PoS (LAT2009) 175 The QCD equation of state and transition at finite temperature (original) (raw)

Equation of state and QCD transition at finite temperature

Physical Review D, 2009

We calculate the equation of state in 2+1 flavor QCD at finite temperature with physical strange quark mass and almost physical light quark masses using lattices with temporal extent Nt=8. Calculations have been performed with two different improved staggered fermion actions, the asqtad and p4 actions. Overall, we find good agreement between results obtained with these two O(a^2) improved staggered fermion discretization schemes. A comparison with earlier calculations on coarser lattices is performed to quantify systematic errors in current studies of the equation of state. We also present results for observables that are sensitive to deconfining and chiral aspects of the QCD transition on Nt=6 and 8 lattices. We find that deconfinement and chiral symmetry restoration happen in the same narrow temperature interval. In an Appendix we present a simple parametrization of the equation of state that can easily be used in hydrodynamic model calculations. In this parametrization we also incorporated an estimate of current uncertainties in the lattice calculations which arise from cutoff and quark mass effects. We estimate these systematic effects to be about 10 MeV

The chiral and deconfinement aspects of the QCD transition

2011

We present results on the chiral and deconfinement properties of the QCD transition at finite temperature. Calculations are performed with 2+1 flavors of quarks using the p4, asqtad and HISQ/tree actions. Lattices with temporal extent N_tau=6, 8 and 12 are used to understand and control discretization errors and to reliably extrapolate estimates obtained at finite lattice spacings to the continuum limit. The chiral transition temperature is defined in terms of the phase transition in a theory with two massless flavors and analyzed using O(N) scaling fits to the chiral condensate and susceptibility. We find consistent estimates from the HISQ/tree and asqtad actions and our main result is T_c=154 +/- 9 MeV.

The equation of state in (2+ 1)-flavor QCD

We present results for the equation of state in (2+1)-flavor QCD using the highly improved staggered quark action and lattices with temporal extent Nτ = 6, 8, 10, and 12. We show that these data can be reliably extrapolated to the continuum limit and obtain a number of thermodynamic quantities and the speed of sound in the temperature range (130-400) MeV. We compare our results with previous calculations, and provide an analytic parameterization of the pressure, from which other thermodynamic quantities can be calculated, for use in phenomenology. We show that the energy density in the crossover region, 145 MeV ≤ T ≤ 163 MeV, defined by the chiral transition, is c = (0.18 − 0.5) GeV/fm 3 , i.e., (1.2 − 3.1) nuclear . At high temperatures, we compare our results with resummed and dimensionally reduced perturbation theory calculations. As a byproduct of our analyses, we obtain the values of the scale parameters r0 from the static quark potential and w0 from the gradient flow.

Chiral and deconfinement aspects of the QCD transition

Physical Review D, 2012

We present results on the chiral and deconfinement properties of the QCD transition at finite temperature. Calculations are performed with 2 + 1 flavors of quarks using the p4, asqtad and HISQ/tree actions. Lattices with temporal extent Nτ = 6, 8 and 12 are used to understand and control discretization errors and to reliably extrapolate estimates obtained at finite lattice spacings to the continuum limit. The chiral transition temperature is defined in terms of the phase transition in a theory with two massless flavors and analyzed using O(N) scaling fits to the chiral condensate and susceptibility. We find consistent estimates from the HISQ/tree and asqtad actions and our main result is Tc = 154 ± 9 MeV.

QCD Phase Transition with Chiral Quarks and Physical Quark Masses

Physical Review Letters, 2014

We report on the first lattice calculation of the QCD phase transition using chiral fermions at physical values of the quark masses. This calculation uses 2+1 quark flavors, spatial volumes between (4 fm) 3 and (11 fm) 3 and temperatures between 139 and 196 MeV . Each temperature was calculated using a single lattice spacing corresponding to a temporal Euclidean extent of Nt = 8. The disconnected chiral susceptibility, χ disc shows a pronounced peak whose position and height depend sensitively on the quark mass. We find no metastability in the region of the peak and a peak height which does not change when a 5 fm spatial extent is increased to 10 fm. Each result is strong evidence that the QCD "phase transition" is not first order but a continuous cross-over for mπ = 135 MeV. The peak location determines a pseudo-critical temperature Tc = 155(1)(8) MeV. Chiral SU (2)L ×SU (2)R symmetry is fully restored above 164 MeV, but anomalous U (1)A symmetry breaking is non-zero above Tc and vanishes as T is increased to 196 MeV.

The QCD Equation of State

Results for the equation of state in 2+1 flavor QCD at zero net baryon density using the Highly Improved Staggered Quark (HISQ) action by the HotQCD collaboration are presented. The strange quark mass was tuned to its physical value and the light (up/down) quark masses fixed to m l = 0.05m s corresponding to a pion mass of 160 MeV in the continuum limit. Lattices with temporal extent N t = 6, 8, 10 and 12 were used. Since the cutoff effects for N t > 6 were observed to be small, reliable continuum extrapolations of the lattice data for the phenomenologically interesting temperatures range 130MeV < T < 400MeV could be performed. We discuss statistical and systematic errors and compare our results with other published works.

The QCD transition temperature: Results with physical masses in the continuum limit

Physics Letters B, 2006

The transition temperature (T c ) of QCD is determined by Symanzik improved gauge and stout-link improved staggered fermionic lattice simulations. We use physical masses both for the light quarks (m ud ) and for the strange quark (m s ). Four sets of lattice spacings (N t =4,6,8 and 10) were used to carry out a continuum extrapolation. It turned out that only N t =6,8 and 10 can be used for a controlled extrapolation, N t =4 is out of the scaling region. Since the QCD transition is a non-singular cross-over there is no unique T c . Thus, different observables lead to different numerical T c values even in the continuum and thermodynamic limit. The peak of the renormalized chiral susceptibility predicts T c =151 MeV, wheres T c -s based on the strange quark number susceptibility and Polyakov loops result in 24(4) MeV and 25(4) MeV larger values, respectively. Another consequence of the cross-over is the non-vanishing width of the peaks even in the thermodynamic limit, which we also determine. These numbers are attempted to be the full result for the T =0 transition, though other lattice fermion formulations (e.g. Wilson) are needed to cross-check them.

Universal critical behavior and the transition temperature in (2+1)-flavor QCD

2011

We discuss the universal critical behavior in (2+1)-flavor QCD by analyzing lattice data from improved staggered fermions generated by the HotQCD Collaboration. We present recent results from two different lattice discretizations and various lattice spacings (Ntau = 6,8,12) at fixed physical strange quark mass (ms) but varying light quark mass (ml). We find that the chiral order-parameter, i.e. the chiral condensate, shows the expected universal scaling that is associated with the critical point in the chiral limit already for light quark masses ml/ms<~0.05. From an analysis of the disconnected chiral susceptibility we estimate a preliminary value of the QCD transition temperature.

Determining the nature of the finite temperature transition of QCD with dynamical fermions

Nuclear Physics B, 1990

Numerical results are presented for lattice QCD with m = 0.1 four-flavour staggered fermions around the finite-temperature transition at /3 5.13 on a i0 3 x 4 volume using the Hybrid Monte Carlo. A method is described that extends the /3 range that can be analysed using data gathered at only one /3 value. The nature of the order of the transition at m 0.1 is discussed using results from 6~x 4-10~x 4 volumes. Over this range, a standard test indicates that the data are more consistent with a sharp crossover and shows that the first-order transition, when it develops on larger lattices, must be rather weak.

One-flavour QCD at finite temperature

Nuclear Physics B-proceedings Supplements - NUCL PHYS B-PROC SUPPL, 1998

We present results, for heavy to moderate quark masses, of a study of thermodynamic properties of 1-flavour QCD, using the multiboson algorithm. Finite-size scaling behaviour is studied on lattices of size 83 × 4, 123 × 4 and 163 × 4. It is shown that, for heavy quarks, the peak of the Polyakov loop susceptibility grows linearly with the spatial volume, indicating a first order phase transition. The deconfinement ratio and the distribution of the norm of the Polyakov loop corroborate this result. For moderately heavy quarks the first-order transition weakens and becomes a crossover. We estimate the end point of the first-order phase transition to occur at a quark mass of about 1.6 GeV.