADS  Google Scholar 

  77. [77]

    C. Sasaki, B. Friman and K. Redlich, Susceptibilities and the Phase Structure of a Chiral Model with Polyakov Loops, Phys. Rev. D 75 (2007) 074013 [hep-ph/0611147] [INSPIRE].

    ADS  Google Scholar 

  78. [78]

    A. Bhattacharyya, P. Deb, S.K. Ghosh and R. Ray, Investigation of Phase Diagram and Bulk Thermodynamic Properties using PNJL Model with Eight-Quark Interactions, Phys. Rev. D 82 (2010) 014021 [arXiv:1003.3337] [INSPIRE].

    ADS  Google Scholar 

  79. [79]

    A. Bhattacharyya, P. Deb, A. Lahiri and R. Ray, Susceptibilities with multi-quark interactions in PNJL model, Phys. Rev. D 82 (2010) 114028 [arXiv:1008.0768] [INSPIRE].

    ADS  Google Scholar 

  80. [80]

    A. Bhattacharyya, P. Deb, A. Lahiri and R. Ray, Correlation between conserved charges in PNJL Model with multi-quark interactions, Phys. Rev. D 83 (2011) 014011 [arXiv:1010.2394] [INSPIRE].

    ADS  Google Scholar 

  81. [81]

    M. Bluhm, B. Kampfer, 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, Phys. Rev. C 76 (2007) 034901 [arXiv:0705.0397] [INSPIRE].

    ADS  Google Scholar 

  82. [82]

    M. Bluhm and B. Kampfer, Quasiparticle model of quark-gluon plasma at imaginary chemical potential, Phys. Rev. D 77 (2008) 034004 [arXiv:0711.0590] [INSPIRE].

    ADS  Google Scholar 

  83. [83]

    V.M. Bannur, Quasi-particle model for QGP with nonzero densities, JHEP 09 (2007) 046 [hep-ph/0604158] [INSPIRE].

    ADS  Article  Google Scholar 

  84. [84]

    V.M. Bannur, Self-consistent quasiparticle model for 2, 3 and (2+1) flavor QGP, Phys. Rev. C 78 (2008) 045206 [arXiv:0712.2886] [INSPIRE].

    ADS  Google Scholar 

  85. [85]

    F.G. Gardim and F.M. Steffens, Thermodynamics of Quasi-Particles at Finite Chemical Potential, Nucl. Phys. A 825 (2009) 222 [arXiv:0905.0667] [INSPIRE].

    ADS  Article  Google Scholar 

  86. [86]

    B.-J. Schaefer, M. Wagner and J. Wambach, QCD thermodynamics with effective models, PoS(CPOD 2009)017.

  87. [87]

    B.-J. Schaefer, M. Wagner and J. Wambach, Thermodynamics of (2+1)-flavor QCD: Confronting Models with Lattice Studies, Phys. Rev. D 81 (2010) 074013 [arXiv:0910.5628] [INSPIRE].

    ADS  Google Scholar 

  88. [88]

    V. Skokov, B. Friman and K. Redlich, Quark number fluctuations in the Polyakov loop-extended quark-meson model at finite baryon density, Phys. Rev. C 83 (2011) 054904 [arXiv:1008.4570] [INSPIRE].

    ADS  Google Scholar 

  89. [89]

    S. Chatterjee and K.A. Mohan, Fluctuations and Correlations of Conserved Charges in the (2 + 1) Polyakov Quark Meson Model, Phys. Rev. D 86 (2012) 114021 [arXiv:1201.3352] [INSPIRE].

    ADS  Google Scholar 

  90. [90]

    G. Cvetič and R. Kogerler, Resummations of free energy at high temperature, Phys. Rev. D 66 (2002) 105009 [hep-ph/0207291] [INSPIRE].

    ADS  Google Scholar 

  91. [91]

    G. Cvetič and R. Kogerler, Resummations of the pressure of quark-gluon plasma by including contributions of order \( g_s^6 \), Phys. Rev. D 70 (2004) 114016 [hep-ph/0406028] [INSPIRE].

    ADS  Google Scholar 

  92. [92]

    G. Cvetič and R. Koegerler, Method for comparing finite temperature field theory results with lattice data, Phys. Rev. D 75 (2007) 054016 [hep-ph/0612130] [INSPIRE].

    ADS  Google Scholar 

  93. [93]

    K.-i. Kim, Y. Kim, S. Takeuchi and T. Tsukioka, Quark Number Susceptibility with Finite Quark Mass in Holographic QCD, Prog. Theor. Phys. 126 (2011) 735 [arXiv:1012.2667] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  94. [94]

    L.-X. Cui, S. Takeuchi and Y.-L. Wu, Quark Number Susceptibility and QCD Phase Transition in the Predictive Soft-wall AdS/QCD Model with Finite Temperature, Phys. Rev. D 84 (2011) 076004 [arXiv:1107.2738] [INSPIRE].

    ADS  Google Scholar 

  95. [95]

    E. Braaten and R.D. Pisarski, Simple effective Lagrangian for hard thermal loops, Phys. Rev. D 45 (1992) 1827 [INSPIRE].

    ADS  Google Scholar 

  96. [96]

    E. Braaten, R.D. Pisarski and T.-C. Yuan, Production of Soft Dileptons in the quark-gluon Plasma, Phys. Rev. Lett. 64 (1990) 2242 [INSPIRE].

    ADS  Article  Google Scholar 

  97. [97]

    C. Greiner, N. Haque, M.G. Mustafa and M.H. Thoma, Low Mass Dilepton Rate from the Deconfined Phase, Phys. Rev. C 83 (2011) 014908 [arXiv:1010.2169] [INSPIRE].

    ADS  Google Scholar 

  98. [98]

    R. Baier, S. Peigne and D. Schiff, Soft photon production rate in resummed perturbation theory of high temperature QCD, Z. Phys. C 62 (1994) 337 [hep-ph/9311329] [INSPIRE].

    ADS  Google Scholar 

  99. [99]

    M.G. Mustafa, M.H. Thoma and P. Chakraborty, Screening of a moving parton in the quark gluon plasma, Phys. Rev. C 71 (2005) 017901 [hep-ph/0403279] [INSPIRE].

    ADS  Google Scholar 

  100. [100]

    M.G. Mustafa, P. Chakraborty and M.H. Thoma, Dynamical screening in a quark gluon plasma, J. Phys. Conf. Ser. 50 (2006) 438 [hep-ph/0504174] [INSPIRE].

    ADS  Article  Google Scholar 

  101. [101]

    P. Chakraborty, M.G. Mustafa and M.H. Thoma, Wakes in the quark-gluon plasma, Phys. Rev. D 74 (2006) 094002 [hep-ph/0606316] [INSPIRE].

    ADS  Google Scholar 

  102. [102]

    P. Chakraborty, M.G. Mustafa, R. Ray and M.H. Thoma, Wakes in a Collisional quark-gluon Plasma, J. Phys. G 34 (2007) 2141 [arXiv:0705.1447] [INSPIRE].

    ADS  Article  Google Scholar 

  103. [103]

    M. Laine, O. Philipsen, P. Romatschke and M. Tassler, Real-time static potential in hot QCD, JHEP 03 (2007) 054 [hep-ph/0611300] [INSPIRE].

    ADS  Article  Google Scholar 

  104. [104]

    A. Dumitru, Y. Guo and M. Strickland, The heavy-quark potential in an anisotropic (viscous) plasma, Phys. Lett. B 662 (2008) 37 [arXiv:0711.4722] [INSPIRE].

    ADS  Article  Google Scholar 

  105. [105]

    A. Dumitru, Y. Guo, A. Mócsy and M. Strickland, Quarkonium states in an anisotropic QCD plasma, Phys. Rev. D 79 (2009) 054019 [arXiv:0901.1998] [INSPIRE].

    ADS  Google Scholar 

  106. [106]

    A. Dumitru, Y. Guo and M. Strickland, The imaginary part of the static gluon propagator in an anisotropic (viscous) QCD plasma, Phys. Rev. D 79 (2009) 114003 [arXiv:0903.4703] [INSPIRE].

    ADS  Google Scholar 

  107. [107]

    L. Thakur, N. Haque, U. Kakade and B.K. Patra, Dissociation of quarkonium in an anisotropic hot QCD medium, Phys. Rev. D 88 (2013) 054022 [arXiv:1212.2803] [INSPIRE].

    ADS  Google Scholar 

  108. [108]

    R.D. Pisarski, Damping rates for moving particles in hot QCD, Phys. Rev. D 47 (1993) 5589 [INSPIRE].

    ADS  Google Scholar 

  109. [109]

    S. Peigne, E. Pilon and D. Schiff, The heavy fermion damping rate puzzle, Z. Phys. C 60 (1993) 455 [hep-ph/9306219] [INSPIRE].

    ADS  Google Scholar 

  110. [110]

    S. Sarkar and A.K. Dutt-Mazumder, Effect of flow on the quasiparticle damping rate in hot QCD plasma, Phys. Rev. D 88 (2013) 054006 [arXiv:1205.4895] [INSPIRE].

    ADS  Google Scholar 

  111. [111]

    A. Abada and N. Daira-Aifa, Photon damping in one-loop HTL perturbation theory, JHEP 04 (2012) 071 [arXiv:1112.6065] [INSPIRE].

    ADS  Article  Google Scholar 

  112. [112]

    E. Braaten and R.D. Pisarski, Resummation and gauge invariance of the gluon amping rate in hot QCD, Phys. Rev. Lett. 64 (1990) 1338 [INSPIRE].

    ADS  Article  Google Scholar 

  113. [113]

    E. Braaten and R.D. Pisarski, Calculation of the gluon damping rate in hot QCD, Phys. Rev. D 42 (1990) 2156 [INSPIRE].

    ADS  Google Scholar 

  114. [114]

    E. Braaten and M.H. Thoma, Energy loss of a heavy fermion in a hot plasma, Phys. Rev. D 44 (1991) 1298 [INSPIRE].

    ADS  Google Scholar 

  115. [115]

    E. Braaten and M.H. Thoma, Energy loss of a heavy quark in the quark-gluon plasma, Phys. Rev. D 44 (1991) 2625 [INSPIRE].

    ADS  Google Scholar 

  116. [116]

    M.H. Thoma and M. Gyulassy, Quark Damping and Energy Loss in the High Temperature QCD, Nucl. Phys. B 351 (1991) 491 [INSPIRE].

    ADS  Article  Google Scholar 

  117. [117]

    P. Romatschke and M. Strickland, Energy loss of a heavy fermion in an anisotropic QED plasma, Phys. Rev. D 69 (2004) 065005 [hep-ph/0309093] [INSPIRE].

    ADS  Google Scholar 

  118. [118]

    P. Romatschke and M. Strickland, Collisional energy loss of a heavy quark in an anisotropic quark-gluon plasma, Phys. Rev. D 71 (2005) 125008 [hep-ph/0408275] [INSPIRE].

    ADS  Google Scholar 

  119. [119]

    M.G. Mustafa, Energy loss of charm quarks in the quark-gluon plasma: collisional versus radiative, Phys. Rev. C 72 (2005) 014905 [hep-ph/0412402] [INSPIRE].

    ADS  Google Scholar 

  120. [120]

    M.G. Mustafa and M.H. Thoma, Quenching of hadron spectra due to the collisional energy loss of partons in the quark gluon plasma, Acta Phys. Hung. A 22 (2005) 93 [hep-ph/0311168] [INSPIRE].

    Article  Google Scholar 

  121. [121]

    M. Djordjevic, Collisional energy loss in a finite size QCD matter, Phys. Rev. C 74 (2006) 064907 [nucl-th/0603066] [INSPIRE].

    ADS  Google Scholar 

  122. [122]

    P. Chakraborty, M.G. Mustafa and M.H. Thoma, Energy gain of heavy quarks by fluctuations in the QGP, Phys. Rev. C 75 (2007) 064908 [hep-ph/0611355] [INSPIRE].

    ADS  Google Scholar 

  123. [123]

    G.-Y. Qin et al., Radiative and collisional jet energy loss in the quark-gluon plasma at RHIC, Phys. Rev. Lett. 100 (2008) 072301 [arXiv:0710.0605] [INSPIRE].

    ADS  Article  Google Scholar 

  124. [124]

    G.-Y. Qin, A. Majumder, H. Song and U. Heinz, Energy and momentum deposited into a QCD medium by a jet shower, Phys. Rev. Lett. 103 (2009) 152303 [arXiv:0903.2255] [INSPIRE].

    ADS  Article  Google Scholar 

  125. [125]

    G.-Y. Qin and A. Majumder, A pQCD-based description of heavy and light flavor jet quenching, Phys. Rev. Lett. 105 (2010) 262301 [arXiv:0910.3016] [INSPIRE].

    ADS  Article  Google Scholar 

  126. [126]

    S. Mrowczynski and M.H. Thoma, Hard loop approach to anisotropic systems, Phys. Rev. D 62 (2000) 036011 [hep-ph/0001164] [INSPIRE].

    ADS  Google Scholar 

  127. [127]

    P. Romatschke and M. Strickland, Collective modes of an anisotropic quark gluon plasma, Phys. Rev. D 68 (2003) 036004 [hep-ph/0304092] [INSPIRE].

    ADS  Google Scholar 

  128. [128]

    P. Romatschke and M. Strickland, Collective modes of an anisotropic quark-gluon plasma II, Phys. Rev. D 70 (2004) 116006 [hep-ph/0406188] [INSPIRE].

    ADS  Google Scholar 

  129. [129]

    A. Rebhan, P. Romatschke and M. Strickland, Hard-loop dynamics of non-Abelian plasma instabilities, Phys. Rev. Lett. 94 (2005) 102303 [hep-ph/0412016] [INSPIRE].

    ADS  Article  Google Scholar 

  130. [130]

    B. Schenke and M. Strickland, Fermionic Collective Modes of an Anisotropic quark-gluon Plasma, Phys. Rev. D 74 (2006) 065004 [hep-ph/0606160] [INSPIRE].

    ADS  Google Scholar 

  131. [131]

    A. Rebhan, M. Strickland and M. Attems, Instabilities of an anisotropically expanding non-Abelian plasma: 1D + 3V discretized hard-loop simulations, Phys. Rev. D 78 (2008) 045023 [arXiv:0802.1714] [INSPIRE].

    ADS  Google Scholar 

  132. [132]

    M. Attems, A. Rebhan and M. Strickland, Instabilities of an anisotropically expanding non-Abelian plasma: 3D + 3V discretized hard-loop simulations, Phys. Rev. D 87 (2013) 025010 [arXiv:1207.5795] [INSPIRE].

    ADS  Google Scholar 

  133. [133]

    P. Graf and F.D. Steffen, Thermal axion production in the primordial quark-gluon plasma, Phys. Rev. D 83 (2011) 075011 [arXiv:1008.4528] [INSPIRE].

    ADS  Google Scholar 

  134. [134]

    C. Kiessig and M. Plümacher, Hard-Thermal-Loop Corrections in Leptogenesis II: Solving the Boltzmann Equations, JCAP 09 (2012) 012 [arXiv:1111.1235] [INSPIRE].

    ADS  Article  Google Scholar 

  135. [135]

    C. Kiessig and M. Plümacher, Hard-Thermal-Loop Corrections in Leptogenesis I: CP-Asymmetries, JCAP 07 (2012) 014 [arXiv:1111.1231] [INSPIRE].

    ADS  Article  Google Scholar 

  136. [136]

    Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].

    ADS  Google Scholar 

  137. [137]

    T. van Ritbergen, J.A.M. Vermaseren and S.A. Larin, The Four loop β-function in quantum chromodynamics, Phys. Lett. B 400 (1997) 379 [hep-ph/9701390] [INSPIRE].

    ADS  Article  Google Scholar 

  138. [138]

    A. Bazavov et al., Determination of α s from the QCD static energy, Phys. Rev. D 86 (2012) 114031 [arXiv:1205.6155] [INSPIRE].

    ADS  Google Scholar 

  139. [139]

    S. Datta, R.V. Gavai and S. Gupta, http://www.ilgti.tifr.res.in/tables, to appear in the proceedings of Lattice 2013.

  140. [140]

    RBC-Bielefeld Collaboration, P. Petreczky et al. Quark number fluctuations at high temperatures, PoS(LAT2009)159.

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Michael Strickland.

Additional information

ArXiv ePrint: 1402.6907

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Haque, N., Bandyopadhyay, A., Andersen, J.O. et al. Three-loop HTLpt thermodynamics at finite temperature and chemical potential. J. High Energ. Phys. 2014, 27 (2014). https://doi.org/10.1007/JHEP05(2014)027

Download citation

Keywords

  • Quark-Gluon Plasma
  • Resummation
  • Phase Diagram of QCD
  • QCD