Skip to main content
SpringerLink
Log in

Estimates for the thermal width of heavy quarkonia in strongly coupled plasmas from holography

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

The gauge/gravity duality is used to investigate the imaginary part of the heavy quark potential (defined via the rectangular Wilson loop) in strongly coupled plasmas. This quantity can be used to estimate the width of heavy quarkonia in a plasma at strong coupling. In this paper the thermal worldsheet fluctuation method, proposed in [J. Noronha and A. Dumitru, Phys. Rev. Lett. 103 (2009) 152304], is revisited and general conditions for the existence of an imaginary part for the heavy quark potential computed within classical gravity models are obtained. We prove a general result that establishes the connection between this imaginary part of the potential determined holographically and the area law displayed by the Wilson loop in the vacuum of confining gauge theories. We also determine the imaginary part of the heavy quark potential in a strongly coupled plasma dual to Gauss-Bonnet gravity. This provides an estimate of how the thermal width of heavy quarkonia changes with the shear viscosity to entropy density ratio, η/s, at strong coupling.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K.G. Wilson, Confinement of quarks, Phys. Rev. D 10 (1974) 2445 [INSPIRE].

    ADS  Google Scholar 

  2. J.-L. Gervais and A. Neveu, The slope of the leading Regge trajectory in quantum chromodynamics, Nucl. Phys. B 163 (1980) 189 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. A.M. Polyakov, Gauge fields as rings of glue, Nucl. Phys. B 164 (1980) 171 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. J.I. Kapusta and C. Gale, Finite temperature field theory, principles and applications, second edition, Cambridge University Press, Cambridge U.K. (2006).

  5. A.M. Polyakov, Thermal properties of gauge fields and quark liberation, Phys. Lett. B 72 (1978) 477 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. G. ’t Hooft, On the phase transition towards permanent quark confinement, Nucl. Phys. B 138 (1978) 1 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. G. ’t Hooft, A property of electric and magnetic flux in non-Abelian gauge theories, Nucl. Phys. B 153 (1979) 141 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. B. Svetitsky and L.G. Yaffe, Critical behavior at finite temperature confinement transitions, Nucl. Phys. B 210 (1982) 423 [INSPIRE].

    Article  ADS  Google Scholar 

  9. L.D. McLerran and B. Svetitsky, A Monte Carlo study of SU(2) Yang-Mills theory at finite temperature, Phys. Lett. B 98 (1981) 195 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. O. Kaczmarek, F. Karsch, P. Petreczky and F. Zantow, Heavy quark anti-quark free energy and the renormalized Polyakov loop, Phys. Lett. B 543 (2002) 41 [hep-lat/0207002] [INSPIRE].

    Article  ADS  Google Scholar 

  11. O. Philipsen, Lattice QCD at non-zero temperature and baryon density, arXiv:1009.4089 [INSPIRE].

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

    Article  ADS  Google Scholar 

  13. M. Laine, A resummed perturbative estimate for the quarkonium spectral function in hot QCD, JHEP 05 (2007) 028 [arXiv:0704.1720] [INSPIRE].

    Article  ADS  Google Scholar 

  14. A. Beraudo, J.-P. Blaizot and C. Ratti, Real and imaginary-time \( Q\overline{Q} \) correlators in a thermal medium, Nucl. Phys. A 806 (2008) 312 [arXiv:0712.4394] [INSPIRE].

    Article  ADS  Google Scholar 

  15. N. Brambilla, J. Ghiglieri, A. Vairo and P. Petreczky, Static quark-antiquark pairs at finite temperature, Phys. Rev. D 78 (2008) 014017 [arXiv:0804.0993] [INSPIRE].

    ADS  Google Scholar 

  16. P. Petreczky, C. Miao and A. Mócsy , Quarkonium spectral functions with complex potential, Nucl. Phys. A 855 (2011) 125 [arXiv:1012.4433] [INSPIRE].

    Article  ADS  Google Scholar 

  17. N. Brambilla, M.A. Escobedo, J. Ghiglieri, J. Soto and A. Vairo, Heavy quarkonium in a weakly-coupled quark-gluon plasma below the melting temperature, JHEP 09 (2010) 038 [arXiv:1007.4156] [INSPIRE].

    Article  ADS  Google Scholar 

  18. Y. Burnier, M. Laine and M. Vepsäläinen, Quarkonium dissociation in the presence of a small momentum space anisotropy, Phys. Lett. B 678 (2009) 86 [arXiv:0903.3467] [INSPIRE].

    Article  ADS  Google Scholar 

  19. 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 

  20. O. Philipsen and M. Tassler, On quarkonium in an anisotropic quark gluon plasma, arXiv:0908.1746 [INSPIRE].

  21. A. Rothkopf, T. Hatsuda and S. Sasaki, Complex heavy-quark potential at finite temperature from lattice QCD, Phys. Rev. Lett. 108 (2012) 162001 [arXiv:1108.1579] [INSPIRE].

    Article  ADS  Google Scholar 

  22. J. Noronha and A. Dumitru, Thermal width of the Υ at large t’ Hooft coupling, Phys. Rev. Lett. 103 (2009) 152304 [arXiv:0907.3062] [INSPIRE].

    Article  ADS  Google Scholar 

  23. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].

  24. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  25. E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  26. S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. J.M. Maldacena, Wilson loops in large-N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. A. Brandhuber, N. Itzhaki, J. Sonnenschein and S. Yankielowicz, Wilson loops in the large-N limit at finite temperature, Phys. Lett. B 434 (1998) 36 [hep-th/9803137] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. S.-J. Rey, S. Theisen and J.-T. Yee, Wilson-Polyakov loop at finite temperature in large-N gauge theory and anti-de Sitter supergravity, Nucl. Phys. B 527 (1998) 171 [hep-th/9803135] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. D. Bak, A. Karch and L.G. Yaffe, Debye screening in strongly coupled N = 4 supersymmetric Yang-Mills plasma, JHEP 08 (2007) 049 [arXiv:0705.0994] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. E. Kiritsis, String theory in a nutshell, Princeton University Press, Princeton U.S.A. (2007).

    MATH  Google Scholar 

  32. J. Noronha, Connecting Polyakov loops to the thermodynamics of SU(N c ) gauge theories using the gauge-string duality, Phys. Rev. D 81 (2010) 045011 [arXiv:0910.1261] [INSPIRE].

    ADS  Google Scholar 

  33. J. Noronha, The heavy quark free energy in QCD and in gauge theories with gravity duals, Phys. Rev. D 82 (2010) 065016 [arXiv:1003.0914] [INSPIRE].

    ADS  Google Scholar 

  34. H.R. Grigoryan and Y.V. Kovchegov, Gravity dual corrections to the heavy quark potential at finite-temperature, Nucl. Phys. B 852 (2011) 1 [arXiv:1105.2300] [INSPIRE].

    Article  ADS  Google Scholar 

  35. Y. Kinar, E. Schreiber and J. Sonnenschein, \( Q\overline{Q} \) potential from strings in curved space-time: classical results, Nucl. Phys. B 566 (2000) 103 [hep-th/9811192] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. J. Sonnenschein, What does the string/gauge correspondence teach us about Wilson loops?, hep-th/0003032 [INSPIRE].

  37. J.L. Albacete, Y.V. Kovchegov and A. Taliotis, Heavy quark potential at finite temperature in AdS/CFT revisited, Phys. Rev. D 78 (2008) 115007 [arXiv:0807.4747] [INSPIRE].

    ADS  Google Scholar 

  38. T. Hayata, K. Nawa and T. Hatsuda, Time-dependent heavy-quark potential at finite temperature from gauge/gravity duality, Phys. Rev. D 87 (2013) 101901 [arXiv:1211.4942] [INSPIRE].

    ADS  Google Scholar 

  39. S. Gradshteyn and I.M. Ryzhik, Table of integrals, series and products, A. Jeffrey and D. Zwillinger eds., seventh edition. Academic Press, U.S.A. (2007).

  40. B. Zwiebach, Curvature squared terms and string theories, Phys. Lett. B 156 (1985) 315 [INSPIRE].

    Article  ADS  Google Scholar 

  41. A. Buchel, R.C. Myers and A. Sinha, Beyond η/s = 1/4π, JHEP 03 (2009) 084 [arXiv:0812.2521] [INSPIRE].

    Article  ADS  Google Scholar 

  42. A. Buchel et al., Holographic GB gravity in arbitrary dimensions, JHEP 03 (2010) 111 [arXiv:0911.4257] [INSPIRE].

    Article  ADS  Google Scholar 

  43. J. Noronha, M. Gyulassy and G. Torrieri, Constraints on AdS/CFT gravity dual models of heavy ion collisions, arXiv:0906.4099 [INSPIRE].

  44. J. Noronha, M. Gyulassy and G. Torrieri, Conformal holography of bulk elliptic flow and heavy quark quenching in relativistic heavy ion collisions, Phys. Rev. C 82 (2010) 054903 [arXiv:1009.2286] [INSPIRE].

    ADS  Google Scholar 

  45. F. Karsch, M. Mehr and H. Satz, Color screening and deconfinement for bound states of heavy quarks, Z. Phys. C 37 (1988) 617 [INSPIRE].

    ADS  Google Scholar 

  46. G. Aarts et al., What happens to the Υ and η b in the quark-gluon plasma? Bottomonium spectral functions from lattice QCD, JHEP 11 (2011) 103 [arXiv:1109.4496] [INSPIRE].

    Article  ADS  Google Scholar 

  47. P. Kovtun, D. Son and A. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].

    Article  ADS  Google Scholar 

  48. R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev. D 65 (2002) 084014 [hep-th/0109133] [INSPIRE].

    ADS  Google Scholar 

  49. M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, The viscosity bound and causality violation, Phys. Rev. Lett. 100 (2008) 191601 [arXiv:0802.3318] [INSPIRE].

    Article  ADS  Google Scholar 

  50. M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity bound violation in higher derivative gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805] [INSPIRE].

    ADS  Google Scholar 

  51. Y. Kats and P. Petrov, Effect of curvature squared corrections in AdS on the viscosity of the dual gauge theory, JHEP 01 (2009) 044 [arXiv:0712.0743] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  52. J. Noronha and A. Dumitru, The heavy quark potential as a function of shear viscosity at strong coupling, Phys. Rev. D 80 (2009) 014007 [arXiv:0903.2804] [INSPIRE].

    ADS  Google Scholar 

  53. K.B. Fadafan, Heavy quarks in the presence of higher derivative corrections from AdS/CFT, Eur. Phys. J. C 71 (2011) 1799 [arXiv:1102.2289] [INSPIRE].

    Article  ADS  Google Scholar 

  54. M. Ali-Akbari and K. Bitaghsir Fadafan, Rotating mesons in the presence of higher derivative corrections from gauge-string duality, Nucl. Phys. B 835 (2010) 221 [arXiv:0908.3921] [INSPIRE].

    Article  ADS  Google Scholar 

  55. M. Strickland, Thermal Υ1s and χ b1 suppression in \( \sqrt{{{s_{NN }}}}=2.76 \) TeV Pb-Pb collisions at the LHC, Phys. Rev. Lett. 107 (2011) 132301 [arXiv:1106.2571] [INSPIRE].

    Article  ADS  Google Scholar 

  56. M. Strickland and D. Bazow, Thermal bottomonium suppression at RHIC and LHC, Nucl. Phys. A 879 (2012) 25 [arXiv:1112.2761] [INSPIRE].

    Article  ADS  Google Scholar 

  57. M. Margotta, K. McCarty, C. McGahan, M. Strickland and D. Yager-Elorriaga, Quarkonium states in a complex-valued potential, Phys. Rev. D 83 (2011) 105019 [Erratum ibid. D 84 2011) 069902] [arXiv:1101.4651] [INSPIRE].

    Google Scholar 

  58. T. Faulkner and H. Liu, Meson widths from string worldsheet instantons, Phys. Lett. B 673 (2009) 161 [arXiv:0807.0063] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  59. D. Mateos and D. Trancanelli, The anisotropic N = 4 super Yang-Mills plasma and its instabilities, Phys. Rev. Lett. 107 (2011) 101601 [arXiv:1105.3472] [INSPIRE].

    Article  ADS  Google Scholar 

  60. D. Mateos and D. Trancanelli, Thermodynamics and instabilities of a strongly coupled anisotropic plasma, JHEP 07 (2011) 054 [arXiv:1106.1637] [INSPIRE].

    Article  ADS  Google Scholar 

  61. 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] [INSPIRE].

    Article  ADS  Google Scholar 

  62. 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] [INSPIRE].

    ADS  Google Scholar 

  63. D. Giataganas, Observables in strongly coupled anisotropic theories, PoS(Corfu2012)122 [arXiv:1306.1404] [INSPIRE].

  64. K.B. Fadafan, D. Giataganas and H. Soltanpanahi, The imaginary part of the static potential in strongly coupled anisotropic plasma, arXiv:1306.2929 [INSPIRE].

  65. L. Álvarez-Gaumé, D.Z. Freedman and S. Mukhi, The background field method and the ultraviolet structure of the supersymmetric nonlinear σ-model, Annals Phys. 134 (1981) 85 [INSPIRE].

    Article  ADS  Google Scholar 

  66. C.W. Misner, K.S. Thorne and J.A. Wheeler, Gravitation, W.H. Freeman, U.S.A. (1973).

    Google Scholar 

  67. A. Brandhuber, N. Itzhaki, J. Sonnenschein and S. Yankielowicz, Wilson loops, confinement and phase transitions in large-N gauge theories from supergravity, JHEP 06 (1998) 001 [hep-th/9803263] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  68. N. Itzhaki, J.M. Maldacena, J. Sonnenschein and S. Yankielowicz, Supergravity and the large-N limit of theories with sixteen supercharges, Phys. Rev. D 58 (1998) 046004 [hep-th/9802042] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Física, Universidade de São Paulo, 05314-970, São Paulo, Brazil

    Stefano I. Finazzo & Jorge Noronha

Authors
  1. Stefano I. Finazzo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jorge Noronha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jorge Noronha.

Additional information

ArXiv ePrint: 1306.2613

Rights and permissions

Reprints and permissions

About this article

Cite this article

Finazzo, S.I., Noronha, J. Estimates for the thermal width of heavy quarkonia in strongly coupled plasmas from holography. J. High Energ. Phys. 2013, 42 (2013). https://doi.org/10.1007/JHEP11(2013)042

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP11(2013)042

Keywords

Search

Navigation