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 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

Appropriate combinations of up to fourth order cumulants of net strangeness fluctuations and their correlations with net baryon number and electric charge fluctuations, obtained from lattice QCD calculations, have been used to probe the strangeness carrying degrees of freedom at high temperatures. For temperatures up to the chiral crossover separate contributions of strange mesons and baryons can be well described by an uncorrelated gas of hadrons. Such a description breaks down in the chiral crossover region, suggesting that the deconfinement of strangeness takes place at the chiral crossover. On the other hand, the strangeness carrying degrees of freedom inside the quark gluon plasma can be described by a weakly interacting gas of quarks only for temperatures larger than twice the chiral crossover temperature. In the intermediate temperature window these observables show considerably richer structures, indicative of the strongly interacting nature of the quark gluon plasma.PACS numbers: 11.10. Wx, 11.15.Ha, 12.38.Aw, 12.38.Gc, 12.38.Mh, 24.60.Ky, 25.75.Gz, 25.75.Nq Introduction.-Strangeness has played a crucial role [1] in the experimental and theoretical investigations of the deconfined phase, namely the Quark Gluon Plasma (QGP) phase, of Quantum Chromodynamics (QCD) at high temperatures. Experimental results from the Relativistic Heavy Ion Collider and the Large Hadron Collider suggest that the QGP has been created during the highly energetic collisions of heavy nuclei [2]. Experimental results showing enhanced production and large collective flow of strange hadrons [3] strongly indicate that deconfined strange quarks existed inside the QGP, despite the absence of real strange quarks within the initially colliding nuclei. However, theoretical understanding of the deconfinement of strangeness remains unclear. A-priori it is not unreasonable to expect that the heavier strange quark may not be largely influenced by the chiral symmetry of QCD and the deconfinement of the strange quarks may not take place at the chiral crossover temperature (T c ). Based on the observations that, compared to the light up and down quarks, the net strange quark number fluctuations [4,5] show a much smoother behavior across the chiral crossover region, it has been suggested [6] that the deconfinement crossover for the strange quarks may take place at a temperature larger than T c . Consequently strange hadronic bound states may exist inside the QGP for temperatures T T c [7].Moreover, the nature of the deconfined QGP for moderately high temperatures also remains elusive. An intriguing open question is whether in this temperature regime the QGP is a strongly coupled medium lacking a quasi-particle description [2] or consists of other degrees of freedom such as colored bound states [8] or massive colored quasi-particles [9]. Knowledge regarding the behav-

Ratios of cumulants of conserved net charge fluctuations are sensitive to the degrees of freedom that are carriers of the corresponding quantum numbers in different phases of strong interaction matter. Using lattice QCD with 2+1 dynamical flavors and quenched charm quarks we calculate second and fourth order cumulants of net charm fluctuations and their correlations with other conserved charges such as net baryon number, electric charge and strangeness. Analyzing appropriate ratios of these cumulants we probe the nature of charmed degrees of freedom in the vicinity of the QCD chiral crossover region. We show that for temperatures above the chiral crossover transition temperature, charmed degrees of freedom can no longer be described by an uncorrelated gas of hadrons. This suggests that the dissociation of open charm hadrons and the emergence of deconfined charm states sets in just near the chiral crossover transition. Till the crossover region we compare these lattice QCD results with two hadron resonance gas models --including only the experimentally established charmed resonances and also including additional states predicted by quark model and lattice QCD calculations. This comparison provides evidence for so far unobserved charmed hadrons that contribute to the thermodynamics in the crossover region.Comment: The published versio

A new approach to study the equation of state in finite-temperature QCD is proposed on the lattice. Unlike the conventional method in which the temporal lattice size Nt is fixed, the temperature T is varied by changing Nt at fixed lattice scale. The pressure of the hot QCD plasma is calculated by the integration of the trace anomaly with respect to T at fixed lattice scale. This "T -integral method" is tested in quenched QCD on isotropic and anisotropic lattices and is shown to give reliable results especially at intermediate and low temperatures.