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Quasinormal modes and dispersion relations for quarkonium in a plasma

  • Nelson R. F. BragaEmail author
  • Luiz F. Ferreira
Open Access
Regular Article - Theoretical Physics
  • 19 Downloads

Abstract

Recent investigations show that the thermal spectral function of heavy \( b\overline{b} \) and \( c\overline{c} \) vector mesons can be described using holography. These studies consider a bottom up model that captures the heavy flavour spectroscopy of masses and decay constants in the vacuum and is consistently extended to finite temperature. The corresponding spectral functions provide a picture of the dissociation process in terms of the decrease of the quasi-state peaks with temperature.

Another related tool that provides important information about the thermal behaviour is the analysis of the quasinormal modes. They are field solutions in a curved background assumed to represent, in gauge/gravity duality, quasi-particle states in a thermal medium. The associated complex frequencies are related to the thermal mass and width. We present here the calculation of quasinormal modes for charmonium and bottomonium using the holographic approach. The temperature dependence of mass and thermal width are investigated. Solutions corresponding to heavy mesons moving into the plasma are also studied. They provide the dependence of the real and imaginary parts of the frequency with the quasi-particle momenta, the so called dispersion relations.

Keywords

Phenomenological Models QCD Phenomenology 

Notes

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.

References

  1. [1]
    T. Matsui and H. Satz, J/ψ suppression by quark-gluon plasma formation, Phys. Lett. B 178 (1986) 416 [INSPIRE].
  2. [2]
    H. Satz, Colour deconfinement and quarkonium binding, J. Phys. G 32 (2006) R25 [hep-ph/0512217] [INSPIRE].
  3. [3]
    N.R.F. Braga, M.A. Martin Contreras and S. Diles, Decay constants in soft wall AdS/QCD revisited, Phys. Lett. B 763 (2016) 203 [arXiv:1507.04708] [INSPIRE].
  4. [4]
    N.R.F. Braga, M.A. Martin Contreras and S. Diles, Holographic picture of heavy vector meson melting, Eur. Phys. J. C 76 (2016) 598 [arXiv:1604.08296] [INSPIRE].
  5. [5]
    N.R.F. Braga and L.F. Ferreira, Bottomonium dissociation in a finite density plasma, Phys. Lett. B 773 (2017) 313 [arXiv:1704.05038] [INSPIRE].
  6. [6]
    N.R.F. Braga, L.F. Ferreira and A. Vega, Holographic model for charmonium dissociation, Phys. Lett. B 774 (2017) 476 [arXiv:1709.05326] [INSPIRE].
  7. [7]
    N.R.F. Braga and L.F. Ferreira, Heavy meson dissociation in a plasma with magnetic fields, Phys. Lett. B 783 (2018) 186 [arXiv:1802.02084] [INSPIRE].
  8. [8]
    Particle Data Group collaboration, Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
  9. [9]
    D.S. Hwang and G.-H. Kim, Decay constant ratios \( {f}_{\eta_c}/{f}_{J/\psi } \) and \( {f}_{\eta_b}/{f}_{\varUpsilon } \), Z. Phys. C 76 (1997) 107 [hep-ph/9703364] [INSPIRE].
  10. [10]
    J. Polchinski and M.J. Strassler, Hard scattering and gauge/string duality, Phys. Rev. Lett. 88 (2002) 031601 [hep-th/0109174] [INSPIRE].
  11. [11]
    H. Boschi-Filho and N.R.F. Braga, QCD/string holographic mapping and glueball mass spectrum, Eur. Phys. J. C 32 (2004) 529 [hep-th/0209080] [INSPIRE].
  12. [12]
    H. Boschi-Filho and N.R.F. Braga, Gauge/string duality and scalar glueball mass ratios, JHEP 05 (2003) 009 [hep-th/0212207] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    A. Karch, E. Katz, D.T. Son and M.A. Stephanov, Linear confinement and AdS/QCD, Phys. Rev. D 74 (2006) 015005 [hep-ph/0602229] [INSPIRE].
  14. [14]
    G.T. Horowitz and V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium, Phys. Rev. D 62 (2000) 024027 [hep-th/9909056] [INSPIRE].
  15. [15]
    D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    A. Núñez and A.O. Starinets, AdS/CFT correspondence, quasinormal modes and thermal correlators in N = 4 SYM, Phys. Rev. D 67 (2003) 124013 [hep-th/0302026] [INSPIRE].
  17. [17]
    P.K. Kovtun and A.O. Starinets, Quasinormal modes and holography, Phys. Rev. D 72 (2005) 086009 [hep-th/0506184] [INSPIRE].
  18. [18]
    A.S. Miranda and V.T. Zanchin, Quasinormal modes of plane-symmetric anti-de Sitter black holes: a complete analysis of the gravitational perturbations, Phys. Rev. D 73 (2006) 064034 [gr-qc/0510066] [INSPIRE].
  19. [19]
    C. Hoyos-Badajoz, K. Landsteiner and S. Montero, Holographic meson melting, JHEP 04 (2007) 031 [hep-th/0612169] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    E. Berti, V. Cardoso and A.O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26 (2009) 163001 [arXiv:0905.2975] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    J. Morgan, V. Cardoso, A.S. Miranda, C. Molina and V.T. Zanchin, Quasinormal modes of black holes in anti-de Sitter space: a numerical study of the eikonal limit, Phys. Rev. D 80 (2009) 024024 [arXiv:0906.0064] [INSPIRE].
  22. [22]
    A.S. Miranda, C.A. Ballon Bayona, H. Boschi-Filho and N.R.F. Braga, Black-hole quasinormal modes and scalar glueballs in a finite-temperature AdS/QCD model, JHEP 11 (2009) 119 [arXiv:0909.1790] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    R.A. Konoplya and A. Zhidenko, Quasinormal modes of black holes: from astrophysics to string theory, Rev. Mod. Phys. 83 (2011) 793 [arXiv:1102.4014] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    L.A.H. Mamani, A.S. Miranda, H. Boschi-Filho and N.R.F. Braga, Vector meson quasinormal modes in a finite-temperature AdS/QCD model, JHEP 03 (2014) 058 [arXiv:1312.3815] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    L.A.H. Mamani, J. Morgan, A.S. Miranda and V.T. Zanchin, From quasinormal modes of rotating black strings to hydrodynamics of a moving CFT plasma, Phys. Rev. D 98 (2018) 026006 [arXiv:1804.01544] [INSPIRE].
  26. [26]
    M. Kaminski, Holographic quark gluon plasma with flavor, Fortsch. Phys. 57 (2009) 3 [arXiv:0808.1114] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    M. Kaminski, K. Landsteiner, F. Pena-Benitez, J. Erdmenger, C. Greubel and P. Kerner, Quasinormal modes of massive charged flavor branes, JHEP 03 (2010) 117 [arXiv:0911.3544] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  28. [28]
    I. Amado, M. Kaminski and K. Landsteiner, Hydrodynamics of holographic superconductors, JHEP 05 (2009) 021 [arXiv:0903.2209] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    M. Kaminski, K. Landsteiner, J. Mas, J.P. Shock and J. Tarrio, Holographic operator mixing and quasinormal modes on the brane, JHEP 02 (2010) 021 [arXiv:0911.3610] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  30. [30]
    S. Janiszewski and M. Kaminski, Quasinormal modes of magnetic and electric black branes versus far from equilibrium anisotropic fluids, Phys. Rev. D 93 (2016) 025006 [arXiv:1508.06993] [INSPIRE].
  31. [31]
    T. Umeda, R. Katayama, O. Miyamura and H. Matsufuru, Study of charmonia near the deconfining transition on an anisotropic lattice with O(a) improved quark action, Int. J. Mod. Phys. A 16 (2001) 2215 [hep-lat/0011085] [INSPIRE].
  32. [32]
    M. Asakawa and T. Hatsuda, J/ψ and η c in the deconfined plasma from lattice QCD, Phys. Rev. Lett. 92 (2004) 012001 [hep-lat/0308034] [INSPIRE].
  33. [33]
    S. Datta, F. Karsch, P. Petreczky and I. Wetzorke, Behavior of charmonium systems after deconfinement, Phys. Rev. D 69 (2004) 094507 [hep-lat/0312037] [INSPIRE].
  34. [34]
    A. Jakovac, P. Petreczky, K. Petrov and A. Velytsky, Quarkonium correlators and spectral functions at zero and finite temperature, Phys. Rev. D 75 (2007) 014506 [hep-lat/0611017] [INSPIRE].
  35. [35]
    G. Aarts, C. Allton, M.B. Oktay, M. Peardon and J.-I. Skullerud, Charmonium at high temperature in two-flavor QCD, Phys. Rev. D 76 (2007) 094513 [arXiv:0705.2198] [INSPIRE].
  36. [36]
    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].ADSCrossRefGoogle Scholar
  37. [37]
    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].
  38. [38]
    G. Aarts et al., Bottomonium above deconfinement in lattice nonrelativistic QCD, Phys. Rev. Lett. 106 (2011) 061602 [arXiv:1010.3725] [INSPIRE].
  39. [39]
    G. Aarts et al., S wave bottomonium states moving in a quark-gluon plasma from lattice NRQCD, JHEP 03 (2013) 084 [arXiv:1210.2903] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    G. Aarts, C. Allton, S. Kim, M.P. Lombardo, S.M. Ryan and J.-I. Skullerud, Melting of P wave bottomonium states in the quark-gluon plasma from lattice NRQCD, JHEP 12 (2013) 064 [arXiv:1310.5467] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    F. Karsch, E. Laermann, S. Mukherjee and P. Petreczky, Signatures of charmonium modification in spatial correlation functions, Phys. Rev. D 85 (2012) 114501 [arXiv:1203.3770] [INSPIRE].
  42. [42]
    K. Morita and S.H. Lee, Mass shift and width broadening of J/ψ in QGP from QCD sum rule, Phys. Rev. Lett. 100 (2008) 022301 [arXiv:0704.2021] [INSPIRE].
  43. [43]
    K. Morita and S.H. Lee, Critical behavior of charmonia across the phase transition: A QCD sum rule approach, Phys. Rev. C 77 (2008) 064904 [arXiv:0711.3998] [INSPIRE].
  44. [44]
    Y.-H. Song, S.H. Lee and K. Morita, In-medium modification of P-wave charmonia from QCD sum rules, Phys. Rev. C 79 (2009) 014907 [arXiv:0808.1153] [INSPIRE].
  45. [45]
    K. Morita and S.H. Lee, Heavy quarkonium correlators at finite temperature: QCD sum rule approach, Phys. Rev. D 82 (2010) 054008 [arXiv:0908.2856] [INSPIRE].
  46. [46]
    P. Gubler, K. Morita and M. Oka, Charmonium spectra at finite temperature from QCD sum rules with the maximum entropy method, Phys. Rev. Lett. 107 (2011) 092003 [arXiv:1104.4436] [INSPIRE].
  47. [47]
    K. Suzuki, P. Gubler, K. Morita and M. Oka, Thermal modification of bottomonium spectra from QCD sum rules with the maximum entropy method, Nucl. Phys. A 897 (2013) 28 [arXiv:1204.1173] [INSPIRE].
  48. [48]
    Y. Kim, J.-P. Lee and S.H. Lee, Heavy quarkonium in a holographic QCD model, Phys. Rev. D 75 (2007) 114008 [hep-ph/0703172] [INSPIRE].
  49. [49]
    M. Fujita, K. Fukushima, T. Misumi and M. Murata, Finite-temperature spectral function of the vector mesons in an AdS/QCD model, Phys. Rev. D 80 (2009) 035001 [arXiv:0903.2316] [INSPIRE].
  50. [50]
    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].
  51. [51]
    M. Laine, A resummed perturbative estimate for the quarkonium spectral function in hot QCD, JHEP 05 (2007) 028 [arXiv:0704.1720] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    C.-Y. Wong, Heavy quarkonia in quark-gluon plasma, Phys. Rev. C 72 (2005) 034906 [hep-ph/0408020] [INSPIRE].
  53. [53]
    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].
  54. [54]
    S. Digal, O. Kaczmarek, F. Karsch and H. Satz, Heavy quark interactions in finite temperature QCD, Eur. Phys. J. C 43 (2005) 71 [hep-ph/0505193] [INSPIRE].
  55. [55]
    W.M. Alberico, A. Beraudo, A. De Pace and A. Molinari, Heavy quark bound states above T c, Phys. Rev. D 72 (2005) 114011 [hep-ph/0507084] [INSPIRE].
  56. [56]
    A. Mócsy and P. Petreczky, Can quarkonia survive deconfinement?, Phys. Rev. D 77 (2008) 014501 [arXiv:0705.2559] [INSPIRE].
  57. [57]
    A. Mócsy and P. Petreczky, Color screening melts quarkonium, Phys. Rev. Lett. 99 (2007) 211602 [arXiv:0706.2183] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    P. Petreczky, C. Miao and A. Mócsy, Quarkonium spectral functions with complex potential, Nucl. Phys. A 855 (2011) 125 [arXiv:1012.4433] [INSPIRE].
  59. [59]
    PHENIX collaboration, Measurement of ϒ(1S + 2S + 3S) production in p+p and Au+Au collisions at \( \sqrt{s_{N\ N}} = 200 \) GeV, Phys. Rev. C 91 (2015) 024913 [arXiv:1404.2246] [INSPIRE].
  60. [60]
    C.A. Ballon Bayona, H. Boschi-Filho, N.R.F. Braga and L.A. Pando Zayas, On a holographic model for confinement/deconfinement, Phys. Rev. D 77 (2008) 046002 [arXiv:0705.1529] [INSPIRE].
  61. [61]
    G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  62. [62]
    P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Instituto de FísicaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

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