Advertisement

Journal of High Energy Physics

, 2010:88 | Cite as

Langevin diffusion of heavy quarks in non-conformal holographic backgrounds

  • Umut Gürsoy
  • Elias Kiritsis
  • Liuba Mazzanti
  • Francesco Nitti
Open Access
Article

Abstract

The Langevin diffusion process of a relativistic heavy quark in a non-conformal holographic setup is analyzed. The bulk geometry is a general, five-dimensional asymptotically AdS black hole. The heavy quark is described by a trailing string attached to a flavor brane, moving at constant velocity. From the equations describing linearized fluctuations of the string world-sheet, the correlation functions defining a generalized Langevin process are constructed via the AdS/CFT prescription. In the local limit, analytic expressions for the Langevin diffusion and friction coefficients are obtained in terms of the bulk string metric. Modified Einstein relations between these quantities are also derived. The spectral densities associated to the Langevin correlators are analyzed, and simple analytic expressions are obtained in the small and large frequency limits. Finally, a numerical analysis of the jet-quenching parameter, and a comparison to RHIC phenomenology are performed in the case of Improved Holographic QCD. It is shown that the jet-quenching parameter is not enough to describe energy loss of very energetic charm quarks and the full Langevin correlators are needed.

Keywords

Gauge-gravity correspondence Black Holes QCD 

References

  1. [1]
    STAR collaboration, J. Adams et al., Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR collaboration’s critical assessment of the evidence from RHIC collisions, Nucl. Phys. A 757 (2005) 102 [nucl-ex/0501009] [SPIRES].ADSGoogle Scholar
  2. [2]
    B.B. Back et al., The PHOBOS perspective on discoveries at RHIC, Nucl. Phys. A 757 (2005) 28 [nucl-ex/0410022] [SPIRES].ADSGoogle Scholar
  3. [3]
    BRAHMS collaboration, I. Arsene et al., Quark Gluon Plasma an Color Glass Condensate at RHIC? The perspective from the BRAHMS experiment, Nucl. Phys. A 757 (2005) 1 [nucl-ex/0410020] [SPIRES].ADSGoogle Scholar
  4. [4]
    PHENIX collaboration, K. Adcox et al., Formation of dense partonic matter in relativistic nucleus nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration, Nucl. Phys. A 757 (2005) 184 [nucl-ex/410003] [SPIRES].ADSGoogle Scholar
  5. [5]
    D.T. Son and A.O. Starinets, Viscosity, Black Holes and Quantum Field Theory, Ann. Rev. Nucl. Part. Sci. 57 (2007) 95 [arXiv:0704.0240] [SPIRES].CrossRefADSGoogle Scholar
  6. [6]
    J. Casalderrey-Solana and C.A. Salgado, Introductory lectures on jet quenching in heavy ion collisions, Acta Phys. Polon. B 38 (2007) 3731 [arXiv:0712.3443] [SPIRES].ADSGoogle Scholar
  7. [7]
    E. Iancu, Partons and jets in a strongly-coupled plasma from AdS/CFT, Acta Phys. Polon. B 39 (2008) 3213 [arXiv:0812.0500] [SPIRES].ADSGoogle Scholar
  8. [8]
    S.S. Gubser, S.S. Pufu, F.D. Rocha and A. Yarom, Energy loss in a strongly coupled thermal medium and the gauge-string duality, arXiv:0902.4041 [SPIRES].
  9. [9]
    U. Gürsoy, E. Kiritsis, L. Mazzanti, G. Michalogiorgakis and F. Nitti, Improved Holographic QCD, arXiv:1006.5461 [SPIRES].
  10. [10]
    C.P. Herzog, A. Karch, P. Kovtun, C. Kozcaz and L.G. Yaffe, Energy loss of a heavy quark moving through N = 4 supersymmetric Yang-Mills plasma, JHEP 07 (2006) 013 [hep-th/0605158] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  11. [11]
    H. Liu, K. Rajagopal and U.A. Wiedemann, Calculating the jet quenching parameter from AdS/CFT, Phys. Rev. Lett. 97 (2006) 182301 [hep-ph/0605178] [SPIRES].CrossRefADSGoogle Scholar
  12. [12]
    H. Liu, K. Rajagopal and U.A. Wiedemann, Wilson loops in heavy ion collisions and their calculation in AdS/CFT, JHEP 03 (2007) 066 [hep-ph/0612168] [SPIRES].CrossRefADSGoogle Scholar
  13. [13]
    S.S. Gubser, Drag force in AdS/CFT, Phys. Rev. D 74 (2006) 126005 [hep-th/0605182] [SPIRES].ADSMathSciNetGoogle Scholar
  14. [14]
    H. Liu, K. Rajagopal and Y. Shi, Robustness and Infrared Sensitivity of Various Observables in the Application of AdS/CFT to Heavy Ion Collisions, JHEP 08 (2008) 048 [arXiv:0803.3214] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  15. [15]
    U. Gürsoy, E. Kiritsis, G. Michalogiorgakis and F. Nitti, Thermal Transport and Drag Force in Improved Holographic QCD, JHEP 12 (2009) 056 [arXiv:0906.1890] [SPIRES].CrossRefGoogle Scholar
  16. [16]
    J. Casalderrey-Solana and D. Teaney, Heavy quark diffusion in strongly coupled N = 4 Yang-Mills, Phys. Rev. D 74 (2006) 085012 [hep-ph/0605199] [SPIRES].ADSGoogle Scholar
  17. [17]
    C.P. Herzog and D.T. Son, Schwinger-Keldysh propagators from AdS/CFT correspondence, JHEP 03 (2003) 046 [hep-th/0212072] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  18. [18]
    S.S. Gubser, Momentum fluctuations of heavy quarks in the gauge-string duality, Nucl. Phys. B 790 (2008) 175 [hep-th/0612143] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  19. [19]
    J. Casalderrey-Solana and D. Teaney, Transverse momentum broadening of a fast quark in a N = 4 Yang-Mills plasma, JHEP 04 (2007) 039 [hep-th/0701123] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  20. [20]
    J. de Boer, V.E. Hubeny, M. Rangamani and M. Shigemori, Brownian motion in AdS/CFT, JHEP 07 (2009) 094 [arXiv:0812.5112] [SPIRES].CrossRefGoogle Scholar
  21. [21]
    D.T. Son and D. Teaney, Thermal Noise and Stochastic Strings in AdS/CFT, JHEP 07 (2009) 021 [arXiv:0901.2338] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  22. [22]
    G.C. Giecold, E. Iancu and A.H. Mueller, Stochastic trailing string and Langevin dynamics from AdS/CFT, JHEP 07 (2009) 033 [arXiv:0903.1840] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  23. [23]
    E. Caceres, M. Chernicoff, A. Guijosa and J.F. Pedraza, Quantum Fluctuations and the Unruh Effect in Strongly-Coupled Conformal Field Theories, JHEP 06 (2010) 078 [arXiv:1003.5332] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  24. [24]
    C. Hoyos-Badajoz, Drag and jet quenching of heavy quarks in a strongly coupled N = 2* plasma, JHEP 09 (2009) 068 [arXiv:0907.5036] [SPIRES].CrossRefADSGoogle Scholar
  25. [25]
    PHENIX collaboration, Y. Akiba, Probing the properties of dense partonic matter at RHIC, Nucl. Phys. A 774 (2006) 403 [nucl-ex/0510008] [SPIRES].ADSGoogle Scholar
  26. [26]
    PHENIX collaboration, S.S. Adler et al., Nuclear modification of electron spectra and implications for heavy quark energy loss in Au + Au collisions at s(NN)**(1/2) = 200-GeV, Phys. Rev. Lett. 96 (2006) 032301 [nucl-ex/0510047] [SPIRES].CrossRefADSGoogle Scholar
  27. [27]
    STAR collaboration, B.I. Abelev et al., Transverse momentum and centrality dependence of high-p T non-photonic electron suppression in Au+Au collisions at \( \sqrt {{{s_{NN}}}} = 200\;GeV \), Phys. Rev. Lett. 98 (2007) 192301 [nucl-ex/0607012] [SPIRES].CrossRefADSGoogle Scholar
  28. [28]
    PHENIX collaboration, A. Adare et al., Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at \( \sqrt {{{s_{NN}}}} = 200\;GeV \), Phys. Rev. Lett. 98 (2007) 172301 [nucl-ex/0611018] [SPIRES].CrossRefADSGoogle Scholar
  29. [29]
    PHENIX collaboration, T.C. Awes, Highlights from PHENIX - II, J. Phys. G 35 (2008) 104007 [arXiv:0805.1636] [SPIRES].ADSGoogle Scholar
  30. [30]
    N. Armesto, M. Cacciari, A. Dainese, C.A. Salgado and U.A. Wiedemann, How sensitive are high-p T electron spectra at RHIC to heavy quark energy loss?, Phys. Lett. B 637 (2006) 362 [hep-ph/0511257] [SPIRES].ADSGoogle Scholar
  31. [31]
    R. Rapp and H. van Hees, Heavy Quarks in the quark-gluon Plasma, arXiv:0903.1096 [SPIRES].
  32. [32]
    Y. Akamatsu, T. Hatsuda and T. Hirano, Heavy Quark Diffusion with Relativistic Langevin Dynamics in the quark-gluon Fluid, Phys. Rev. C 79 (2009) 054907 [arXiv:0809.1499] [SPIRES].ADSGoogle Scholar
  33. [33]
    F. Debbasch, K. Mallick and J.P. Rivet, Relativistic Ornstein-Uhlenbeck process, J. Stat. Phys. 88 (1997) 945.CrossRefMATHADSMathSciNetGoogle Scholar
  34. [34]
    F. Debbasch and J.P. Rivet, A diffusion equation from the relativistic Ornstein-Uhlenbeck process, J. Stat. Phys. 90 (1998) 1179. CrossRefMATHMathSciNetGoogle Scholar
  35. [35]
    C. Chevalier and F. Debbasch, Relativistic diffusions: a unifying approach., J. Math. Phys. 49 (2008) 043303. CrossRefADSMathSciNetGoogle Scholar
  36. [36]
    J. Dunkel and P. Hänggi, Relativistic Brownian Motion, Phys. Rep. 471 (2009) 1 [arXiv:0812.1996].CrossRefADSMathSciNetGoogle Scholar
  37. [37]
    S.S. Gubser, Comparing the drag force on heavy quarks in N = 4 super-Yang-Mills theory and QCD, Phys. Rev. D 76 (2007) 126003 [hep-th/0611272] [SPIRES].ADSGoogle Scholar
  38. [38]
    U. Gürsoy and E. Kiritsis, Exploring improved holographic theories for QCD: Part I, JHEP 02 (2008) 032 [arXiv:0707.1324] [SPIRES].CrossRefGoogle Scholar
  39. [39]
    U. Gürsoy, E. Kiritsis and F. Nitti, Exploring improved holographic theories for QCD: Part II, JHEP 02 (2008) 019 [arXiv:0707.1349] [SPIRES].CrossRefGoogle Scholar
  40. [40]
    S.S. Gubser and A. Nellore, Mimicking the QCD equation of state with a dual black hole, Phys. Rev. D 78 (2008) 086007 [arXiv:0804.0434] [SPIRES].ADSGoogle Scholar
  41. [41]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Deconfinement and Gluon Plasma Dynamics in Improved Holographic QCD, Phys. Rev. Lett. 101 (2008) 181601 [arXiv:0804.0899] [SPIRES].CrossRefADSGoogle Scholar
  42. [42]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Holography and Thermodynamics of 5D Dilaton-gravity, JHEP 05 (2009) 033 [arXiv:0812.0792] [SPIRES].CrossRefGoogle Scholar
  43. [43]
    E. Kiritsis, Dissecting the string theory dual of QCD, Fortsch. Phys. 57 (2009) 396 [arXiv:0901.1772] [SPIRES].CrossRefMATHMathSciNetGoogle Scholar
  44. [44]
    U. Gürsoy, E. Kiritsis, L. Mazzanti and F. Nitti, Improved Holographic Yang-Mills at Finite Temperature: Comparison with Data, Nucl. Phys. B 820 (2009) 148 [arXiv:0903.2859] [SPIRES]. CrossRefADSGoogle Scholar
  45. [45]
    M. Panero, Thermodynamics of the QCD plasma and the large-N limit, Phys. Rev. Lett. 103 (2009) 232001 [arXiv:0907.3719] [SPIRES].CrossRefADSGoogle Scholar
  46. [46]
    E. Kiritsis, Supergravity, D-brane probes and thermal super Yang-Mills: A comparison, JHEP 10 (1999) 010 [hep-th/9906206] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  47. [47]
    A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [SPIRES]. CrossRefADSMathSciNetGoogle Scholar
  48. [48]
    J. Casalderrey-Solana, D. Fernandez and D. Mateos, A New Mechanism of Quark Energy Loss, Phys. Rev. Lett. 104 (2010) 172301 [arXiv:0912.3717] [SPIRES].CrossRefADSGoogle Scholar
  49. [49]
    L.F. Cugliandolo, J. Kurchan and L. Peliti, Energy flow, partial equilibration and effective temperatures in systems with slow dynamics, Phys. Rev. E 55 (1997) 3898 [SPIRES]. ADSGoogle Scholar
  50. [50]
    D. Cubero, J. Casado-Pascual, J. Dunkel, P. Talkner and P. Hänggi, Thermal equilibrium and statistical thermometers in special relativity, Phys. Rev. Lett. 99 (2007) 170601 [arXiv:0705.3328]. CrossRefADSGoogle Scholar
  51. [51]
    N. Iqbal and H. Liu, Universality of the hydrodynamic limit in AdS/CFT and the membrane paradigm, Phys. Rev. D 79 (2009) 025023 [arXiv:0809.3808] [SPIRES].ADSGoogle Scholar
  52. [52]
    D. Teaney, Finite temperature spectral densities of momentum and R-charge correlators in N = 4 Yang-Mills theory, Phys. Rev. D 74 (2006) 045025 [hep-ph/0602044] [SPIRES].ADSGoogle Scholar
  53. [53]
    J. Casalderrey-Solana and C.A. Salgado, Introductory lectures on jet-quenching in heavy ion collisions, Acta Phys. Polon. B 38 (2007) 3731 [arXiv:0712.3443] [SPIRES].ADSGoogle Scholar
  54. [54]
    R.P. Feynman and F.L. Vernon, The theory of a general quantum system interacting with a linear dissipative system, Annals Phys. 24 (1963) 118 [Annals Phys. 281 (2000) 547] [SPIRES]. CrossRefADSMathSciNetGoogle Scholar
  55. [55]
    H. Kleinert, PATH INTEGRALS in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, World Scientific, Singapore (2004) [SPIRES].MATHGoogle Scholar
  56. [56]
    S.S. Gubser, Comparing the drag force on heavy quarks in N = 4 super-Yang-Mills theory and QCD, Phys. Rev. D 76 (2007) 126003 [hep-th/0611272] [SPIRES].ADSGoogle Scholar
  57. [57]
    D.T. Son and A.O. Starinets, Minkowski-space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [SPIRES].CrossRefADSMathSciNetGoogle Scholar
  58. [58]
    S.S. Gubser, S.S. Pufu and F.D. Rocha, Bulk viscosity of strongly coupled plasmas with holographic duals, JHEP 08 (2008) 085 [arXiv:0806.0407] [SPIRES].CrossRefADSGoogle Scholar
  59. [59]
    K.B. Fadafan, H. Liu, K. Rajagopal and U.A. Wiedemann, Stirring Strongly Coupled Plasma, Eur. Phys. J. C 61 (2009) 553 [arXiv:0809.2869] [SPIRES].CrossRefADSGoogle Scholar
  60. [60]
    F. Bigazzi et al., D3-D7 quark-gluon Plasmas, JHEP 11 (2009) 117 [arXiv:0909.2865] [SPIRES].CrossRefADSGoogle Scholar
  61. [61]
    C. Núñez, A. Paredes and A.V. Ramallo, Unquenched flavor in the gauge/gravity correspondence, Adv. High Energy Phys. 2010 (2010) 196714 [arXiv:1002.1088] [SPIRES].Google Scholar
  62. [62]
    G. Bertoldi, F. Bigazzi, A.L. Cotrone and J.D. Edelstein, Holography and Unquenched Quark-Gluon Plasmas, Phys. Rev. D 76 (2007) 065007 [hep-th/0702225] [SPIRES].ADSGoogle Scholar
  63. [63]
    F. Karsch, D. Kharzeev and K. Tuchin, Universal properties of bulk viscosity near the QCD phase transition, Phys. Lett. B 663 (2008) 217 [arXiv:0711.0914] [SPIRES].ADSGoogle Scholar

Copyright information

© The Author(s) 2010

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

Authors and Affiliations

  • Umut Gürsoy
    • 1
  • Elias Kiritsis
    • 2
    • 4
  • Liuba Mazzanti
    • 3
  • Francesco Nitti
    • 4
  1. 1.Institute for Theoretical PhysicsUtrecht UniversityUtrechtThe Netherlands
  2. 2.Crete Center for Theoretical Physics, Department of PhysicsUniversity of CreteHeraklionGreece
  3. 3.Departamento de Física de PartículasUniversidade de Santiago de Compostela and Instituto Galego de Física de Altas Enerxías (IGFAE)Santiago de CompostelaSpain
  4. 4.APC, UMR du CNRS 7164, Université Paris 7Paris Cedex 13France

Personalised recommendations