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.

We present results for pseudo-critical temperatures of QCD chiral crossovers at zero and non-zero values of baryon (B), strangeness (S), electric charge (Q), and isospin (I) chemical potentials µ X=B,Q,S,I . The results were obtained using lattice QCD calculations carried out with two degenerate up and down dynamical quarks and a dynamical strange quark, with quark masses corresponding to physical values of pion and kaon masses in the continuum limit. By parameterizing pseudo-critical temperatures as (0)) 4 , we determined κ X 2 and κ X 4 from Taylor expansions of chiral observables in µ X . We obtained a precise result for T c (0) = (156.5 ± 1.5) MeV. For analogous thermal conditions at the chemical freeze-out of relativistic heavy-ion collisions, i.e., µ S (T, µ B ) and µ Q (T, µ B ) fixed from strangeness-neutrality and isospin-imbalance, we found κ B 2 =0.012(4) and κ B 4 =0.000(4). For µ B 300 MeV, the chemical freeze-out takes place in the vicinity of the QCD phase boundary, which coincides with the lines of constant energy density of 0.42(6) GeV/fm 3 and constant entropy density of 3.7(5) fm −3 .

HotQCD Collaboration)We present a lattice-QCD-based determination of the chiral phase transition temperature in QCD with two degenerate, massless quarks and a physical strange quark mass using lattice QCD calculations with the Highly Improved Staggered Quarks action. We propose and calculate two novel estimators for the chiral transition temperature for several values of the light quark masses, corresponding to Goldstone pion masses in the range of 58 MeV < ∼ mπ < ∼ 163 MeV. The chiral phase transition temperature is determined by extrapolating to vanishing pion mass using universal scaling analysis. Finite-volume effects are controlled by extrapolating to the thermodynamic limit using spatial lattice extents in the range of 2.8-4.5 times the inverse of the pion mass. Continuum extrapolations are carried out by using three different values of the lattice cutoff, corresponding to lattices with temporal extents Nτ = 6, 8 and 12. After thermodynamic, continuum, and chiral extrapolations we find the chiral phase transition temperature T 0 c = 132 +3 −6 MeV.Introduction.-For physical values of the light up, down, and heavier strange quark masses strongly interacting matter undergoes a transition from a lowtemperature hadronic regime to a high-temperature region that is best described by quark and gluon degrees of freedom. This smooth crossover between the two asymptotic regimes is not a phase transition [1]. It is characterized by a pseudocritical temperature, T pc , that has been determined in several numerical studies of Quantum Chromodynamics (QCD) [2][3][4]. A recent determination of T pc extracted from the maximal fluctuations of several chiral observables gave T pc = (156.5 ± 1.5) MeV [5].

We compare lattice QCD results for appropriate combinations of net strangeness fluctuations and their correlations with net baryon number fluctuations with predictions from two hadron resonance gas (HRG) models having different strange hadron content. The conventionally used HRG model based on experimentally established strange hadrons fails to describe the lattice QCD results in the hadronic phase close to the QCD crossover. Supplementing the conventional HRG with additional, experimentally uncharted strange hadrons predicted by quark model calculations and observed in lattice QCD spectrum calculations leads to good descriptions of strange hadron thermodynamics below the QCD crossover. We show that the thermodynamic presence of these additional states gets imprinted in the yields of the ground-state strange hadrons leading to a systematic 5-8 MeV decrease of the chemical freeze-out temperatures of ground-state strange baryons.PACS numbers: 11.10. Wx, 11.15.Ha, 12.38.Gc, 12.38.Mh Introduction.-With increasing temperature the strong interaction among constituents of ordinary nuclear matter, mesons and baryons, results in the copious production of new hadronic resonances. The newly produced resonances account for the interaction among hadrons to an extent that bulk thermodynamic properties become well described by a gas of uncorrelated hadronic resonances [1]. The hadron resonance gas (HRG) model is extremely successful in describing the hot hadronic matter created in heavy ion experiments [2]. Abundances of various hadron species measured in heavy ion experiments at different beam energies are well described by thermal distributions characterized by a freeze-out temperature and a set of chemical potentials µ = (µ B , µ Q , µ S ) for net baryon number (B), electric charge (Q) and strangeness (S) [3]. Nonetheless, details of the freeze-out pattern may provide evidence for a more complex sequential freezeout pattern [4,5]. In particular, in the case of strange hadrons arguments have been put forward in favor of a greater freeze-out temperature than that of nonstrange hadrons [6][7][8].At the temperature T c = (154 ± 9) MeV [9] strong interaction matter undergoes a chiral crossover to a new phase. In the same crossover region HRG-based descriptions of the fluctuations and correlations of conserved charges for light [10], strange [6,11], as well as charm [12] degrees of freedom break down. Below T c , bulk thermodynamic properties as well as conserved charge distributions are generally well described by a HRG containing all experimentally observed resonances (PDG-HRG) listed in the particle data tables [13]. However, there are