Lattice-QCD-based equations of state at finite temperature and density
The equation of state (EoS) of QCD is a crucial input for the modeling of heavy-ion-collision (HIC) and neutron-star-merger systems. Calculations of the fundamental theory of QCD, which could yield the true EoS, are hindered by the infamous Fermi sign problem which only allows direct simulations at zero or imaginary baryonic chemical potential. As a direct consequence, the current coverage of the QCD phase diagram by lattice simulations is limited. In these proceedings, two different equations of state based on first-principle lattice QCD (LQCD) calculations are discussed. The first is solely informed by the fundamental theory by utilizing all available diagonal and non-diagonal susceptibilities up to O(µ 4 B) in order to reconstruct a full EoS at finite baryon number, electric charge and strangeness chemical potentials. For the second, we go beyond information from the lattice in order to explore the conjectured phase structure, not yet determined by LQCD methods, to assist the experimental HIC community in their search for the critical point. We incorporate critical behavior into this EoS by relying on the principle of universality classes, of which QCD belongs to the 3D Ising Model. This allows one to study the effects of a singularity on the thermodynamical quantities that make up the equation of state used for hydrodynamical simulations of HICs. Additionally, we ensure that these EoSs are valid for applications to HICs by enforcing conditions of strangeness neutrality and fixed charge-to-baryonnumber ratio.
S. Borsanyi, et al., The QCD equation of state with dynamical quarks, JHEP 11 (2010) 077, 10.1007/JHEP11(2010)077
S. Borsanyi, et al., Full result for the QCD equation of state with 2+1 flavors, Phys. Lett. B 730 (2014) 99, 10.1016/j.physletb.2014.01.007
A. Bazavov, et al., Equation of state in ( 2+1 )-flavor QCD, Phys. Rev. D 90 (2014) 094503, 10.1103/PhysRevD.90.094503
J. N. Guenther, et al., The QCD equation of state at finite density from analytical continuation, Nucl. Phys. A 967 (2017) 720, 10.1016/j.nuclphysa.2017.05.044
J. Günther, et al., The QCD equation of state at finite density from analytical continuation, EPJ Web Conf. 137 (2017) 07008, 10.1051/epjconf/201713707008
A. Bazavov et al., The QCD Equation of State to O(µ 6 B) from Lattice QCD, Phys. Rev. D 95 (2017) 054504, 10.1103/ PhysRevD.95.054504
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
S. Mondal, S. Mukherjee, and P. Hegde, Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansion (arXiv:2106.03165, 2021)
P. F. Kolb, J. Sollfrank, and U. W. Heinz, Anisotropic transverse flow and the quark hadron phase transition, Phys. Rev. C 62 (2000) 054909, 10.1103/PhysRevC.62.054909
P. Huovinen, et al., Radial and elliptic flow at RHIC: Further predictions, Phys. Lett. B 503 (2001) 58, 10.1016/S0370-2693(01)00219-2
P. F. Kolb and R. Rapp, Transverse flow and hadrochemistry in Au+Au collisions at (S(NN))**(1/2) = 200-GeV, Phys. Rev. C 67 (2003) 044903, 10.1103/PhysRevC.67.044903
P. F. Kolb and U. W. Heinz, Hydrodynamic description of ultrarelativistic heavy ion collisions (arXiv:nucl-th/0305084, 2003)
U. Heinz and R. Snellings, Collective flow and viscosity in relativistic heavy-ion collisions, Ann. Rev. Nucl. Part. Sci. 63 (2013) 123, 10.1146/annurev-nucl-102212-170540
X. An et al., The BEST framework for the search for the QCD critical point and the chiral magnetic effect, Nucl. Phys. A 1017 (2022) 122343, 10.1016/j.nuclphysa.2021.122343
J. Noronha-Hostler, et al., Lattice-based equation of state at finite baryon number, electric charge and strangeness chemical potentials, Phys. Rev. C 100 (2019) 064910, 10.1103/PhysRevC.100.064910
P. Parotto, et al., QCD equation of state matched to lattice data and exhibiting a critical point singularity, Phys. Rev. C 101 (2020) 034901, 10.1103/PhysRevC.101.034901
J. M. Karthein, et al., Strangeness-neutral equation of state for QCD with a critical point, Eur. Phys. J. Plus 136 (2021) 621, 10.1140/epjp/s13360-021-01615-5
M. D’Elia, G. Gagliardi, and F. Sanfilippo, Higher order quark number fluctuations via imaginary chemical potentials in Nf = 2 + 1 QCD, Phys. Rev. D 95 (2017) 094503, 10.1103/PhysRevD.95.094503
A. Bazavov et al., Fluctuations and Correlations of net baryon number, electric charge, and strangeness: A comparison of lattice QCD results with the hadron resonance gas model, Phys. Rev. D 86 (2012) 034509, 10.1103/PhysRevD.86.034509
S. Borsanyi, et al., Higher order fluctuations and correlations of conserved charges from lattice QCD, JHEP 10 (2018) 205, 10.1007/JHEP10(2018)205
J. Gunther, et al., The QCD equation of state at finite density from analytical continuation, EPJ Web Conf. 137 (2017) 07008, 10.1051/epjconf/201713707008
T. Schäfer and D. Teaney, Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas, Rept. Prog. Phys. 72 (2009) 126001, 10.1088/0034-4885/72/12/126001
J. E. Bernhard, et al., Applying Bayesian parameter estimation to relativistic heavy-ion collisions: simultaneous characterization of the initial state and quark-gluon plasma medium, Phys. Rev. C94 (2016) 024907, 10.1103/PhysRevC.94.024907
R. D. Pisarski and F. Wilczek, Remarks on the Chiral Phase Transition in Chromodynamics, Phys. Rev. D 29 (1984) 338, 10.1103/PhysRevD.29.338
K. Rajagopal and F. Wilczek, Static and dynamic critical phenomena at a second order QCD phase transition, Nucl. Phys. B 399 (1993) 395, 10.1016/0550-3213(93)90502-G
R. Guida and J. Zinn-Justin, 3-D Ising model: The Scaling equation of state, Nucl. Phys. B 489 (1997) 626, 10.1016/S0550-3213(96)00704-3
C. Nonaka and M. Asakawa, Hydrodynamical evolution near the QCD critical end point, Phys. Rev. C 71 (2005) 044904, 10.1103/PhysRevC.71.044904
M. A. Stephanov, K. Rajagopal, and E. V. Shuryak, Signatures of the tricritical point in QCD, Phys. Rev. Lett. 81 (1998) 4816, 10.1103/PhysRevLett.81.4816
M. Stephanov, On the sign of kurtosis near the QCD critical point, Phys. Rev. Lett. 107 (2011) 052301, 10.1103/PhysRevLett.107.052301
E. Brezin, J. Le Guillou, and J. Zinn-Justin, Phase Transitions and Critical Phenomena, In Phase Transitions and Critical Phenomena, vol. 6 (1976).
R. Bellwied, et al., The QCD phase diagram from analytic continuation, Phys. Lett. B 751 (2015) 559, 10.1016/j. physletb.2015.11.011
D. Mroczek, et al., Quartic cumulant of baryon number in the presence of QCD critical point, Phys. Rev. C 103 (2021) 034901, 10.1103/PhysRevC.103.034901
A. Monnai, B. Schenke, and C. Shen, Equation of state at finite densities for QCD matter in nuclear collisions, Phys. Rev. C 100 (2019) 024907, 10.1103/PhysRevC.100.024907
The code to generate the Equation of State, as well as the Equation of State tables can be downloaded at the following link, http://nsmn1.uh.edu/cratti/EoS_BQS.html.
The BES-EoS code can be downloaded at the following link, https://www.bnl.gov/physics/best/resources.php.
How to Cite
Copyright (c) 2022 Jamie M. Karthein, Debora Mroczek, Angel R. Nava Acuña, Jacquelyn Noronha-Hostler, Paolo Parotto, Damien R. P. Price, Claudia Ratti (Author)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Suplemento de la Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.