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Register a new userThe equation of state at high temperatures from lattice QCD
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We present results for the equation of state upto previously unreachable, high temperatures. Since the temperature range is quite large, a comparison with perturbation theory can be done directly.
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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 $Tin [135~{rm MeV}, 330~{rm MeV}]$ using up to four different sets of lattice cut-offs corresponding to lattices of size $N_sigma^3times N_tau$ 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 ($mu_Ble 2T$). 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 $mu_B/Tle 2$ and $T/T_c(mu_B=0) > 0.9$.
Taylor expansion of the equation of state of QCD suffers from shortcomings at chemical potentials $mu_B geq (2-2.5)T$. First, one faces difficulties inherent in performing such an expansion with a limited number of coefficients; second, higher order coefficients determined from lattice calculations suffer from a poor signal-to-noise ratio. In this work, we present a novel scheme for extrapolating the equation of state of QCD to finite, real chemical potential that can extend its reach further than previous methods. We present continuum extrapolated lattice results for the new expansion coefficients and show the thermodynamic observables up to $mu_B/Tle3.5$.
We have continued our study of the phase diagram of high temperature QCD with three flavors of improved staggered quarks. We are performing simulations with three degenerate quarks with masses less than or equal to the strange quark mass m_s and with degenerate up and down quarks with masses m_{u,d} less than the strange quark mass. For the quark masses studied to date, we find a crossover that strengthens as m_{u,d} decreases, rather than a bona fide phase transition. We present new results for the crossover temperature extrapolated to the physical value of m_{u,d}, and for quark number susceptibilities.
We determine the equation of state of QCD at finite chemical potential, to order $(mu_B/T)^6$, for a system of 2+1 quark flavors. The simulations are performed at the physical mass for the light and strange quarks on several lattice spacings; the results are continuum extrapolated using lattices of up to $N_t=16$ temporal resolution. The QCD pressure and interaction measure are calculated along the isentropic trajectories in the $(T,~mu_B)$ plane corresponding to the RHIC Beam Energy Scan collision energies. Their behavior is determined through analytic continuation from imaginary chemical potentials of the baryonic density. We also determine the Taylor expansion coefficients around $mu_B=0$ from the simulations at imaginary chemical potentials. Strangeness neutrality and charge conservation are imposed, to match the experimental conditions.
We present an N_t=4 lattice study for the equation of state of 2+1 flavour staggered, dynamical QCD at finite temperature and chemical potential. We use the overlap improving multi-parameter reweighting technique to extend the equation of state for non-vanishing chemical potentials. The results are obtained on the line of constant physics and our physical parameters extend in temperature and baryon chemical potential upto approx 500-600 MeV.
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