Advertisement

Journal of High Energy Physics

, 2018:205 | Cite as

Higher order fluctuations and correlations of conserved charges from lattice QCD

  • Szabolcs BorsanyiEmail author
  • Zoltan Fodor
  • Jana N. Guenther
  • Sandor K. Katz
  • Attila Pasztor
  • Israel Portillo
  • Claudia Ratti
  • K. K. Szabó
Open Access
Regular Article - Theoretical Physics

Abstract

We calculate several diagonal and non-diagonal fluctuations of conserved charges in a system of 2+1+1 quark flavors with physical masses, on a lattice with size 483 × 12. Higher order fluctuations at μB = 0 are obtained as derivatives of the lower order ones, simulated at imaginary chemical potential. From these correlations and fluctuations we construct ratios of net-baryon number cumulants as functions of temperature and chemical potential, which satisfy the experimental conditions of strangeness neutrality and proton/baryon ratio. Our results qualitatively explain the behavior of the measured cumulant ratios by the STAR collaboration.

Keywords

Lattice QCD Phase Diagram of QCD Quark-Gluon Plasma 

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]
    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].
  2. [2]
    Y. Aoki, Z. Fodor, S.D. Katz and K.K. Szabo, The QCD transition temperature: Results with physical masses in the continuum limit, Phys. Lett. B 643 (2006) 46 [hep-lat/0609068] [INSPIRE].
  3. [3]
    Y. Aoki et al., The QCD transition temperature: results with physical masses in the continuum limit II., JHEP 06 (2009) 088 [arXiv:0903.4155] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    Wuppertal-Budapest collaboration, S. Borsányi et al., Is there still any T c mystery in lattice QCD? Results with physical masses in the continuum limit III, JHEP 09 (2010) 073 [arXiv:1005.3508] [INSPIRE].
  5. [5]
    T. Bhattacharya et al., QCD Phase Transition with Chiral Quarks and Physical Quark Masses, Phys. Rev. Lett. 113 (2014) 082001 [arXiv:1402.5175] [INSPIRE].
  6. [6]
    A. Bazavov et al., The chiral and deconfinement aspects of the QCD transition, Phys. Rev. D 85 (2012) 054503 [arXiv:1111.1710] [INSPIRE].
  7. [7]
    C.R. Allton et al., The QCD thermal phase transition in the presence of a small chemical potential, Phys. Rev. D 66 (2002) 074507 [hep-lat/0204010] [INSPIRE].
  8. [8]
    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].
  9. [9]
    R.V. Gavai and S. Gupta, QCD at finite chemical potential with six time slices, Phys. Rev. D 78 (2008) 114503 [arXiv:0806.2233] [INSPIRE].
  10. [10]
    MILC collaboration, S. Basak et al., QCD equation of state at non-zero chemical potential, PoS(LATTICE2008)171 (2008) [arXiv:0910.0276] [INSPIRE].
  11. [11]
    O. Kaczmarek et al., Phase boundary for the chiral transition in (2+1)-flavor QCD at small values of the chemical potential, Phys. Rev. D 83 (2011) 014504 [arXiv:1011.3130] [INSPIRE].
  12. [12]
    Z. Fodor and S.D. Katz, A New method to study lattice QCD at finite temperature and chemical potential, Phys. Lett. B 534 (2002) 87 [hep-lat/0104001] [INSPIRE].
  13. [13]
    P. de Forcrand and O. Philipsen, The QCD phase diagram for small densities from imaginary chemical potential, Nucl. Phys. B 642 (2002) 290 [hep-lat/0205016] [INSPIRE].
  14. [14]
    M. D’Elia and M.-P. Lombardo, Finite density QCD via imaginary chemical potential, Phys. Rev. D 67 (2003) 014505 [hep-lat/0209146] [INSPIRE].
  15. [15]
    Z. Fodor and S.D. Katz, Lattice determination of the critical point of QCD at finite T and mu, JHEP 03 (2002) 014 [hep-lat/0106002] [INSPIRE].
  16. [16]
    Z. Fodor and S.D. Katz, Critical point of QCD at finite T and mu, lattice results for physical quark masses, JHEP 04 (2004) 050 [hep-lat/0402006] [INSPIRE].
  17. [17]
    C. Bonati, M. D’Elia, F. Negro, F. Sanfilippo and K. Zambello, Curvature of the pseudocritical line in QCD: Taylor expansion matches analytic continuation, Phys. Rev. D 98 (2018) 054510 [arXiv:1805.02960] [INSPIRE].
  18. [18]
    F. Karsch, Determination of Freeze-out Conditions from Lattice QCD Calculations, Central Eur. J. Phys. 10 (2012) 1234 [arXiv:1202.4173] [INSPIRE].ADSGoogle Scholar
  19. [19]
    A. Bazavov et al., Freeze-out Conditions in Heavy Ion Collisions from QCD Thermodynamics, Phys. Rev. Lett. 109 (2012) 192302 [arXiv:1208.1220] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    S. Borsányi, Z. Fodor, S.D. Katz, S. Krieg, C. Ratti and K.K. Szabo, Freeze-out parameters: lattice meets experiment, Phys. Rev. Lett. 111 (2013) 062005 [arXiv:1305.5161] [INSPIRE].
  21. [21]
    S. Borsányi, Z. Fodor, S.D. Katz, S. Krieg, C. Ratti and K.K. Szabo, Freeze-out parameters from electric charge and baryon number fluctuations: is there consistency?, Phys. Rev. Lett. 113 (2014) 052301 [arXiv:1403.4576] [INSPIRE].
  22. [22]
    C. Ratti, Lattice QCD and heavy ion collisions: a review of recent progress, Rept. Prog. Phys. 81 (2018) 084301 [arXiv:1804.07810] [INSPIRE].
  23. [23]
    HotQCD collaboration, A. Bazavov et al., Skewness and kurtosis of net baryon-number distributions at small values of the baryon chemical potential, Phys. Rev. D 96 (2017) 074510 [arXiv:1708.04897] [INSPIRE].
  24. [24]
    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].
  25. [25]
    M. Cheng et al., The QCD equation of state with almost physical quark masses, Phys. Rev. D 77 (2008) 014511 [arXiv:0710.0354] [INSPIRE].
  26. [26]
    J.N. Guenther et al., The QCD equation of state at finite density from analytical continuation, Nucl. Phys. A 967 (2017) 720 [arXiv:1607.02493] [INSPIRE].
  27. [27]
    M. D’Elia, G. Gagliardi and F. Sanfilippo, Higher order quark number fluctuations via imaginary chemical potentials in N f = 2 + 1 QCD, Phys. Rev. D 95 (2017) 094503 [arXiv:1611.08285] [INSPIRE].
  28. [28]
    R. Bellwied et al., Fluctuations and correlations in high temperature QCD, Phys. Rev. D 92 (2015) 114505 [arXiv:1507.04627] [INSPIRE].
  29. [29]
    A. Roberge and N. Weiss, Gauge Theories With Imaginary Chemical Potential and the Phases of QCD, Nucl. Phys. B 275 (1986) 734 [INSPIRE].
  30. [30]
    V. Vovchenko, A. Pasztor, Z. Fodor, S.D. Katz and H. Stoecker, Repulsive baryonic interactions and lattice QCD observables at imaginary chemical potential, Phys. Lett. B 775 (2017) 71 [arXiv:1708.02852] [INSPIRE].
  31. [31]
    J.I. Kapusta and C. Gale, Finite-Temperature Field Theory, second edition, Cambridge University Press (2006).Google Scholar
  32. [32]
    A. Vuorinen, Quark number susceptibilities of hot QCD up to g**6 ln g, Phys. Rev. D 67 (2003) 074032 [hep-ph/0212283] [INSPIRE].
  33. [33]
    O. Philipsen and C. Pinke, Nature of the Roberge-Weiss transition in N f = 2 QCD with Wilson fermions, Phys. Rev. D 89 (2014) 094504 [arXiv:1402.0838] [INSPIRE].
  34. [34]
    C. Czaban, F. Cuteri, O. Philipsen, C. Pinke and A. Sciarra, Roberge-Weiss transition in N f = 2 QCD with Wilson fermions and N τ = 6, Phys. Rev. D 93 (2016) 054507 [arXiv:1512.07180] [INSPIRE].
  35. [35]
    C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro and F. Sanfilippo, Roberge-Weiss endpoint at the physical point of N f = 2 + 1 QCD, Phys. Rev. D 93 (2016) 074504 [arXiv:1602.01426] [INSPIRE].
  36. [36]
    C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro and F. Sanfilippo, Curvature of the chiral pseudocritical line in QCD: Continuum extrapolated results, Phys. Rev. D 92 (2015) 054503 [arXiv:1507.03571] [INSPIRE].
  37. [37]
    R. Bellwied et al., The QCD phase diagram from analytic continuation, Phys. Lett. B 751 (2015) 559 [arXiv:1507.07510] [INSPIRE].
  38. [38]
    P. Cea, L. Cosmai and A. Papa, Critical line of 2+1 flavor QCD: Toward the continuum limit, Phys. Rev. D 93 (2016) 014507 [arXiv:1508.07599] [INSPIRE].
  39. [39]
    A. Bazavov et al., The QCD Equation of State to \( \mathcal{O}\left({\mu}_B^6\right) \) from Lattice QCD, Phys. Rev. D 95 (2017) 054504 [arXiv:1701.04325] [INSPIRE].
  40. [40]
    C. McNeile, C.T.H. Davies, E. Follana, K. Hornbostel and G.P. Lepage, High-Precision c and b Masses and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD, Phys. Rev. D 82 (2010) 034512 [arXiv:1004.4285] [INSPIRE].
  41. [41]
    N. Haque, J.O. Andersen, M.G. Mustafa, M. Strickland and N. Su, Three-loop pressure and susceptibility at finite temperature and density from hard-thermal-loop perturbation theory, Phys. Rev. D 89 (2014) 061701 [arXiv:1309.3968] [INSPIRE].
  42. [42]
    N. Haque, A. Bandyopadhyay, J.O. Andersen, M.G. Mustafa, M. Strickland and N. Su, Three-loop HTLpt thermodynamics at finite temperature and chemical potential, JHEP 05 (2014) 027 [arXiv:1402.6907] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    H.T. Ding, S. Mukherjee, H. Ohno, P. Petreczky and H.P. Schadler, Diagonal and off-diagonal quark number susceptibilities at high temperatures, Phys. Rev. D 92 (2015) 074043 [arXiv:1507.06637] [INSPIRE].
  44. [44]
    H. Akaike, A New Look at the Statistical Model Identification, IEEE Trans. Automat. Contr. 19 (1974) 716.ADSMathSciNetCrossRefzbMATHGoogle Scholar
  45. [45]
    S. Dürr et al., Ab-Initio Determination of Light Hadron Masses, Science 322 (2008) 1224 [arXiv:0906.3599] [INSPIRE].ADSCrossRefGoogle Scholar
  46. [46]
    STAR collaboration, X. Luo, Energy Dependence of Moments of Net-Proton and Net-Charge Multiplicity Distributions at STAR, PoS(CPOD2014)019 (2015) [arXiv:1503.02558] [INSPIRE].
  47. [47]
    STAR collaboration, J. Thäder, Higher Moments of Net-Particle Multiplicity Distributions, Nucl. Phys. A 956 (2016) 320 [arXiv:1601.00951] [INSPIRE].
  48. [48]
    A. Andronic, P. Braun-Munzinger and J. Stachel, Hadron production in central nucleus-nucleus collisions at chemical freeze-out, Nucl. Phys. A 772 (2006) 167 [nucl-th/0511071] [INSPIRE].
  49. [49]
    P. Alba et al., Constraining the hadronic spectrum through QCD thermodynamics on the lattice, Phys. Rev. D 96 (2017) 034517 [arXiv:1702.01113] [INSPIRE].
  50. [50]
    Jülich Supercomputing Centre, JUQUEEN: IBM Blue Gene/Q Supercomputer System at the Jülich Supercomputing Centre, JLSRF 1 (2015) A1.Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of WuppertalWuppertalGermany
  2. 2.Eötvös UniversityBudapestHungary
  3. 3.Jülich Supercomputing CentreJülichGermany
  4. 4.Department of PhysicsUniversity of RegensburgRegensburgGermany
  5. 5.Department of PhysicsUniversity of HoustonHoustonU.S.A.

Personalised recommendations