Physics of Particles and Nuclei Letters

, Volume 11, Issue 4, pp 342–351 | Cite as

Phase diagrams in nonlocal Polyakov-Nambu-Jona-Lasinio models constrained by lattice QCD results

  • G. A. Contrera
  • A. G. Grunfeld
  • D. B. Blaschke
Physics of Elementary Particles and Atomic Nuclei. Theory


Based on lattice QCD-adjusted SU(2)f nonlocal Polyakov-Nambu-Jona-Lasinio (PNJL) models, we investigate how the location of the critical endpoint in the QCD phase diagram depends on the strenght of the vector meson coupling, as well as the Polyakov-loop (PL) potential and the form factors of the covariant model. The latter are constrained by lattice QCD data for the quark propagator. The strength of the vector coupling is adjusted such as to reproduce the slope of the pseudocritical temperature for the chiral phase transition at low chemical potential extracted recently from lattice QCD simulations. Our study supports the existence of a critical endpoint in the QCD phase diagram albeit the constraint for the vector coupling shifts its location to lower temperatures and higher baryochemical potentials than in the case without it.


Nucleus Letter Quark Matter Polyakov Loop Mean Field Approximation Quark Propagator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    M. A. Stephanov, “QCD phase diagram,” in An Overview, PoS LAT 2006 024 (2006).Google Scholar
  2. 2.
    A. Bazavov et al., “The chiral and deconfinement aspects of the QCD transition,” Phys. Rev. D 85, 054503 (2012).ADSCrossRefGoogle Scholar
  3. 3.
    S. Ejiri, “Lattice QCD at finite temperature,” Nucl. Phys. Proc. Suppl. 94, 19 (2001).ADSCrossRefGoogle Scholar
  4. 4.
    N. M. Bratovic, T. Hatsuda, and W. Weise, “Role of vector interaction and axial anomaly in the PNJL modeling of the QCD phase diagram,” Phys. Lett. B 719, 131 (2013).ADSCrossRefGoogle Scholar
  5. 5.
    S. Carignano, D. Nickel, and M. Buballa, “Influence of vector interaction and Polyakov loop dynamics on inhomogeneous chiral symmetry breaking phases,” Phys. Rev. D 82, 054009 (2010).ADSCrossRefGoogle Scholar
  6. 6.
    M. Kitazawa et al., “Chiral and color superconducting phase transitions with vector interaction in a simple model,” Prog. Theor. Phys. 108, 929 (2002).ADSCrossRefMATHGoogle Scholar
  7. 7.
    D. Blaschke, M. K. Volkov, and V. L. Yudichev, “Coexistence of color superconductivity and chiral symmetry breaking within the NJL model,” Eur. Phys. J. A 17, 103 (2003).ADSCrossRefGoogle Scholar
  8. 8.
    T. Hatsuda et al., “New critical point induced by the axial anomaly in dense QCD,” Phys. Rev. Lett. 97, 122001 (2006).ADSCrossRefGoogle Scholar
  9. 9.
    E. S. Bowman and J. I. Kapusta, “Critical points in the linear sigma model with quarks,” Phys. Rev. C 79, 015202 (2009).ADSCrossRefGoogle Scholar
  10. 10.
    T. Kunihiro, Y. Minami, and Z. Zhang, “QCD critical points and their associated soft modes,” Prog. Theor. Phys. Suppl. 186, 447 (2010).ADSCrossRefGoogle Scholar
  11. 11.
    Z. Zhang and T. Kunihiro, “Vector interaction, charge neutrality and multiple chiral critical point structures,” Phys. Rev. D 80, 014015 (2009).ADSCrossRefGoogle Scholar
  12. 12.
    D. Blaschke et al., “Exploring the QCD phase diagram with compact stars,” Nucl. Phys. Proc. Suppl. 141, 137 (2005).ADSCrossRefGoogle Scholar
  13. 13.
    A. Andronic et al., “Hadron production in ultra-relativistic nuclear collisions: Quarkyonic matter and a triple point in the phase diagram of QCD,” Nucl. Phys. A 837, 65 (2010).ADSCrossRefGoogle Scholar
  14. 14.
    Y. Nambu and G. Jona-Lasinio, “Dynamical model of elementary particles based on an analogy with superconductivity,” Phys. Rev. 122, 345 (1961); 124, 246 (1961).ADSCrossRefGoogle Scholar
  15. 15.
    U. Vogl and W. Weise, “The Nambu and Jona Lasinio model: Its implications for hadrons and nuclei,” Prog. Part. Nucl. Phys. 27, 195 (1991).ADSCrossRefGoogle Scholar
  16. 16.
    S. P. Klevansky, “The Nambu-Jona-Lasinio model of quantum chromodynamics,” Rev. Mod. Phys. 64, 649 (1992).ADSCrossRefMathSciNetGoogle Scholar
  17. 17.
    T. Hatsuda and T. Kunihiro, “QCD phenomenology based on a chiral effective Lagrangian,” Phys. Rept. 247, 221 (1994).ADSCrossRefGoogle Scholar
  18. 18.
    C. Ratti, M. A. Thaler, and W. Weise, “Phases of QCD: Lattice thermodynamics and a field theoretical model,” Phys. Rev. D 73, 014019 (2006).ADSCrossRefGoogle Scholar
  19. 19.
    S. Roessner, C. Ratti, and W. Weise, “Polyakov loop, diquarks and the two-flavour phase diagram,” Phys. Rev. D 75, 034007 (2007).ADSCrossRefGoogle Scholar
  20. 20.
    C. Sasaki, B. Friman, and K. Redlich, “Susceptibilities and the Phase Structure of a Chiral Model with Polyakov Loops,” Phys. Rev. D 75, 074013 (2007).ADSCrossRefGoogle Scholar
  21. 21.
    K. Fukushima, “Phase diagrams in the three-flavor Nambu-Jona-Lasinio model with the Polyakov loop,” Phys. Rev. D 77, 114028 (2008); ibid. 78, 039902 (2008).ADSCrossRefGoogle Scholar
  22. 22.
    H. Abuki et al., “Chiral crossover, deconfinement and quarkyonic matter within a Nambu-Jona Lasinio model with the Polyakov loop,” Phys. Rev. D 78, 034034 (2008).ADSCrossRefGoogle Scholar
  23. 23.
    S. M. Schmidt, D. Blaschke, and Y. L. Kalinovsky, “Scalar-pseudoscalar meson masses in nonlocal effective QCD at finite temperature,” Phys. Rev. C 50, 435 (1994).ADSCrossRefGoogle Scholar
  24. 24.
    G. V. Efimov and S. N. Nedelko, “Nambu-Jona-Lasinio model with the homogeneous background gluon field,” Phys. Rev. D 51, 176 (1995).ADSCrossRefGoogle Scholar
  25. 25.
    G. A. Contrera, D. Gomez Dumm, and N. N. Scoccola, “Nonlocal SU(3) chiral quark models at finite temperature: the role of the Polyakov loop,” Phys. Lett. B 661, 113 (2008).ADSCrossRefGoogle Scholar
  26. 26.
    P. Demorest et al., “Shapiro delay measurement of a two solar mass neutron star,” Nature 467, 1081 (2010).ADSCrossRefGoogle Scholar
  27. 27.
    J. Antoniadis et al., “A massive pulsar in a compact relativistic binary,” Science 340, 6131 (2013).ADSCrossRefGoogle Scholar
  28. 28.
    T. Klähn et al., “Modern compact star observations and the quark matter equation of state,” Phys. Lett. B 654, 170 (2007).ADSCrossRefGoogle Scholar
  29. 29.
    M. Orsaria et al., “Quark-hybrid matter in the cores of massive neutron stars,” Phys. Rev. D 87, 023001 (2013).ADSCrossRefGoogle Scholar
  30. 30.
    T. Klahn, D. B. Blaschke, and R. Lastowiecki, “Implications of the measurement of pulsars with two solar masses for quark matter in compact stars and HIC. A NJL model case study,” Phys. Rev. D 88, 085001 (2013).ADSCrossRefGoogle Scholar
  31. 31.
    M. Orsaria et al., Quark Deconfinement in High-Mass Neutron Stars, Phys. Rev. C 89, 015806 (2014).ADSCrossRefGoogle Scholar
  32. 32.
    G. Y. Shao et al., Isoscalar-Vector Interaction and Hybrid Quark Core in Massive Neutron Stars, Phys. Rev. D 87, 096012 (2013).ADSCrossRefGoogle Scholar
  33. 33.
    D. B. Blaschke et al., “Hybrid stars within a covariant, nonlocal chiral quark model,” Phys. Rev. C 75, 065804 (2007).ADSCrossRefGoogle Scholar
  34. 34.
    D. Blaschke et al., Nonlocal PNJL Models and Heavy Hybrid Stars, PoS ConfinementX, 2012, 249.Google Scholar
  35. 35.
    D. Blaschke, D. E. Alvarez-Castillo, and S. Benic, Mass-Radius Constraints for Compact Stars and a Critical Endpoint, PoS CPOD 2013, 063; [arXiv:1310.3803 [nucl-th]].Google Scholar
  36. 36.
    D. E. Alvarez-Castillo et al., Crossover Transition to Quark Matter in Heavy Hybrid Stars, Acta Phys. Polon. Supp. 7, 203 (2014).Google Scholar
  37. 37.
    G. A. Contrera, M. Orsaria, and N. N. Scoccola, “Nonlocal Polyakov-Nambu-Jona-Lasinio model with wave function renormalization at finite temperature and chemical potential,” Phys. Rev. D 82, 054026 (2010).ADSCrossRefGoogle Scholar
  38. 38.
    D. Gomez Dumm and N. N. Scoccola, “Characteristics of the chiral phase transition in nonlocal quark models,” Phys. Rev. C 72, 014909 (2005).ADSCrossRefGoogle Scholar
  39. 39.
    S. Noguera and N. N. Scoccola, “Nonlocal chiral quark models with wavefunction renormalization: sigma properties and pion-pion scattering parameters,” Phys. Rev. D 78, 114002 (2008).ADSCrossRefGoogle Scholar
  40. 40.
    D. Gomez Dumm et al., “Color neutrality effects in the phase diagram of the PNJL model,” Phys. Rev. D 78, 114021 (2008).ADSCrossRefGoogle Scholar
  41. 41.
    M. B. Parappilly et al., “Scaling behavior of quark propagator in full QCD,” Phys. Rev. D 73, 054504 (2006).ADSCrossRefGoogle Scholar
  42. 42.
    W. Kamleh et al., “Unquenching effects in the quark and gluon propagator,” Phys. Rev. D 76, 094501 (2007).ADSCrossRefGoogle Scholar
  43. 43.
    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, 014504 (2011).ADSCrossRefGoogle Scholar
  44. 44.
    V. A. Dexheimer and S. Schramm, “A novel approach to model hybrid stars,” Phys. Rev. C 81, 045201 (2010).ADSCrossRefGoogle Scholar
  45. 45.
    B.-J. Schaefer, J. M. Pawlowski, and J. Wambach, “The phase structure of the Polyakov-Quark-Meson model,” Phys. Rev. D 76, 074023 (2007).ADSCrossRefGoogle Scholar
  46. 46.
    V. Pagura, D. Gomez Dumm, and N. N. Scoccola, “Deconfinement and chiral restoration in non-local PNJL models at zero and imaginary chemical potential,” Phys. Lett. B 707, 76 (2012).ADSCrossRefGoogle Scholar
  47. 47.
    D. Horvatic et al., “Width of the QCD transition in a Polyakov-loop DSE model,” Phys. Rev. D 84, 016005 (2011).ADSCrossRefGoogle Scholar
  48. 48.
    Y. Sakai et al., “Entanglement between deconfinement transition and chiral symmetry restoration,” Phys. Rev. D 82, 076003 (2010).ADSCrossRefGoogle Scholar
  49. 49.
    M. Dutra et al., “Polyakov-Nambu-Jona-Lasinio phase diagrams and quarkyonic phase from order parameters,” Phys. Rev. D 88, 114013 (2013).ADSCrossRefGoogle Scholar
  50. 50.
    D. B. Blaschke et al., “Accessibility of color superconducting quark matter phases in heavy-ion collisions,” Acta Phys. Polon. Supp. 3, 741 (2010).Google Scholar
  51. 51.
    G. Y. Shao et al., “Phase diagrams in the Hadron-PNJL model,” Phys. Rev. D 84, 034028 (2011).ADSCrossRefGoogle Scholar
  52. 52.
    T. Sasaki et al., “QCD phase diagram at finite baryon and isospin chemical potentials,” Phys. Rev. D 82, 116004 (2010).ADSCrossRefGoogle Scholar
  53. 53.
    T. Hell, K. Kashiwa, and W. Weise, “Impact of vectorcurrent interactions on the QCD phase diagram,” J. Mod. Phys. 4, 644 (2013).CrossRefGoogle Scholar
  54. 54.
    C. Sasaki and K. Redlich, “An effective gluon potential and hybrid approach to Yang-Mills thermodynamics,” Phys. Rev. D 86, 014007 (2012).ADSCrossRefGoogle Scholar
  55. 55.
    M. Ruggieri et al., “Polyakov loop and gluon quasiparticles in Yang-Mills thermodynamics,” Phys. Rev. D 86, 054007 (2012).ADSCrossRefGoogle Scholar
  56. 56.
    K. Fukushima and K. Kashiwa, “Polyakov loop and QCD thermodynamics from the gluon and ghost propagators,” Phys. Lett. B 723, 360 (2013).ADSCrossRefGoogle Scholar
  57. 57.
    A. E. Radzhabov et al., “Nonlocal PNJL model beyond mean field and the QCD phase transition,” Phys. Rev. D 83, 116004 (2011).ADSCrossRefMathSciNetGoogle Scholar
  58. 58.
    D. B. Blaschke et al., “Chiral condensate and chemical freeze-out,” Phys. Part. Nucl. Lett. 8, 811 (2011); “Few body systems,” 53, 99 (2012).CrossRefGoogle Scholar
  59. 59.
    L. Turko et al., “Mott-Hagedorn resonance gas and lattice QCD results,” Acta Phys. Polon. Supp. 5, 485 (2012).CrossRefGoogle Scholar
  60. 60.
    L. Turko et al., “An effective model of QCD thermodynamics,” J. Phys. Conf. Ser. 455, 012056 (2013).ADSCrossRefGoogle Scholar
  61. 61.
    A. Wergieluk et al., “Pion dissociation and Levinson’s theorem in hot PNJL quark matter,” Phys. Part. Nucl. Lett. 10, 660 (2013).CrossRefGoogle Scholar
  62. 62.
    A. Dubinin, D. Blaschke, and Y. L. Kalinovsky, Pion and Sigma Meson Dissociation in a Modified NJL Model at Finite Temperature, Acta Phys. Polon. Supp. 7, 215 (2014).CrossRefGoogle Scholar
  63. 63.
    S. Benic and D. Blaschke, “Finite temperature Mott transition in a nonlocal PNJL model,” Acta Phys. Polon. Supp. 6, 947 (2013).CrossRefGoogle Scholar
  64. 64.
    S. Benic et al., “Medium induced Lorentz symmetry breaking effects in nonlocal PNJL models,” Phys. Rev. D 89, 016007 (2014).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • G. A. Contrera
    • 1
    • 2
    • 3
  • A. G. Grunfeld
    • 2
    • 4
  • D. B. Blaschke
    • 3
    • 5
  1. 1.Gravitation, Astrophysics and Cosmology GroupFCAyG, UNLPLa PlataArgentina
  2. 2.CONICETBuenos AiresArgentina
  3. 3.Institute for Theoretical PhysicsUniversity of WroclawWroclawPoland
  4. 4.Departamento de FisicaComision Nacional de Energia AtomicaBuenos AiresArgentina
  5. 5.Bogoliubov Laboratory for Theoretical PhysicsJINRDubnaRussia

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