QCD equation of state to O(μB6) from lattice QCD

Bazavov, A.; Ding, H. -T.; Hegde, P.; Kaczmarek, O.; Karsch, F.; Laermann, E.; Maezawa, Y.; Mukherjee, Swagato; Ohno, H.; Petreczky, P.; Sandmeyer, H.; Steinbrecher, P.; Schmidt, C.; Sharma, S.; Soeldner, W.; Wagner, M.

doi:10.1103/PhysRevD.95.054504

Title: QCD equation of state to $O (μ_{B}^{6})$ from lattice QCD

Journal Article · Tue Mar 07 00:00:00 EST 2017 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.95.054504· OSTI ID:1376098

Bazavov, A. ^[1]; Ding, H. -T. ^[2]; Hegde, P. ^[3]; Kaczmarek, O. ^[4]; Karsch, F. ^[5]; Laermann, E. ^[6]; Maezawa, Y. ^[7]; Mukherjee, Swagato ^[8]; Ohno, H. ^[9]; Petreczky, P. ^[8]; Sandmeyer, H. ^[6]; Steinbrecher, P. ^[10]; Schmidt, C. ^[6]; Sharma, S. ^[8]; Soeldner, W. ^[11]; Wagner, M. ^[12]

Michigan State Univ., East Lansing, MI (United States). Department of Computational Mathematics, Science and Engineering and Department of Physics and Astronomy
China Central Normal Univ., Wuhan (China). Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics
Indian Institute of Science, Bangalore (India). Center for High Energy Physics
China Central Normal Univ., Wuhan (China). Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics; University of Bielefeld (Germany). Faculty of Physics
University of Bielefeld (Germany). Faculty of Physics; Brookhaven National Lab. (BNL), Upton, NY (United States). Physics Department
University of Bielefeld (Germany). Faculty of Physics
Kyoto University (Japan). Yukawa Institute for Theoretical Physics
Brookhaven National Lab. (BNL), Upton, NY (United States). Physics Department
Brookhaven National Lab. (BNL), Upton, NY (United States). Physics Department; University of Tsukuba (Japan). Center for Computational Sciences
University of Bielefeld (Germany). Faculty of Physics ; Brookhaven National Lab. (BNL), Upton, NY (United States). Physics Department
University of Regensburg (Germany). Institute of Theoretical Physics
NVIDIA GmbH (Germany)

In this work, we calculated the QCD equation of state using Taylor expansions that include contributions from up to sixth order in the baryon, strangeness and electric charge chemical potentials. Calculations have been performed with the Highly Improved Staggered Quark action in the temperature range T ϵ [135 MeV, 330 MeV] using up to four different sets of lattice cut-offs corresponding to lattices of size N$$3\atop{σ}$$ × N_τ with aspect ratio N_σ/N_τ = 4 and N_τ = 6-16. The strange quark mass is tuned to its physical value and we use two strange to light quark mass ratios m_s/m_l = 20 and 27, which in the continuum limit correspond to a pion mass of about 160 MeV and 140 MeV respectively. Sixth-order results for Taylor expansion coefficients are used to estimate truncation errors of the fourth-order expansion. We show that truncation errors are small for baryon chemical potentials less then twice the temperature (µ_B ≤ 2T ). The fourth-order equation of state thus is suitable for √the modeling of dense matter created in heavy ion collisions with center-of-mass energies down to √sNN ~ 12 GeV. We provide a parametrization of basic thermodynamic quantities that can be readily used in hydrodynamic simulation codes. The results on up to sixth order expansion coefficients of bulk thermodynamics are used for the calculation of lines of constant pressure, energy and entropy densities in the T -µ_B plane and are compared with the crossover line for the QCD chiral transition as well as with experimental results on freeze-out parameters in heavy ion collisions. These coefficients also provide estimates for the location of a possible critical point. Lastly, we argue that results on sixth order expansion coefficients disfavor the existence of a critical point in the QCD phase diagram for µ_B/T ≤ 2 and T/T_c(µ_B = 0) > 0.9.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0012704; SC001270; 05P12PBCTA

OSTI ID:: 1376098

Alternate ID(s):: OSTI ID: 1346090; OSTI ID: 1431282

Report Number(s):: BNL-113924-2017-JA; BNL-203400-2018-JAAM

Journal Information:: Physical Review. D., Vol. 95, Issue 5; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 279 works

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Critical point signatures in the cluster expansion in fugacities Vovchenko, Volodymyr; Greiner, Carsten; Koch, Volker Physical Review D, Vol. 101, Issue 1 https://doi.org/10.1103/physrevd.101.014015	journal	January 2020
Lattice-based equation of state at finite baryon number, electric charge and strangeness chemical potentials Noronha-Hostler, J.; Parotto, P.; Ratti, C. arXiv https://doi.org/10.48550/arxiv.1902.06723	text	January 2019
Baryon number fluctuations in chiral effective models and their phenomenological implications Almási, Gábor András; Friman, Bengt; Redlich, Krzysztof Physical Review D, Vol. 96, Issue 1 https://doi.org/10.1103/physrevd.96.014027	journal	July 2017
Susceptibilities of strongly interacting matter in a finite volume Spieles, Christian; Bleicher, Marcus; Greiner, Carsten Journal of Physics G: Nuclear and Particle Physics, Vol. 46, Issue 2 https://doi.org/10.1088/1361-6471/aaf82f	journal	January 2019
Exploring the partonic phase at finite chemical potential within an extended off-shell transport approach Moreau, Pierre; Soloveva, Olga; Oliva, Lucia Physical Review C, Vol. 100, Issue 1 https://doi.org/10.1103/physrevc.100.014911	journal	July 2019
Reliable estimation of the radius of convergence in finite density QCD Giordano, Matteo; Pásztor, Attila arXiv https://doi.org/10.48550/arxiv.1904.01974	text	January 2019
Thermodynamical consistency of quasiparticle model at finite baryon density Ma, Hong-Hao; Lin, Kai; Qian, Wei-Liang Physical Review C, Vol. 100, Issue 1 https://doi.org/10.1103/physrevc.100.015206	journal	July 2019
Constraining the hadronic spectrum through QCD thermodynamics on the lattice Alba, Paolo; Bellwied, Rene; Borsanyi, Szabolcs arXiv https://doi.org/10.48550/arxiv.1702.01113	text	January 2017
Temperature Dependence of the Axion Mass in a Scenario Where the Restoration of Chiral Symmetry Drives the Restoration of the $U_A(1)$ Symmetry Horvatić, Davor; Kekez, Dalibor; Klabučar, Dubravko arXiv https://doi.org/10.48550/arxiv.1909.09879	text	January 2019
Landau and Eckart frames for relativistic fluids in nuclear collisions Monnai, Akihiko arXiv https://doi.org/10.48550/arxiv.1904.11940	text	January 2019
Wigner solution of the quark gap equation Cui, Zhu-Fang; Xu, Shu-Sheng; Li, Bo-Lin The European Physical Journal C, Vol. 78, Issue 9 https://doi.org/10.1140/epjc/s10052-018-6264-4	journal	September 2018
Functional renormalization group study of the quark-meson model with $ω$ meson Zhang, Hui; Hou, Defu; Kojo, Toru Physical Review D, Vol. 96, Issue 11 https://doi.org/10.1103/physrevd.96.114029	journal	December 2017
Looking for the Phase Transition—Recent NA61/SHINE Results Turko, Ludwik Universe, Vol. 4, Issue 3 https://doi.org/10.3390/universe4030052	journal	March 2018
Temperature Dependence of the Axion Mass in a Scenario Where the Restoration of Chiral Symmetry Drives the Restoration of the UA(1) Symmetry Horvatić, Davor; Kekez, Dalibor; Klabučar, Dubravko Universe, Vol. 5, Issue 10 https://doi.org/10.3390/universe5100208	journal	October 2019
Baryon number probability distribution at finite temperature Sun, Ke-xin; Wen, Rui; Fu, Wei-jie arXiv https://doi.org/10.48550/arxiv.1805.12025	text	January 2018
Equation of state of a quark-meson mixture in the improved Polyakov–Nambu–Jona-Lasinio model at finite chemical potential Torres-Rincon, Juan M.; Aichelin, Joerg Physical Review C, Vol. 96, Issue 4 https://doi.org/10.1103/physrevc.96.045205	journal	October 2017
Landau and Eckart frames for relativistic fluids in nuclear collisions Monnai, Akihiko Physical Review C, Vol. 100, Issue 1 https://doi.org/10.1103/physrevc.100.014901	journal	July 2019
Dynamical versus equilibrium properties of the QCD phase transition: A holographic perspective Rougemont, Romulo; Critelli, Renato; Noronha-Hostler, Jacquelyn Physical Review D, Vol. 96, Issue 1 https://doi.org/10.1103/physrevd.96.014032	journal	July 2017
Search for the QCD critical point with fluctuations of conserved quantities in relativistic heavy-ion collisions at RHIC: an overview Luo, Xiaofeng; Xu, Nu Nuclear Science and Techniques, Vol. 28, Issue 8 https://doi.org/10.1007/s41365-017-0257-0	journal	July 2017
The analytic structure of thermodynamic systems with repulsive interactions Taradiy, Kirill; Motornenko, Anton; Vovchenko, Volodymyr arXiv https://doi.org/10.48550/arxiv.1904.08259	text	January 2019
Analytic structure of thermodynamic systems with repulsive interactions Taradiy, Kirill; Motornenko, Anton; Vovchenko, Volodymyr Physical Review C, Vol. 100, Issue 6 https://doi.org/10.1103/physrevc.100.065202	journal	December 2019
Thermodynamics of a quark-gluon plasma at finite baryon density Khaidukov, Z. V.; Simonov, Yu. A. Physical Review D, Vol. 100, Issue 7 https://doi.org/10.1103/physrevd.100.076009	journal	October 2019
Lattice-based equation of state at finite baryon number, electric charge, and strangeness chemical potentials Noronha-Hostler, J.; Parotto, P.; Ratti, C. Physical Review C, Vol. 100, Issue 6 https://doi.org/10.1103/physrevc.100.064910	journal	December 2019
Calculating the equation of state of dense quark-gluon plasma using the complex Langevin equation Sexty, Dénes Physical Review D, Vol. 100, Issue 7 https://doi.org/10.1103/physrevd.100.074503	journal	October 2019
Critical point signatures in the cluster expansion in fugacities Vovchenko, Volodymyr; Greiner, Carsten; Koch, Volker GSI Helmholtzzentrum fuer Schwerionenforschung, GSI, Darmstadt https://doi.org/10.15120/gsi-2021-00617	text	January 2020
Cluster expansion model for QCD baryon number fluctuations: No phase transition at $μ_{B} / T < π$ Vovchenko, Volodymyr; Steinheimer, Jan; Philipsen, Owe Physical Review D, Vol. 97, Issue 11 https://doi.org/10.1103/physrevd.97.114030	journal	June 2018
Strangeness neutrality and baryon-strangeness correlations Fu, Wei-jie; Pawlowski, Jan M.; Rennecke, Fabian arXiv https://doi.org/10.48550/arxiv.1809.01594	text	January 2018
Cosmic QCD Epoch at Nonvanishing Lepton Asymmetry Wygas, Mandy M.; Oldengott, Isabel M.; Bödeker, Dietrich Physical Review Letters, Vol. 121, Issue 20 https://doi.org/10.1103/physrevlett.121.201302	journal	November 2018
Thermodynamic Geometry of Nambu -- Jona Lasinio model Castorina, P.; Lanteri, D.; Mancani, S. arXiv https://doi.org/10.48550/arxiv.1905.05296	text	January 2019
Baryon clustering at the critical line and near the hypothetical critical point in heavy-ion collisions Shuryak, Edward; Torres-Rincon, Juan M. Physical Review C, Vol. 100, Issue 2 https://doi.org/10.1103/physrevc.100.024903	journal	August 2019
The phase structure of QCD Schmidt, Christian; Sharma, Sayantan Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 10 https://doi.org/10.1088/1361-6471/aa824a	journal	August 2017
Equation of state at finite densities for QCD matter in nuclear collisions Monnai, Akihiko; Schenke, Björn; Shen, Chun Physical Review C, Vol. 100, Issue 2 https://doi.org/10.1103/physrevc.100.024907	journal	August 2019
Modeling baryonic interactions with the Clausius-type equation of state Vovchenko, Volodymyr; Gorenstein, Mark I.; Stoecker, Horst The European Physical Journal A, Vol. 54, Issue 2 https://doi.org/10.1140/epja/i2018-12399-3	journal	February 2018
Skewness and kurtosis of net baryon-number distributions at small values of the baryon chemical potential Bazavov, A.; Ding, H. -T.; Hegde, P. Universität Regensburg https://doi.org/10.5283/epub.39653	text	January 2017
Thermodynamical consistency of quasiparticle model at finite baryon density Ma, Hong-Hao; Lin, Kai; Qian, Wei-Liang arXiv https://doi.org/10.48550/arxiv.1804.05376	text	January 2018
QCD phase structure at finite temperature and density Fu, Wei-jie; Pawlowski, Jan M.; Rennecke, Fabian Physical Review D, Vol. 101, Issue 5 https://doi.org/10.1103/physrevd.101.054032	journal	March 2020
Cosmic QCD Epoch at Nonvanishing Lepton Asymmetry Wygas, Mandy M.; Oldengott, Isabel M.; Bodeker, Dietrich arXiv https://doi.org/10.48550/arxiv.1807.10815	text	January 2018
Modeling baryonic interactions with the Clausius-type equation of state Vovchenko, Volodymyr; Gorenstein, Mark I.; Stoecker, Horst arXiv https://doi.org/10.48550/arxiv.1709.10097	text	January 2017
Anisotropic pressure of deconfined QCD matter in presence of strong magnetic field within one-loop approximation Karmakar, Bithika; Ghosh, Ritesh; Bandyopadhyay, Aritra Physical Review D, Vol. 99, Issue 9 https://doi.org/10.1103/physrevd.99.094002	journal	May 2019
Baryon clustering at the critical line and near the hypothetical critical point in heavy-ion collisions Shuryak, Edward; Torres-Rincon, Juan M. arXiv https://doi.org/10.48550/arxiv.1805.04444	text	January 2018
Effects of the QCD equation of state and lepton asymmetry on primordial gravitational waves Hajkarim, Fazlollah; Schaffner-Bielich, Jürgen; Wystub, Stephan Physical Review D, Vol. 99, Issue 10 https://doi.org/10.1103/physrevd.99.103527	journal	May 2019
Thermodynamic and transport properties in Au + Au collisions at RHIC energies from the clustering of color strings Sahoo, Pragati; Tiwari, Swatantra Kumar; De, Sudipan arXiv https://doi.org/10.48550/arxiv.1708.06689	text	January 2017

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