The QCD phase diagram at nonzero quark density

  • G. Endrődi
  • Z. Fodor
  • S. D. Katz
  • and K. K. Szabó
Article

Abstract

We determine the phase diagram of QCD on the μ − T plane for small to moderate chemical potentials. Two transition lines are defined with two quantities, the chiral condensate and the strange quark number susceptibility. The calculations are carried out on Nt =6, 8 and 10 lattices generated with a Symanzik improved gauge and stout-link improved 2+ 1 flavor staggered fermion action using physical quark masses. After carrying out the continuum extrapolation we find that both quantities result in a similar curvature of the transition line. Furthermore, our results indicate that in leading order the width of the transition region remains essentially the same as the chemical potential is increased.

Keywords

Lattice QCD Lattice Gauge Field Theories Lattice Quantum Field Theory 

References

  1. [1]
    PHENIX collaboration, A. Adare et al., Detailed measurement of the e + e pair continuum in p + p and Au+Au collisions at \( \sqrt {{{s_{NN}}}} = 200 \) GeV and implications for direct photon production, Phys. Rev. C 81 (2010) 034911 [arXiv:0912.0244] [SPIRES].ADSGoogle Scholar
  2. [2]
    Y. Aoki, G. Endrődi, Z. Fodor, S.D. Katz and K.K. Szabó, The order of the quantum chromodynamics transition predicted by the standard model of particle physics, Nature 443 (2006) 675 [hep-lat/0611014] [SPIRES].ADSCrossRefGoogle Scholar
  3. [3]
    J.I. Kapusta and E.S. Bowman, Multiple Critical Points in the QCD Phase Diagram, PoS (CPOD 2009)018 [arXiv:0908.0726] [SPIRES].
  4. [4]
    M. Cheng et al., The transition temperature in QCD, Phys. Rev. D 74 (2006) 054507 [hep-lat/0608013] [SPIRES].ADSGoogle Scholar
  5. [5]
    Y. Aoki, Z. Fodor, S.D. Katz and K.K. Szabó, The QCD transition temperature: Results with physical masses in the continuum limit, Phys. Lett. B 643 (2006) 46 [hep-lat/0609068] [SPIRES].ADSGoogle Scholar
  6. [6]
    Y. Aoki et al., The QCD transition temperature: results with physical masses in the continuum limit II, JHEP 06 (2009) 088 [arXiv:0903.4155] [SPIRES].ADSCrossRefGoogle Scholar
  7. [7]
    A. Bazavov et al., Equation of state and QCD transition at finite temperature, Phys. Rev. D 80 (2009) 014504 [arXiv:0903.4379] [SPIRES].ADSGoogle Scholar
  8. [8]
    Wuppertal -Budapest collaboration, S. Borsányi et al., Is there still any Tc mystery in lattice QCD? Results with physical masses in the continuum limit III, JHEP 09 (2010) 073 [arXi v: 1005. 3508] [SPIRES].ADSCrossRefGoogle Scholar
  9. [9]
    S. Borsányi et al., The QCD equation of state with dynamical quarks, JHEP 11 (2010) 077 [arXiv:1007.2580] [SPIRES].ADSCrossRefGoogle Scholar
  10. [10]
    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] [SPIRES].ADSGoogle Scholar
  11. [11]
    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] [SPIRES].ADSCrossRefGoogle Scholar
  12. [12]
    Z. Fodor, S.D. Katz and K.K. Szabo, The QCD equation of state at nonzero densities: Lattice result, Phys. Lett. B 568 (2003) 73 [hep-lat/0208078] [SPIRES].ADSGoogle Scholar
  13. [13]
    F. Csikor et al., Equation of state at finite temperature and chemical potential, lattice QCD results, JHEP 05 (2004) 046 [hep-lat/0401016] [SPIRES].ADSCrossRefGoogle Scholar
  14. [14]
    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] [SPIRES].ADSCrossRefGoogle Scholar
  15. [15]
    Z. Fodor, S.D. Katz and C. Schmidt, The density of states method at non-zero chemical potential, JHEP 03 (2007) 121 [hep-lat/0701022] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    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] [SPIRES].ADSGoogle Scholar
  17. [17]
    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] [SPIRES].ADSGoogle Scholar
  18. [18]
    R.V. Gavai and S. Gupta, QCD at finite chemical potential with six time slices, Phys. Rev. D 78 (2008) 114503 [arXiv:0806.2233] [SPIRES].ADSGoogle Scholar
  19. [19]
    MILC collaboration, S. Basak et al., QCD equation of state at non-zero chemical potential, PoS(LATTICE 2008)171 [arXiv:0910.0276] [SPIRES].
  20. [20]
    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] [SPIRES].ADSGoogle Scholar
  21. [21]
    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] [SPIRES].ADSCrossRefGoogle Scholar
  22. [22]
    M. D’Elia and M.-P. Lombardo, Finite density QCD via imaginary chemical potential, Phys. Rev. D 67 (2003) 014505 [hep-lat/0209146] [SPIRES].ADSGoogle Scholar
  23. [23]
    L.-K. Wu, X.-Q. Luo and H.-S. Chen, Phase structure of lattice QCD with two flavors of Wilson quarks at finite temperature and chemical potential, Phys. Rev. D 76 (2007) 034505 [hep-lat/0611035] [SPIRES].ADSGoogle Scholar
  24. [24]
    M. D’Elia, F. Di Renzo and M.P. Lombardo, The strongly interacting Quark Gluon Plasma and the critical behaviour of QCD at imaginary chemical potential, Phys. Rev. D 76 (2007) 114509 [arXiv:0705.3814] [SPIRES].ADSGoogle Scholar
  25. [25]
    S. Conradi and M. D’Elia, Imaginary chemical potentials and the phase of the fermionic determinant, Phys. Rev. D 76 (2007) 074501 [arXiv:0707.1987] [SPIRES].ADSGoogle Scholar
  26. [26]
    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] [SPIRES].
  27. [27]
    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] [SPIRES].CrossRefGoogle Scholar
  28. [28]
    M. D’Elia and F. Sanfilippo, Thermodynamics of two flavor QCD from imaginary chemical potentials, Phys. Rev. D 80 (2009) 014502 [arXiv:0904.1400] [SPIRES].ADSGoogle Scholar
  29. [29]
    J.T. Moscicki, M. Wos, M. Lamanna, P. de Forcrand and O. Philipsen, Lattice QCD Thermodynamics on the Grid, Comput. Phys. Commun. 181 (2010) 1715 [arXiv:0911.5682] [SPIRES].ADSMATHCrossRefGoogle Scholar
  30. [30]
    A. Alexandru, M. Faber, I. Horvath and K.-F. Liu, Lattice QCD at finite density via a new canonical approach, Phys. Rev. D 72 (2005) 114513 [hep-lat/0507020] [SPIRES].ADSGoogle Scholar
  31. [31]
    S. Kratochvila and P. de Forcrand, The canonical approach to finite density QCD, PoS(LAT2005)167 [hep-lat/0509143] [SPIRES].
  32. [32]
    S. Ejiri, Canonical partition function and finite density phase transition in lattice QCD, Phys. Rev. D 78 (2008) 074507 [arXiv:0804.3227] [SPIRES].ADSGoogle Scholar
  33. [33]
    K.N. Anagnostopoulos and J. Nishimura, New approach to the complex-action problem and its application to a nonperturbative study of superstring theory, Phys. Rev. D 66 (2002) 106008 [hep-th/0108041] [SPIRES].MathSciNetADSGoogle Scholar
  34. [34]
    J. Ambjørn, K.N. Anagnostopoulos, J. Nishimura and J.J.M. Verbaarschot, The factorization method for systems with a complex action -a test in Random Matrix Theory for finite density QCD-, JHEP 10 (2002) 062 [hep-lat/0208025] [SPIRES].ADSCrossRefGoogle Scholar
  35. [35]
    M.A. Clark and A.D. Kennedy, Accelerating Dynamical Fermion Computations using the Rational Hybrid Monte Carlo (RHMC) Algorithm with Multiple Pseudofermion Fields, Phys. Rev. Lett. 98 (2007) 051601 [hep-lat/0608015] [SPIRES].ADSCrossRefGoogle Scholar
  36. [36]
    Y. Aoki, Z. Fodor, S.D. Katz and K.K. Szabó, The equation of state in lattice QCD: With physical quark masses towards the continuum limit, JHEP 01 (2006) 089 [hep-lat/0510084] [SPIRES].ADSCrossRefMATHGoogle Scholar
  37. [37]
    G.I. Egri et al., Lattice QCD as a video game, Comput. Phys. Commun. 177 (2007) 631 [hep-lat/0611022] [SPIRES].ADSCrossRefGoogle Scholar
  38. [38]
    J. Cleymans and K. Redlich, Unified description of freeze-out parameters in relativistic heavy ion collisions, Phys. Rev. Lett. 81 (1998) 5284 [nucl-th/9808030] [SPIRES].ADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • G. Endrődi
    • 1
    • 2
  • Z. Fodor
    • 2
    • 3
    • 4
  • S. D. Katz
    • 2
  • and K. K. Szabó
    • 3
  1. 1.Institut für Theoretische PhysikUniversität RegensburgRegensburgGermany
  2. 2.Institute for T heoretical PhysicsEötvös UniversityBudapestHungary
  3. 3.Department of PhysicsUniversity of WuppertalWuppertalGermany
  4. 4.Jülich Supercomputing CenterJülichGermany

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