Abstract
With a modified chemical potential dependent effective model for the gluon propagator, we try to locate the critical end point (CEP) of strongly interacting matter in the framework of Dyson-Schwinger equations (DSE). Beyond the chiral limit, we find that Nambu solution and Wigner solution could coexist in some area. Using the CornwallJackiw-Tomboulis (CJT) effective action, we show that these two phases are connected by a first order phase transition. We then locate CEP as the end point of the first order phase transition line. Meanwhile, based on CJT effective action, we give a direct calculation for the chiral susceptibility and thereby study the crossover.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Asakawa and K. Yazaki, Chiral Restoration at Finite Density and Temperature, Nucl. Phys. A 504 (1989) 668 [INSPIRE].
H. Meyer-Ortmanns, Phase transitions in quantum chromodynamics, Rev. Mod. Phys. 68 (1996) 473 [hep-lat/9608098] [INSPIRE].
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].
S.-x. Qin, L. Chang, H. Chen, Y.-x. Liu and C.D. Roberts, Phase diagram and critical endpoint for strongly-interacting quarks, Phys. Rev. Lett. 106 (2011) 172301 [arXiv:1011.2876] [INSPIRE].
P. Maris and P.C. Tandy, Bethe-Salpeter study of vector meson masses and decay constants, Phys. Rev. C 60 (1999) 055214 [nucl-th/9905056] [INSPIRE].
M.A. Stephanov, QCD phase diagram: An Overview, PoS(LAT2006)024 [hep-lat/0701002] [INSPIRE].
H. Min, J. Yu, S. Wei-Min and Z. Hong-Shi, Chiral susceptibility in an effective interaction model, Phys. Rev. D 77 (2008) 076008 [INSPIRE].
H. Chen, M. Baldo, G.F. Burgio and H.-J. Schulze, Hybrid stars with the Dyson-Schwinger quark model, Phys. Rev. D 84 (2011) 105023 [arXiv:1107.2497] [INSPIRE].
C.S. Fischer and J. Luecker, Propagators and phase structure of Nf = 2 and N f = 2 + 1 QCD, Phys. Lett. B 718 (2013) 1036 [arXiv:1206.5191] [INSPIRE].
C.S. Fischer, L. Fister, J. Luecker and J.M. Pawlowski, Polyakov loop potential at finite density, Phys. Lett. B 732 (2014) 273 [arXiv:1306.6022] [INSPIRE].
E. Gutierrez, A. Ahmad, A. Ayala, A. Bashir and A. Raya, The QCD phase diagram from Schwinger-Dyson equations, J. Phys. G 41 (2014) 075002 [arXiv:1304.8065] [INSPIRE].
Y. Jiang, H. Chen, W.-M. Sun and H.-S. Zong, Chiral phase transition of QCD at finite chemical potential, JHEP 04 (2013) 014 [INSPIRE].
Y. Jiang, H. Gong, W.-m. Sun and H.-s. Zong, The Wigner solution of quark gap equation at nonzero current quark mass and partial restoration of chiral symmetry at finite chemical potential, Phys. Rev. D 85 (2012) 034031 [arXiv:1107.5111] [INSPIRE].
Z.-F. Cui, C. Shi, Y.-H. Xia, Y. Jiang and H.-S. Zong, The Wigner solution of quark gap equation and chiral phase transition of QCD at finite temperature and nonzero chemical potential, Eur. Phys. J. C 73 (2013) 2612 [INSPIRE].
Z.-f. Cui, C. Shi, W.-m. Sun, Y.-l. Wang and H.-s. Zong, The Wigner Solution and QCD Phase Transitions in a Modified PNJL Model, Eur. Phys. J. C 74 (2014) 2782 [arXiv:1311.4014] [INSPIRE].
C. D. Roberts, Sebastian and M. Schmidt, Dyson-Schwinger equations: Density, temperature and continuum strong QCD, Prog. Part. Nucl. Phys. 45 (2000) s1.
P. Maris and C.D. Roberts, π- and K meson Bethe-Salpeter amplitudes, Phys. Rev. C 56 (1997) 3369 [nucl-th/9708029] [INSPIRE].
P. Maris, A. Raya, C.D. Roberts and S.M. Schmidt, Facets of confinement and dynamical chiral symmetry breaking, Eur. Phys. J. A 18 (2003) 231 [nucl-th/0208071] [INSPIRE].
J.M. Cornwall, R. Jackiw and E. Tomboulis, Effective Action for Composite Operators, Phys. Rev. D 10 (1974) 2428 [INSPIRE].
Y. Hatta and T. Ikeda, Universality, the QCD critical/tricritical point and the quark number susceptibility, Phys. Rev. D 67 (2003) 014028 [hep-ph/0210284] [INSPIRE].
K. Stam, Dynamical chiral symmetry breaking, Phys. Lett. B 152 (1985) 238 [INSPIRE].
P. Zhuang, J. Hufner and S.P. Klevansky, Thermodynamics of a quark - meson plasma in the Nambu-Jona-Lasinio model, Nucl. Phys. A 576 (1994) 525 [INSPIRE].
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].
D. Blaschke, A. Holl, C.D. Roberts and S.M. Schmidt, Analysis of chiral and thermal susceptibilities, Phys. Rev. C 58 (1998) 1758 [nucl-th/9803030] [INSPIRE].
M. He, F. Hu, W.-M. Sun and H.-S. Zong, Crossover from a continuum study of chiral susceptibility, Phys. Lett. B 675 (2009) 32 [arXiv:0904.0059] [INSPIRE].
H.S. Zong, J.L. Ping, H.T. Yang, X.F. Lü and F. Wang, The Calculation of vacuum properties from the global color symmetry model, Phys. Rev. D 67 (2003) 074004 [nucl-th/0201001] [INSPIRE].
F. Karsch and E. Laermann, Susceptibilities, the specific heat and a cumulant in two flavor QCD, Phys. Rev. D 50 (1994) 6954 [hep-lat/9406008] [INSPIRE].
E. Laermann and O. Philipsen, The Status of lattice QCD at finite temperature, Ann. Rev. Nucl. Part. Sci. 53 (2003) 163 [hep-ph/0303042] [INSPIRE].
A.M. Halasz, A.D. Jackson, R.E. Shrock, M.A. Stephanov and J.J.M. Verbaarschot, On the phase diagram of QCD, Phys. Rev. D 58 (1998) 096007 [hep-ph/9804290] [INSPIRE].
Z. Fodor and S.D. Katz, Lattice determination of the critical point of QCD at finite T and μ, JHEP 03 (2002) 014 [hep-lat/0106002] [INSPIRE].
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].
G. Endrodi, Z. Fodor, S.D. Katz and K.K. Szabo, The QCD phase diagram at nonzero quark density, JHEP 04 (2011) 001 [arXiv:1102.1356] [INSPIRE].
B.-J. Schaefer, J.M. Pawlowski and J. Wambach, The Phase Structure of the Polyakov-Quark-Meson Model, Phys. Rev. D 76 (2007) 074023 [arXiv:0704.3234] [INSPIRE].
I.M. Barbour, S.E. Morrison, E.G. Klepfish, J.B. Kogut and M.P. Lombardo, Results on finte density QCD, Nucl. Phys. Proc. Suppl. 60 (1998) 220 [INSPIRE].
Y. Jiang, Y.M. Shi, H. Li, W.M. Sun and H.S. Zong, The Calculation of f π and m π at Finite Chemical Potential, Phys. Rev. D 78 (2008) 116005 [arXiv:0810.0750] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1403.3797
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Shi, C., Wang, Yl., Jiang, Y. et al. Locate QCD critical end point in a continuum model study. J. High Energ. Phys. 2014, 14 (2014). https://doi.org/10.1007/JHEP07(2014)014
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2014)014