{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:31:06Z","timestamp":1772253066670,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,21]],"date-time":"2021-03-21T00:00:00Z","timestamp":1616284800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["18-02-40137"],"award-info":[{"award-number":["18-02-40137"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010334","name":"National Research Nuclear University MEPhI","doi-asserted-by":"publisher","award":["02.a03.21.0005"],"award-info":[{"award-number":["02.a03.21.0005"]}],"id":[{"id":"10.13039\/501100010334","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, we present a unified approach to the thermodynamics of hadron\u2013quark\u2013gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth\u2013Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that fulfills the Levinson theorem. The change in the composition of the system from a hadron resonance gas to a quark\u2013gluon plasma takes place in the narrow temperature interval of 150\u2013190 MeV, where the Mott dissociation of hadrons is triggered by the dropping quark mass as a result of the restoration of chiral symmetry. The deconfinement of quark and gluon degrees of freedom is regulated by the Polyakov loop variable that signals the breaking of the Z(3) center symmetry of the color SU(3) group of QCD. We suggest a Polyakov-loop quark\u2013gluon plasma model with O(\u03b1s) virial correction and solve the stationarity condition of the thermodynamic potential (gap equation) for the Polyakov loop. The resulting pressure is in excellent agreement with lattice QCD simulations up to high temperatures.<\/jats:p>","DOI":"10.3390\/sym13030514","type":"journal-article","created":{"date-parts":[[2021,3,21]],"date-time":"2021-03-21T23:47:41Z","timestamp":1616370461000},"page":"514","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quark Cluster Expansion Model for Interpreting Finite-T Lattice QCD Thermodynamics"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8399-5183","authenticated-orcid":false,"given":"David","family":"Blaschke","sequence":"first","affiliation":[{"name":"Instytut Fizyki Teoretycznej, Uniwersytet Wroc\u0142awski, 50-204 Wroc\u0142aw, Poland"},{"name":"Department of Theoretical Nuclear Physics, National Research Nuclear University (MEPhI), 115409 Moscow, Russia"},{"name":"Bogoliubov Laboratory of Theoretical Physics, JINR Dubna, 141980 Dubna, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kirill A.","family":"Devyatyarov","sequence":"additional","affiliation":[{"name":"Department of Theoretical Nuclear Physics, National Research Nuclear University (MEPhI), 115409 Moscow, Russia"},{"name":"Bogoliubov Laboratory of Theoretical Physics, JINR Dubna, 141980 Dubna, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6986-2341","authenticated-orcid":false,"given":"Olaf","family":"Kaczmarek","sequence":"additional","affiliation":[{"name":"Fakult\u00e4t f\u00fcr Physik, Universit\u00e4t Bielefeld, D-33615 Bielefeld, Germany"},{"name":"Key Laboratory of Quark &amp; Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,21]]},"reference":[{"key":"ref_1","first-page":"73","article-title":"Is there still any Tc mystery in lattice QCD? Results with physical masses in the continuum limit III","volume":"1009","author":"Fodor","year":"2010","journal-title":"J. High Energy Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"054503","DOI":"10.1103\/PhysRevD.85.054503","article-title":"The chiral and deconfinement aspects of the QCD transition","volume":"85","author":"Bazavov","year":"2012","journal-title":"Phys. Rev. D"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.physletb.2014.01.007","article-title":"Full result for the QCD equation of state with 2+1 flavors","volume":"730","author":"Borsanyi","year":"2014","journal-title":"Phys. Lett. B"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"094503","DOI":"10.1103\/PhysRevD.90.094503","article-title":"Equation of state in (2 + 1)-flavor QCD","volume":"90","author":"Bazavov","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"S1","DOI":"10.1016\/S0146-6410(00)90011-5","article-title":"Dyson-Schwinger equations: Density, temperature and continuum strong QCD","volume":"45","author":"Roberts","year":"2000","journal-title":"Prog. Part. Nucl. Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ppnp.2019.01.002","article-title":"QCD at finite temperature and chemical potential from Dyson\u2013Schwinger equations","volume":"105","author":"Fischer","year":"2019","journal-title":"Prog. Part. Nucl. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"034010","DOI":"10.1103\/PhysRevD.89.034010","article-title":"Spectral Functions for the Quark-Meson Model Phase Diagram from the Functional Renormalization Group","volume":"89","author":"Tripolt","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"034027","DOI":"10.1103\/PhysRevD.102.034027","article-title":"QCD phase structure from functional methods","volume":"102","author":"Gao","year":"2020","journal-title":"Phys. Rev. D"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/0550-3213(89)90349-0","article-title":"Hadrons Below the Chiral Phase Transition","volume":"321","author":"Gerber","year":"1989","journal-title":"Nucl. Phys. B"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"054029","DOI":"10.1103\/PhysRevD.99.054029","article-title":"Bound state properties from the functional renormalization group","volume":"99","author":"Alkofer","year":"2019","journal-title":"Phys. Rev. D"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1016\/j.physletb.2014.02.045","article-title":"Thermodynamics of QCD at vanishing density","volume":"731","author":"Herbst","year":"2014","journal-title":"Phys. Lett. B"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1006\/aphy.1994.1080","article-title":"Thermodynamics of a quark plasma beyond the mean field: A generalized Beth-Uhlenbeck approach","volume":"234","author":"Klevansky","year":"1994","journal-title":"Ann. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1016\/0375-9474(94)90743-9","article-title":"Thermodynamics of a quark - meson plasma in the Nambu-Jona-Lasinio model","volume":"576","author":"Zhuang","year":"1994","journal-title":"Nucl. Phys. A"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1134\/S1547477113070169","article-title":"Pion dissociation and Levinson\u2019s theorem in hot PNJL quark matter","volume":"10","author":"Wergieluk","year":"2013","journal-title":"Phys. Part. Nucl. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.nuclphysa.2013.05.018","article-title":"Quark-Hadron Phase Transition in the PNJL model for interacting quarks","volume":"913","author":"Yamazaki","year":"2013","journal-title":"Nucl. Phys. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.aop.2014.06.002","article-title":"Generalized Beth\u2013Uhlenbeck approach to mesons and diquarks in hot, dense quark matter","volume":"348","author":"Blaschke","year":"2014","journal-title":"Ann. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.nuclphysa.2013.12.010","article-title":"Quark-hadron phase transition in a three flavor PNJL model for interacting quarks","volume":"922","author":"Yamazaki","year":"2014","journal-title":"Nucl. Phys. A"},{"key":"ref_18","unstructured":"Torres-Rincon, J.M., and Aichelin, J. (2016). Equation of state of a quark-Polyakov loop-meson mixture in the PNJL model at finite temperature. arXiv."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"045205","DOI":"10.1103\/PhysRevC.96.045205","article-title":"Equation of state of a quark-meson mixture in the improved Polyakov\u2013Nambu\u2013Jona-Lasinio model at finite chemical potential","volume":"96","author":"Aichelin","year":"2017","journal-title":"Phys. Rev. C"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"094008","DOI":"10.1103\/PhysRevD.96.094008","article-title":"Mott dissociation of pions and kaons in hot, dense quark matter","volume":"96","author":"Blaschke","year":"2017","journal-title":"Phys. Rev. D"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Blaschke, D., Dubinin, A., and Turko, L. (2016). Mott-hadron resonance gas and lattice QCD thermodynamics. arXiv.","DOI":"10.1134\/S1063779615050093"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"473","DOI":"10.5506\/APhysPolBSupp.10.473","article-title":"Generalized Beth-Uhlenbeck approach to the equation of state for quark-hadron matter","volume":"10","author":"Blaschke","year":"2017","journal-title":"Acta Phys. Polon. Supp."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"215","DOI":"10.5506\/APhysPolBSupp.7.215","article-title":"Pion and sigma meson dissociation in a modified NJL model at finite temperature","volume":"7","author":"Dubinin","year":"2014","journal-title":"Acta Phys. Polon. Supp."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"014511","DOI":"10.1103\/PhysRevD.77.014511","article-title":"The QCD equation of state with almost physical quark masses","volume":"77","author":"Cheng","year":"2008","journal-title":"Phys. Rev. D"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.physletb.2019.05.013","article-title":"Chiral crossover in QCD at zero and non-zero chemical potentials","volume":"795","author":"Bazavov","year":"2019","journal-title":"Phys. Lett. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"485","DOI":"10.5506\/APhysPolBSupp.5.485","article-title":"Mott-Hagedorn Resonance Gas and Lattice QCD Results","volume":"5","author":"Turko","year":"2012","journal-title":"Acta Phys. Polon. Supp."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"014019","DOI":"10.1103\/PhysRevD.73.014019","article-title":"Phases of QCD: Lattice thermodynamics and a field theoretical model","volume":"73","author":"Ratti","year":"2006","journal-title":"Phys. Rev. D"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Kapusta, J.I. (1989). Finite Temperature Field Theory, Cambridge University Press.","DOI":"10.1088\/0954-3899\/15\/3\/005"},{"key":"ref_29","unstructured":"Peshier, A., K\u00e4mpfer, B., and Soff, G. (2003). The QCD equation of state and quark star properties. arXiv."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1023\/A:1024560420051","article-title":"On the Fourier transformation of renormalization invariant coupling","volume":"136","author":"Shirkov","year":"2003","journal-title":"Theor. Math. Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1140\/epjc\/s2005-02327-5","article-title":"Heavy quark potential and quarkonia dissociation rates","volume":"43","author":"Blaschke","year":"2005","journal-title":"Eur. Phys. J. C"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"114502","DOI":"10.1103\/PhysRevD.93.114502","article-title":"Polyakov loop in 2 + 1 flavor QCD from low to high temperatures","volume":"93","author":"Bazavov","year":"2016","journal-title":"Phys. Rev. D"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"014510","DOI":"10.1103\/PhysRevD.97.014510","article-title":"Equation of State in 2 + 1 Flavor QCD at High Temperatures","volume":"97","author":"Bazavov","year":"2018","journal-title":"Phys. Rev. D"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"054508","DOI":"10.1103\/PhysRevD.71.054508","article-title":"Thermodynamics of two flavor QCD to sixth order in quark chemical potential","volume":"71","author":"Allton","year":"2005","journal-title":"Phys. Rev. D"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"094029","DOI":"10.1103\/PhysRevD.90.094029","article-title":"QCD above Tc: Hadrons, partons, and the continuum","volume":"90","author":"Biro","year":"2014","journal-title":"Phys. Rev. D"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"012056","DOI":"10.1088\/1742-6596\/455\/1\/012056","article-title":"An effective model of QCD thermodynamics","volume":"455","author":"Turko","year":"2013","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"00134","DOI":"10.1051\/epjconf\/20147100134","article-title":"Effective degrees of freedom in QCD thermodynamics","volume":"71","author":"Turko","year":"2014","journal-title":"EPJ Web Conf."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Bastian, N.U.F., Blaschke, D., Fischer, T., and R\u00f6pke, G. (2018). Towards a Unified Quark-Hadron Matter Equation of State for Applications in Astrophysics and Heavy-Ion Collisions. Universe, 4.","DOI":"10.3390\/universe4060067"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"125040","DOI":"10.1103\/PhysRevD.91.125040","article-title":"Polyakov-loop suppression of colored states in a quark-meson-diquark plasma","volume":"91","author":"Blaschke","year":"2015","journal-title":"Phys. Rev. D"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Blaschke, D., Dubinin, A.S., and Zablocki, D. (2015). NJL model approach to diquarks and baryons in quark matter. PoS BaldinISHEPPXXII, 083.","DOI":"10.22323\/1.225.0083"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1140\/epja\/s10050-021-00343-9","article-title":"A unified quark-nuclear matter equation of state from the cluster virial expansion within the generalized Beth\u2013Uhlenbeck approach","volume":"57","author":"Bastian","year":"2021","journal-title":"Eur. Phys. J. A"},{"key":"ref_42","unstructured":"Plumberg, C.J., Welle, T., and Kapusta, J.I. (2018). QCD matter with a crossover and a first-order phase transition. PoS CORFU2018, 157."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"034901","DOI":"10.1103\/PhysRevC.101.034901","article-title":"QCD equation of state matched to lattice data and exhibiting a critical point singularity","volume":"101","author":"Parotto","year":"2020","journal-title":"Phys. Rev. C"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/3\/514\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:38:50Z","timestamp":1760161130000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/3\/514"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,21]]},"references-count":43,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,3]]}},"alternative-id":["sym13030514"],"URL":"https:\/\/doi.org\/10.3390\/sym13030514","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints202101.0106.v1","asserted-by":"object"}]},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,21]]}}}