The QCD Equation of State to $\mathcal{O}({\mu }_B^6)$ 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 $T\in [135\mathrm{MeV},330\mathrm{MeV}]$ using up to four different sets of lattice cut-offs corresponding to lattices of size $N_{\sigma }^3\times N_{\tau }$ with aspect ratio $N_{\sigma }/N_{\tau }=4$ and $N_{\tau }=6-16$. 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 espectively. 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 (${\mu }_B\le 2T$). 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 $\sqrt{s_{NN}}\sim 12$ 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 $T$-${\mu }_B$ 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. We argue that results on sixth order expansion coefficients disfavor the existence of a critical point in the QCD phase diagram for ${\mu }_B/T\le 2$ and $T/T_c({\mu }_B=0)>0.9$.

Updated to correspond to journal version. The ancillary files, which contain tables of the basic thermodynamic observables calculated for baryon chemical potentials μ_B/T < 2.2 in the temperature range 135 MeV < T < 280 MeV and for the cases μ_Q = μ_S = 0 and n_S=0, n_Q/n_B=0.4, can be found in version v1

References in corpus (11)

• The equation of state in (2+1)-flavor QCD
• Highly Improved Staggered Quarks on the Lattice, with Applications to Charm Physics
• Freeze-out Conditions in Heavy Ion Collisions from QCD Thermodynamics
• The phase boundary for the chiral transition in (2+1)-flavor QCD at small values of the chemical potential
• The QCD phase diagram at nonzero quark density
• Additional Strange Hadrons from QCD Thermodynamics and Strangeness Freeze-out in Heavy Ion Collisions
• Hadron yields and the phase diagram of strongly interacting matter
• Hadron Mass Spectrum from Lattice QCD
• Identified particle production and freeze-out properties in heavy-ion collisions at RHIC Beam Energy Scan program
• Critical Hadronization Pressure
• QCD phase transition studied by means of hadron production

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