Skip to main content
SpringerLink
Log in

Conserved charge fluctuations and susceptibilities in strongly interacting matter

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

Abstract

We study the conserved charge fluctuations, as quantified by the corresponding susceptibilities, in strongly interacting matter as motived by the quark-gluon plasma. Using the gauge-gravity correspondence approach, we study the patterns of conserved charge fluctuations in two types of holographic models for QCD, the D4/D8 and the D3/D7 models. We compute and compare the quark number susceptibilities in both models and find an interesting common feature of the two: at very strong coupling higher order susceptibilities are suppressed and the conserved charge fluctuations become purely Guassian. In light of the state-of-the-art lattice QCD results we also discuss what we can learn from these susceptibilities about the underlying degrees of freedom in the 1 ~ 2T c quark-gluon plasma and examine the viability of different ideas such as holography, quasi-particles, as well as bound states. From analyzes of second order susceptibilities we conclude that the bound states exist and are important in the 1 ~ 2T c region. We further construct and make predictions for several ratios of fourth-order susceptibilities that can sensitively reveal such bound states.

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. P. Braun-Munzinger and J. Wambach, The phase diagram of strongly-interacting matter, Rev. Mod. Phys. 81 (2009) 1031 [arXiv:0801.4256] [INSPIRE].

    Article  ADS  Google Scholar 

  2. M.A. Stephanov, QCD phase diagram: an overview, PoS(LAT2006)024 [hep-lat/0701002] [INSPIRE].

  3. N. Itoh, Hydrostatic equilibrium of hypothetical quark stars, Prog. Theor. Phys. 44 (1970) 291 [INSPIRE].

    Article  ADS  Google Scholar 

  4. M. Gyulassy and L. McLerran, New forms of QCD matter discovered at RHIC, Nucl. Phys. A 750 (2005) 30 [nucl-th/0405013] [INSPIRE].

    ADS  Google Scholar 

  5. E.V. Shuryak, Why does the quark gluon plasma at RHIC behave as a nearly ideal fluid?, Prog. Part. Nucl. Phys. 53 (2004) 273 [hep-ph/0312227] [INSPIRE].

    Article  ADS  Google Scholar 

  6. E.V. Shuryak, What RHIC experiments and theory tell us about properties of quark-gluon plasma?, Nucl. Phys. A 750 (2005) 64 [hep-ph/0405066] [INSPIRE].

    ADS  Google Scholar 

  7. E.V. Shuryak, Physics of strongly coupled quark-gluon plasma, Prog. Part. Nucl. Phys. 62 (2009) 48 [arXiv:0807.3033] [INSPIRE].

    Article  ADS  Google Scholar 

  8. J. Liao and E.V. Shuryak, Strongly coupled plasma with electric and magnetic charges, Phys. Rev. C 75 (2007) 054907 [hep-ph/0611131] [INSPIRE].

    ADS  Google Scholar 

  9. J. Liao and E.V. Shuryak, Magnetic component of quark-gluon plasma is also a liquid!, Phys. Rev. Lett. 101 (2008) 162302 [arXiv:0804.0255] [INSPIRE].

    Article  ADS  Google Scholar 

  10. J. Liao and E.V. Shuryak, Angular dependence of jet quenching indicates its strong enhancement near the QCD phase transition, Phys. Rev. Lett. 102 (2009) 202302 [arXiv:0810.4116] [INSPIRE].

    Article  ADS  Google Scholar 

  11. J. Liao and E.V. Shuryak, Effect of light fermions on the confinement transition in QCD-like theories, Phys. Rev. Lett. 109 (2012) 152001 [arXiv:1206.3989] [INSPIRE].

    Article  ADS  Google Scholar 

  12. C. Ratti and E.V. Shuryak, The role of monopoles in a gluon plasma, Phys. Rev. D 80 (2009) 034004 [arXiv:0811.4174] [INSPIRE].

    ADS  Google Scholar 

  13. D. Simic and M. Ünsal, Deconfinement in Yang-Mills theory through toroidal compactification with deformation, Phys. Rev. D 85 (2012) 105027 [arXiv:1010.5515] [INSPIRE].

    ADS  Google Scholar 

  14. E. Poppitz, T. Schäfer and M. Ünsal, Continuity, deconfinement and (super) Yang-Mills theory, JHEP 10 (2012) 115 [arXiv:1205.0290] [INSPIRE].

    Article  ADS  Google Scholar 

  15. E. Poppitz, T. Schäfer and M. Ünsal, Universal mechanism of (semi-classical) deconfinement and θ-dependence for all simple groups, JHEP 03 (2013) 087 [arXiv:1212.1238] [INSPIRE].

    Article  ADS  Google Scholar 

  16. Z. Fodor and S.D. Katz, Critical point of QCD at finite T and μ, lattice results for physical quark masses, JHEP 04 (2004) 050 [hep-lat/0402006] [INSPIRE].

    Article  ADS  Google Scholar 

  17. Y. Aoki, G. Endrodi, Z. Fodor, S.D. Katz and K.K. Szabo, The order of the quantum chromodynamics transition predicted by the standard model of particle physics, Nature 443 (2006) 675 [hep-lat/0611014] [INSPIRE].

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. A. Bazavov et al., The chiral and deconfinement aspects of the QCD transition, Phys. Rev. D 85 (2012) 054503 [arXiv:1111.1710] [INSPIRE].

    ADS  Google Scholar 

  20. F. Karsch et al., Where is the chiral critical point in three flavor QCD?, Nucl. Phys. Proc. Suppl. 129 (2004) 614 [hep-lat/0309116] [INSPIRE].

    Article  ADS  Google Scholar 

  21. P. de Forcrand and O. Philipsen, The chiral critical point of N f = 3 QCD at finite density to the order (μ/T)4, JHEP 11 (2008) 012 [arXiv:0808.1096] [INSPIRE].

    Article  Google Scholar 

  22. P. de Forcrand, S. Kim and O. Philipsen, A QCD chiral critical point at small chemical potential: is it there or not?, PoS(LATTICE 2007)178 [arXiv:0711.0262] [INSPIRE].

  23. R.D. Pisarski and F. Wilczek, Remarks on the chiral phase transition in chromodynamics, Phys. Rev. D 29 (1984) 338 [INSPIRE].

    ADS  Google Scholar 

  24. M.A. Stephanov, K. Rajagopal and E.V. Shuryak, Signatures of the tricritical point in QCD, Phys. Rev. Lett. 81 (1998) 4816 [hep-ph/9806219] [INSPIRE].

    Article  ADS  Google Scholar 

  25. M.A. Stephanov, K. Rajagopal and E.V. Shuryak, Event-by-event fluctuations in heavy ion collisions and the QCD critical point, Phys. Rev. D 60 (1999) 114028 [hep-ph/9903292] [INSPIRE].

    ADS  Google Scholar 

  26. STAR collaboration, X. Luo, Search for the QCD critical point by higher moments of net-proton multiplicity distributions at STAR, Nucl. Phys. A904-905 (2013) 911c [arXiv:1210.5573] [INSPIRE].

    ADS  Google Scholar 

  27. X.-F. Luo, B. Mohanty, H.G. Ritter and N. Xu, Search for the QCD critical point: higher moments of net-proton multiplicity distributions, Phys. Atom. Nucl. 75 (2012) 676 [arXiv:1105.5049] [INSPIRE].

    Article  ADS  Google Scholar 

  28. STAR collaboration, X.-F. Luo, Probing the QCD critical point with higher moments of net-proton multiplicity distributions, J. Phys. Conf. Ser. 316 (2011) 012003 [arXiv:1106.2926] [INSPIRE].

    Article  ADS  Google Scholar 

  29. X. Luo, J. Xu, B. Mohanty and N. Xu, Techniques in the moment analysis of net-proton multiplicity distributions in heavy-ion collisions, arXiv:1302.2332 [INSPIRE].

  30. J. Liao and E.V. Shuryak, What do lattice baryonic susceptibilities tell us about quarks, diquarks and baryons at T > T c ?, Phys. Rev. D 73 (2006) 014509 [hep-ph/0510110] [INSPIRE].

    ADS  Google Scholar 

  31. V. Koch, A. Majumder and J. Randrup, Baryon-strangeness correlations: a diagnostic of strongly interacting matter, Phys. Rev. Lett. 95 (2005) 182301 [nucl-th/0505052] [INSPIRE].

    Article  ADS  Google Scholar 

  32. C.R. Allton et al., Thermodynamics of two flavor QCD to sixth order in quark chemical potential, Phys. Rev. D 71 (2005) 054508 [hep-lat/0501030] [INSPIRE].

    ADS  Google Scholar 

  33. M. Cheng et al., Baryon number, strangeness and electric charge fluctuations in QCD at high temperature, Phys. Rev. D 79 (2009) 074505 [arXiv:0811.1006] [INSPIRE].

    ADS  Google Scholar 

  34. R.V. Gavai and S. Gupta, Simple patterns for non-linear susceptibilities near T c , Phys. Rev. D 72 (2005) 054006 [hep-lat/0507023] [INSPIRE].

    ADS  Google Scholar 

  35. R.V. Gavai and S. Gupta, The critical end point of QCD, Phys. Rev. D 71 (2005) 114014 [hep-lat/0412035] [INSPIRE].

    Google Scholar 

  36. R.V. Gavai and S. Gupta, Pressure and nonlinear susceptibilities in QCD at finite chemical potentials, Phys. Rev. D 68 (2003) 034506 [hep-lat/0303013] [INSPIRE].

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

    Article  ADS  Google Scholar 

  38. 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].

  39. S. Jeon and V. Koch, Event by event fluctuations, in Quark gluon plasma, R.C. Hwa and X.-N. Wang eds., World Scientific, pp. 430–490 [hep-ph/0304012] [INSPIRE].

  40. V. Koch, Hadronic fluctuations and correlations, arXiv:0810.2520 [INSPIRE].

  41. A. Bzdak, V. Koch and J. Liao, Charge-dependent correlations in relativistic heavy ion collisions and the chiral magnetic effect, Lect. Notes Phys. 871 (2013) 503 [arXiv:1207.7327] [INSPIRE].

    Article  Google Scholar 

  42. A. Bzdak, V. Koch and J. Liao, Remarks on possible local parity violation in heavy ion collisions, Phys. Rev. C 81 (2010) 031901 [arXiv:0912.5050] [INSPIRE].

    ADS  Google Scholar 

  43. A. Bazavov et al., Freeze-out conditions in heavy ion collisions from QCD thermodynamics, Phys. Rev. Lett. 109 (2012) 192302 [arXiv:1208.1220] [INSPIRE].

    Article  ADS  Google Scholar 

  44. S. Gupta, X. Luo, B. Mohanty, H.G. Ritter and N. Xu, Scale for the phase diagram of quantum chromodynamics, Science 332 (2011) 1525 [arXiv:1105.3934] [INSPIRE].

    Article  ADS  Google Scholar 

  45. K.-y. Kim and J. Liao, On the baryonic density and susceptibilities in a holographic model of QCD, Nucl. Phys. B 822 (2009) 201 [arXiv:0906.2978] [INSPIRE].

  46. J. Casalderrey-Solana, H. Liu, D. Mateos, K. Rajagopal and U.A. Wiedemann, Gauge/string duality, hot QCD and heavy ion collisions, arXiv:1101.0618 [INSPIRE].

  47. Y. Kim, Y. Matsuo, W. Sim, S. Takeuchi and T. Tsukioka, Quark number susceptibility with finite chemical potential in holographic QCD, JHEP 05 (2010) 038 [arXiv:1001.5343] [INSPIRE].

    Article  ADS  Google Scholar 

  48. J. Casalderrey-Solana and D. Mateos, Off-diagonal flavour susceptibilities from AdS/CFT, JHEP 08 (2012) 165 [arXiv:1202.2533] [INSPIRE].

    Article  ADS  Google Scholar 

  49. T. Sakai and S. Sugimoto, Low energy hadron physics in holographic QCD, Prog. Theor. Phys. 113 (2005) 843 [hep-th/0412141] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  50. T. Sakai and S. Sugimoto, More on a holographic dual of QCD, Prog. Theor. Phys. 114 (2005) 1083 [hep-th/0507073] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  51. O. Aharony, J. Sonnenschein and S. Yankielowicz, A holographic model of deconfinement and chiral symmetry restoration, Annals Phys. 322 (2007) 1420 [hep-th/0604161] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. A. Parnachev and D.A. Sahakyan, Chiral phase transition from string theory, Phys. Rev. Lett. 97 (2006) 111601 [hep-th/0604173] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  53. K. Peeters, J. Sonnenschein and M. Zamaklar, Holographic melting and related properties of mesons in a quark gluon plasma, Phys. Rev. D 74 (2006) 106008 [hep-th/0606195] [INSPIRE].

    ADS  Google Scholar 

  54. K.-Y. Kim, S.-J. Sin and I. Zahed, Dense hadronic matter in holographic QCD, hep-th/0608046 [INSPIRE].

  55. K.-Y. Kim, S.-J. Sin and I. Zahed, Dense holographic QCD in the Wigner-Seitz approximation, JHEP 09 (2008) 001 [arXiv:0712.1582] [INSPIRE].

    Article  ADS  Google Scholar 

  56. K.-Y. Kim, S.-J. Sin and I. Zahed, The chiral model of Sakai-Sugimoto at finite baryon density, JHEP 01 (2008) 002 [arXiv:0708.1469] [INSPIRE].

    Article  ADS  Google Scholar 

  57. N. Horigome and Y. Tanii, Holographic chiral phase transition with chemical potential, JHEP 01 (2007) 072 [hep-th/0608198] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  58. O. Bergman, G. Lifschytz and M. Lippert, Holographic nuclear physics, JHEP 11 (2007) 056 [arXiv:0708.0326] [INSPIRE].

    Article  ADS  Google Scholar 

  59. M. Rozali, H.-H. Shieh, M. Van Raamsdonk and J. Wu, Cold nuclear matter in holographic QCD, JHEP 01 (2008) 053 [arXiv:0708.1322] [INSPIRE].

    Article  ADS  Google Scholar 

  60. J.L. Davis, M. Gutperle, P. Kraus and I. Sachs, Stringy NJLS and Gross-Neveu models at finite density and temperature, JHEP 10 (2007) 049 [arXiv:0708.0589] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  61. K. Nawa, H. Suganuma and T. Kojo, Brane-induced skyrmion on S 3 : baryonic matter in holographic QCD, Phys. Rev. D 79 (2009) 026005 [arXiv:0810.1005] [INSPIRE].

    ADS  Google Scholar 

  62. L. McLerran and R.D. Pisarski, Phases of cold, dense quarks at large-N c , Nucl. Phys. A 796 (2007) 83 [arXiv:0706.2191] [INSPIRE].

    ADS  Google Scholar 

  63. Y. Hidaka, L.D. McLerran and R.D. Pisarski, Baryons and the phase diagram for a large number of colors and flavors, Nucl. Phys. A 808 (2008) 117 [arXiv:0803.0279] [INSPIRE].

    ADS  Google Scholar 

  64. T. Kojo, Y. Hidaka, L. McLerran and R.D. Pisarski, Quarkyonic chiral spirals, Nucl. Phys. A 843 (2010) 37 [arXiv:0912.3800] [INSPIRE].

    ADS  Google Scholar 

  65. D. Mateos, R.C. Myers and R.M. Thomson, Holographic phase transitions with fundamental matter, Phys. Rev. Lett. 97 (2006) 091601 [hep-th/0605046] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  66. S. Kobayashi, D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite baryon density, JHEP 02 (2007) 016 [hep-th/0611099] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  67. D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite chemical potential, JHEP 11 (2007) 085 [arXiv:0709.1225] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  68. S. Nakamura, Y. Seo, S.-J. Sin and K.P. Yogendran, Baryon-charge chemical potential in AdS/CFT, Prog. Theor. Phys. 120 (2008) 51 [arXiv:0708.2818] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  69. K. Ghoroku, M. Ishihara and A. Nakamura, D3/D7 holographic gauge theory and chemical potential, Phys. Rev. D 76 (2007) 124006 [arXiv:0708.3706] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  70. A. Karch and A. O’Bannon, Holographic thermodynamics at finite baryon density: some exact results, JHEP 11 (2007) 074 [arXiv:0709.0570] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  71. C. Ratti, S. Roessner and W. Weise, Quark number susceptibilities: lattice QCD versus PNJL model, Phys. Lett. B 649 (2007) 57 [hep-ph/0701091] [INSPIRE].

  72. 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].

  73. 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 

  74. M. Bluhm and B. Kampfer, Flavor diagonal and off-diagonal susceptibilities in a quasiparticle model of the quark-gluon plasma, Phys. Rev. D 77 (2008) 114016 [arXiv:0801.4147] [INSPIRE].

    ADS  Google Scholar 

  75. M. Bluhm, B. Kampfer and G. Soff, The QCD equation of state near T c within a quasi-particle model, Phys. Lett. B 620 (2005) 131 [hep-ph/0411106] [INSPIRE].

  76. A. Dumitru, Y. Guo, Y. Hidaka, C.P.K. Altes and R.D. Pisarski, Effective matrix model for deconfinement in pure gauge theories, Phys. Rev. D 86 (2012) 105017 [arXiv:1205.0137] [INSPIRE].

    ADS  Google Scholar 

  77. K. Kashiwa, R.D. Pisarski and V.V. Skokov, Critical endpoint for deconfinement in matrix and other effective models, Phys. Rev. D 85 (2012) 114029 [arXiv:1205.0545] [INSPIRE].

    ADS  Google Scholar 

  78. S. Lin and E. Shuryak, The rise and fall of baryons, arXiv:0910.4947 [INSPIRE].

  79. E. Braaten and R.D. Pisarski, Soft amplitudes in hot gauge theories: a general analysis, Nucl. Phys. B 337 (1990) 569 [INSPIRE].

    Article  ADS  Google Scholar 

  80. J.-P. Blaizot and E. Iancu, The quark gluon plasma: collective dynamics and hard thermal loops, Phys. Rept. 359 (2002) 355 [hep-ph/0101103] [INSPIRE].

  81. 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].

  82. E.V. Shuryak and I. Zahed, Towards a theory of binary bound states in the quark gluon plasma, Phys. Rev. D 70 (2004) 054507 [hep-ph/0403127] [INSPIRE].

  83. E.V. Shuryak and I. Zahed, Rethinking the properties of the quark gluon plasma at T approximately T c , Phys. Rev. C 70 (2004) 021901 [hep-ph/0307267] [INSPIRE].

  84. J. Liao and E.V. Shuryak, Polymer chains and baryons in a strongly coupled quark-gluon plasma, Nucl. Phys. A 775 (2006) 224 [hep-ph/0508035] [INSPIRE].

  85. J. Liao and E.V. Shuryak, Electric flux tube in magnetic plasma, Phys. Rev. C 77 (2008) 064905 [arXiv:0706.4465] [INSPIRE].

    ADS  Google Scholar 

  86. J. Liao and E.V. Shuryak, Static \( \overline{Q} \) Q potentials and the magnetic component of QCD plasma near T c , Phys. Rev. D 82 (2010) 094007 [arXiv:0804.4890] [INSPIRE].

    ADS  Google Scholar 

  87. C. Ratti, R. Bellwied, M. Cristoforetti and M. Barbaro, Are there hadronic bound states above the QCD transition temperature?, Phys. Rev. D 85 (2012) 014004 [arXiv:1109.6243] [INSPIRE].

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, Tsinghua University, Beijing, 100084, China

    Shuzhe Shi

  2. Physics Department and Center for Exploration of Energy and Matter, Indiana University, 2401 N Milo B. Sampson Lane, Bloomington, IN, 47408, U.S.A.

    Shuzhe Shi & Jinfeng Liao

  3. RIKEN BNL Research Center, Bldg. 510A, Brookhaven National Laboratory, Upton, NY, 11973, U.S.A.

    Jinfeng Liao

Authors
  1. Shuzhe Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jinfeng Liao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jinfeng Liao.

Additional information

ArXiv ePrint: 1304.7752

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shi, S., Liao, J. Conserved charge fluctuations and susceptibilities in strongly interacting matter. J. High Energ. Phys. 2013, 104 (2013). https://doi.org/10.1007/JHEP06(2013)104

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP06(2013)104

Keywords

Search

Navigation