QCD equation of state to $\mathcal{O}\left({\mu}_{B}^{6}\right)$ from lattice QCD
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 cutoffs corresponding to lattices of size N$$3\atop{σ}$$ × N _{τ} with aspect ratio N _{σ}/N _{τ} = 4 and N _{τ} = 616. 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. Sixthorder results for Taylor expansion coefficients are used to estimate truncation errors of the fourthorder expansion. We show that truncation errors are small for baryon chemical potentials less then twice the temperature (µ _{B} ≤ 2T ). The fourthorder equation of state thus is suitable for √the modeling of dense matter created in heavy ion collisions with centerofmass 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 freezeout 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.
 Authors:

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 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)
 Publication Date:
 Report Number(s):
 BNL1139242017JA; BNL2034002018JAAM
Journal ID: ISSN 24700010
 Grant/Contract Number:
 SC0012704; SC001270; 05P12PBCTA
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 95; Journal Issue: 5; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Research Org:
 Brookhaven National Laboratory (BNL), Upton, NY (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Nuclear Physics (NP) (SC26); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS
 OSTI Identifier:
 1376098
 Alternate Identifier(s):
 OSTI ID: 1346090; OSTI ID: 1431282
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., and Wagner, M.. QCD equation of state to O(μB6) from lattice QCD. United States: N. p.,
Web. doi:10.1103/PhysRevD.95.054504.
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.. QCD equation of state to O(μB6) from lattice QCD. United States. doi:10.1103/PhysRevD.95.054504.
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., and Wagner, M.. 2017.
"QCD equation of state to O(μB6) from lattice QCD". United States.
doi:10.1103/PhysRevD.95.054504. https://www.osti.gov/servlets/purl/1376098.
@article{osti_1376098,
title = {QCD equation of state to O(μB6) from lattice QCD},
author = {Bazavov, A. and Ding, H. T. and Hegde, P. and Kaczmarek, O. and Karsch, F. and Laermann, E. and Maezawa, Y. and Mukherjee, Swagato and Ohno, H. and Petreczky, P. and Sandmeyer, H. and Steinbrecher, P. and Schmidt, C. and Sharma, S. and Soeldner, W. and Wagner, M.},
abstractNote = {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 cutoffs corresponding to lattices of size N$3\atop{σ}$ × Nτ with aspect ratio Nσ/Nτ = 4 and Nτ = 616. The strange quark mass is tuned to its physical value and we use two strange to light quark mass ratios ms/ml = 20 and 27, which in the continuum limit correspond to a pion mass of about 160 MeV and 140 MeV respectively. Sixthorder results for Taylor expansion coefficients are used to estimate truncation errors of the fourthorder expansion. We show that truncation errors are small for baryon chemical potentials less then twice the temperature (µB ≤ 2T ). The fourthorder equation of state thus is suitable for √the modeling of dense matter created in heavy ion collisions with centerofmass 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 µB plane and are compared with the crossover line for the QCD chiral transition as well as with experimental results on freezeout 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 µB/T ≤ 2 and T/Tc(µB = 0) > 0.9.},
doi = {10.1103/PhysRevD.95.054504},
journal = {Physical Review D},
number = 5,
volume = 95,
place = {United States},
year = {2017},
month = {3}
}