Plasma screening and the critical end point in the QCD phase diagram


  • Alejandro Ayala ICN-UNAM
  • B. Almeida Universidad de Sonora
  • J. J. Cobos-Martínez Universidad de Sonora
  • S. Hernández-Ortiz University of Washington
  • L. Hernández Universidad Autónoma Metropolitana
  • A. Raya Universidad Michoacana de San Nicolás de Hidalgo
  • M. E. Tejeda-Yeomans Universidad de Colima



Linear Sigma Model, CEP, HRGM


In heavy-ion collisions, fluctuations of conserved charges are known to be sensitive observables to probe criticality for the QCD phase transition and to locate the position of the putative critical end point (CEP). In this work we seek to show that the Linear Sigma Model with quarks produces an effective description of the QCD phase diagram in which deviations from a Hadron Resonance Gas are due to plasma screening effects, encoded in the contribution of the ring diagrams. Accounting for these, it is possible to include in the description the effect of long-range correlations. To set the model parameters we use LQCD results for the crossover transition at vanishing chemical potential. Finally, studying baryon number fluctuations from the model, we show that the CEP can be located within the HADES and/or the lowest end of the NICA energy domain, √ sNN ∼ 2 GeV.


Adam, J. and others, Nonmonotonic Energy Dependence of Net-Proton Number Fluctuations, Phys. Rev. Lett. 126 (2021) 092301, 10.1103/PhysRevLett.126.092301

Adamczewski-Musch, J. and others, Proton-number fluctuations in √ sNN =2.4 GeV Au + Au collisions studied with the High-Acceptance DiElectron Spectrometer (HADES), Phys. Rev. C 102 (2020) 024914, 10.1103/PhysRevC.102.024914

V. Kekelidze, et al., Feasibility study of heavy-ion collision physics at NICA JINR, Nucl. Phys. A 967 (2017) 884, 10.1016/j.nuclphysa.2017.06.031

V. Abgaryan et al., Status and initial physics performance studies of the MPD experiment at NICA (2022)

Senger, P., The heavy-ion program of the future FAIR facility, J. Phys. Conf. Ser. 798 (2017) 012062, 10.1088/1742-6596/798/1/012062

S. Borsanyi, et al., QCD Crossover at Finite Chemical Potential from Lattice Simulations, Phys. Rev. Lett. 125 (2020) 052001, 10.1103/PhysRevLett.125.052001

A. Bazavov et al., Chiral crossover in QCD at zero and non-zero chemical potentials, Phys. Lett. B 795 (2019) 15, 10.1016/j.physletb.2019.05.013

Y. Aoki, et al., The Order of the quantum chromodynamics transition predicted by the standard model of particle physics, Nature 443 (2006) 675, 10.1038/nature05120

Roessner, Simon and Ratti, Claudia and Weise, W., Polyakov loop, diquarks and the two-flavour phase diagram, Phys. Rev. D 75 (2007) 034007, 10.1103/PhysRevD.75.034007

A. Ayala, et al., On the critical end point in a two-flavor linear sigma model coupled to quarks, Eur. Phys. J. A 56 (2020) 71, 10.1140/epja/s10050-020-00086-z

M. Asakawa and K. Yazaki, Chiral Restoration at Finite Density and Temperature, Nucl. Phys. A 504 (1989) 668, 10.1016/0375-9474(89)90002-X

A. Ayala, S. Hernandez-Ortiz, and L. A. Hernandez, QCD phase diagram from chiral symmetry restoration: analytic approach at high and low temperature using the Linear Sigma Model with Quarks, Rev. Mex. Fis. 64 (2018) 302, 10.31349/RevMexFis.64.302

F. Gao and Y.-x. Liu, QCD phase transitions via a refined truncation of Dyson-Schwinger equations, Phys. Rev. D 94 (2016) 076009, 10.1103/PhysRevD.94.076009

F. Gao and J. M. Pawlowski, Chiral phase structure and critical end point in QCD (2020)

H.-T. Ding, F. Karsch, and S. Mukherjee, Thermodynamics of strong-interaction matter from Lattice QCD, Int. J. Mod. Phys. E 24 (2015) 1530007, 10.1142/S0218301315300076

S. Sharma, The QCD Equation of state and critical endpoint estimates at O(µ 6 B), Nucl. Phys. A 967 (2017) 728, 10.1016/j.nuclphysa.2017.05.008

S. Borsányi, et al., Lattice QCD equation of state at finite chemical potential from an alternative expansion scheme, Phys. Rev. Lett. 126 (2021) 232001, 10.1103/PhysRevLett.126.232001

F. Karsch, Lattice QCD results on cumulant ratios at freezeout, J. Phys. Conf. Ser. 779 (2017) 012015, 10.1088/1742-6596/779/1/012015

P. Braun-Munzinger, K. Redlich, and J. Stachel, Particle production in heavy ion collisions (2003)

M. Asakawa and M. Kitazawa, Fluctuations of conserved charges in relativistic heavy ion collisions: An introduction, Prog. Part. Nucl. Phys. 90 (2016) 299, 10.1016/j.ppnp.2016.04.002

J. Adam et al., Beam energy dependence of net- Λ fluctuations measured by the STAR experiment at the BNL Relativistic Heavy Ion Collider, Phys. Rev. C 102 (2020) 024903, 10.1103/PhysRevC.102.024903

M. Abdallah et al., Cumulants and Correlation Functions of Net-proton, Proton and Antiproton Multiplicity Distributions in Au+Au Collisions at RHIC (2021)

M. Abdallah et al., Measurement of the sixth-order cumulant of net-proton multiplicity distributions in Au+Au collisions at √ sNN = 27, 54.4, and 200 GeV at RHIC (2021)

Y. Hatta and T. Ikeda, Universality, the QCD critical / tricritical point and the quark number susceptibility, Phys. Rev. D 67 (2003) 014028, 10.1103/PhysRevD.67.014028

M. A. Stephanov, K. Rajagopal, and E. V. Shuryak, Eventby-event fluctuations in heavy ion collisions and the QCD critical point, Phys. Rev. D 60 (1999) 114028, 10.1103/PhysRevD.60.114028

A. Bzdak, V. Koch, and N. Strodthoff, Cumulants and correlation functions versus the QCD phase diagram, Phys. Rev. C 95 (2017) 054906, 10.1103/PhysRevC.95.054906

A. Bzdak, et al., Mapping the Phases of Quantum Chromodynamics with Beam Energy Scan, Phys. Rept. 853 (2020) 1, 10.1016/j.physrep.2020.01.005

C. Athanasiou, K. Rajagopal, and M. Stephanov, Using Higher Moments of Fluctuations and their Ratios in the Search for the QCD Critical Point, Phys. Rev. D 82 (2010) 074008, 10.1103/PhysRevD.82.074008

D. Mroczek, et al., Quartic cumulant of baryon number in the presence of a QCD critical point, Phys. Rev. C 103 (2021) 034901, 10.1103/PhysRevC.103.034901

M. A. Stephanov, Non-Gaussian fluctuations near the QCD critical point, Phys. Rev. Lett. 102 (2009) 032301, 10.1103/PhysRevLett.102.032301

M. A. Stephanov, On the sign of kurtosis near the QCD critical point, Phys. Rev. Lett. 107 (2011) 052301, 10.1103/PhysRevLett.107.052301

A. Ayala, et al., Collision energy dependence of the critical end point from baryon number fluctuations in the Linear Sigma Model with quarks, The European Physical Journal A 58 (2022) 87, 10.1140/epja/s10050-022-00732-8

A. Ayala, et al., QCD phase diagram in a magnetized medium from the chiral symmetry perspective: the linear sigma model with quarks and the Nambu–Jona-Lasinio model effective descriptions, Eur. Phys. J. A 57 (2021) 234, 10.1140/epja/s10050-021-00534-4

J. N. Guenther, Overview of the QCD phase diagram: Recent progress from the lattice, Eur. Phys. J. A 57 (2021) 136, 10.1140/epja/s10050-021-00354-6

J. Cleymans, et al., Comparison of chemical freeze-out criteria in heavy-ion collisions, Phys. Rev. C 73 (2006) 034905, 10.1103/PhysRevC.73.034905

X. Luo, Search for the QCD Critical Point with Fluctuations of Conserved Quantities in Relativistic Heavy-Ion Collisions at RHIC, EPJ Web Conf. 141 (2017) 04001, 10.1051/epjconf/201714104001

J. Xu, et al., Cumulants of net-proton, net-kaon, and netcharge multiplicity distributions in Au + Au collisions at √ sNN =7.7 , 11.5, 19.6, 27, 39, 62.4, and 200 GeV within the UrQMD model, Phys. Rev. C 94 (2016) 024901, 10.1103/PhysRevC.94.024901

S. He, et al., Effects of Nuclear Potential on the Cumulants of Net-Proton and Net-Baryon Multiplicity Distributions in Au+Au Collisions at √ sNN = 5 GeV, Phys. Lett. B 762 (2016) 296, 10.1016/j.physletb.2016.09.053




How to Cite

Ayala A, Almeida B, Cobos-Martínez JJ, Hernández-Ortiz S, Hernández L, Raya A, Tejeda-Yeomans ME. Plasma screening and the critical end point in the QCD phase diagram. Supl. Rev. Mex. Fis. [Internet]. 2022 Dec. 10 [cited 2024 Apr. 16];3(4):040917 1-8. Available from: