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We construct a family of equations of state for QCD in the temperature range 30 MeV T 800 MeV and in the chemical potential range 0 μ B 450 MeV. These equations of state match available lattice QCD results up to O(μ 4 B ) and in each of them we place a critical point in the three-dimensional (3D) Ising model universality class. The position of this critical point can be chosen in the range of chemical potentials covered by the second Beam Energy Scan at the Relativistic Heavy Ion Collider. We discuss possible choices for the free parameters, which arise from mapping the Ising model onto QCD. Our results for the pressure, entropy density, baryon density, energy density, and speed of sound can be used as inputs in the hydrodynamical simulations of the fireball created in heavy ion collisions. We also show our result for the second cumulant of the baryon number in thermal equilibrium, displaying its divergence at the critical point. In the future, comparisons between RHIC data and the output of the hydrodynamic simulations, including calculations of fluctuation observables, built upon the model equations of state that we have constructed may be used to locate the critical point in the QCD phase diagram, if there is one to be found.

Fluctuations of conserved charges allow to study the chemical composition of hadronic matter. A comparison between lattice simulations and the Hadron Resonance Gas (HRG) model suggested the existence of missing strange resonances. To clarify this issue we calculate the partial pressures of mesons and baryons with different strangeness quantum numbers using lattice simulations in the confined phase of QCD. In order to make this calculation feasible, we perform simulations at imaginary strangeness chemical potentials. We systematically study the effect of different hadronic spectra on thermodynamic observables in the HRG model and compare to lattice QCD results. We show that, for each hadronic sector, the well established states are not enough in order to have agreement with the lattice results. Additional states, either listed in the Particle Data Group booklet (PDG) but not well established, or predicted by the Quark Model (QM), are necessary in order to reproduce the lattice data. For mesons, it appears that the PDG and the quark model do not list enough strange mesons, or that, in this sector, interactions beyond those included in the HRG model are needed to reproduce the lattice QCD results. INTRODUCTIONThe precision achieved by recent lattice simulations of QCD thermodynamics allows to extract, for the first time, quantitative predictions which provide a new insight into our understanding of strongly interacting matter. Recent examples include the precise determination of the QCD transition temperature [1][2][3][4], the QCD equation of state at zero [5][6][7] and small chemical potential [8][9][10] and fluctuations of quark flavors and/or conserved charges near the QCD transition [11][12][13]. The latter are particularly interesting because they can be related to experimental measurements of particle multiplicity cumulants, thus allowing to extract the freeze-out parameters of heavy-ion collisions from first principles [14][15][16][17][18]. Furthermore, they can be used to study the chemical composition of strongly interacting matter and identify the degrees of freedom which populate the system in the vicinity of the QCD phase transition [19][20][21].The vast majority of lattice results for QCD thermodynamics can be described, in the hadronic phase, by a non-interacting gas of hadrons and resonances which includes the measured hadronic spectrum up to a certain mass cut-off. This approach is commonly known as the Hadron Resonance Gas (HRG) model [22][23][24][25][26]. There is basically no free parameter in such a model, the only uncertainty being the number of states, which is determined by the spectrum listed in the Particle Data Book. It has been proposed recently to use the precise lattice QCD results on specific observables, and their possible discrepancy with the HRG model predictions, to infer the existence of higher mass states [27][28][29], not yet measured but predicted by Quark Model (QM) calculations [30,31] and lattice QCD simulations [32]. This leads to a better agreement between selected lattice...

The QCD equation of state at zero baryon chemical potential is the only element of the standard dynamical framework to describe heavy ion collisions that can be directly determined from first principles. Continuum extrapolated lattice QCD equations of state have been computed using 2+1 quark flavors (up/down and strange) as well as 2+1+1 flavors to investigate the effect of thermalized charm quarks on QCD thermodynamics. Lattice results have also indicated the presence of new strange resonances that not only contribute to the equation of state of QCD matter but also affect hadronic afterburners used to model the later stages of heavy ion collisions. We investigate how these new developments obtained from first principles calculations affect multiparticle correlations in heavy ion collisions. We compare the commonly used equation of state S95n-v1, which was constructed using what are now considered outdated lattice results and hadron states, to the current state-of-the-art lattice QCD equations of state with 2+1 and 2+1+1 flavors coupled to the most upto-date hadronic resonances and their decays. New hadronic resonances lead to an enhancement in the hadronic spectra at intermediate pT . Using an outdated equation of state can directly affect the extraction of the shear viscosity to entropy density ratio, η/s, of the quark-gluon plasma and results for different flow observables. The effects of the QCD equation of state on multiparticle correlations of identified particles are determined for both AuAu √ sNN = 200 GeV and PbPb √ sNN = 5.02 TeV collisions. New insights into the v2{2} to v3{2} puzzle in ultracentral collisions are found. Flow observables of heavier particles exhibit more non-linear behavior regardless of the assumptions about the equation of state, which may provide a new way to constrain the temperature dependence of η/s.