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

Abstract

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 ∈ [135 MeV, 330 MeV] using up to four different sets of lattice cut-offs corresponding to lattices of size N 3 σ × Nτ with aspect ratio Nσ/Nτ = 4 and Nτ = 6 − 16. The strange quark mass is tuned to its physical value and we use two strange to light quark mass ratios ms/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 (µB ≤ 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 -µB 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. 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.

Chiral Phase Transition in Linear Sigma Model with Nonextensive Statistical Mechanics

“…More and more attentions have already been attracted to the QCD phase transition both theoretically and experimentally [1][2][3][4][5][6][7][8]. Though experimental studies and lattice Monte-Carlo simulations have made it possible to research on the phase diagram quantitatively, there still remains uncertainty at high baryon density region [9].…”

Equation of state of a quark-meson mixture in the improved Polyakov–Nambu–Jona-Lasinio model at finite chemical potential

“…(46). In the right panel, we observe an additional violation due to the presence of the Landau cut (s < 0) at finite momentum, not present at T = 0.…”

“…13. [46]. Notice that vector interactions among quarks-not considered in this work-can modify these values at mean field, and lower the critical temperature [11].…”

“…Finally, we present a calculation of the pressure compared to recent lattice-QCD results at finite chemical potential [46]. To be consistent with lattice-QCD data we have used µ s = µ q = µ B /3, so we have recomputed all our results using a nonzero strange quark chemical potential.…”

“…(9), (46), and (20), respectively. Notice that all parameters have been fixed at mean-field level, so that the mesonic contribution is parameter free for every temperature.…”