We present the crossover line between the quark gluon plasma and the hadron gas phases for small real chemical potentials. First we determine the effect of imaginary values of the chemical potential on the transition temperature using lattice QCD simulations. Then we use various formulas to perform an analytic continuation to real values of the baryo-chemical potential. Our data set maintains strangeness neutrality to match the conditions of heavy ion physics. The systematic errors are under control up to μ B ≈ 300 MeV. For the curvature of the transition line we find that there is an approximate agreement between values from three different observables: the chiral susceptibility, chiral condensate and strange quark susceptibility. The continuum extrapolation is based on N t = 10, 12 and 16 lattices. By combining the analysis for these three observables we find, for the curvature, the value κ = 0.0149 ± 0.0021.

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...

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Abstract. An efficient way to study the QCD phase diagram at small finite density is to extrapolate thermodynamical observables from imaginary chemical potential. In this talk we present results on several observables for the equation of state to order (µ B /T ) 6 . The observables are calculated along the isentropic trajectories in the (T , µ B ) plane corresponding to the RHIC Beam Energy Scan collision energies. The simulations are performed at the physical mass for the light and strange quarks. µ S was tuned in a way to enforce strangeness neutrality to match the experimental conditions; the results are continuum extrapolated using lattices of up to N t = 16 temporal resolution.

We propose a recursive algorithm for the calculation of multibaryon correlation functions that combines the advantages of a recursive approach with those of the recently proposed unified contraction algorithm. The independent components of the correlators are built recursively by adding the baryons one after the other in a given order. The list of nonzero independent components is also constructed in a recursive manner, significantly reducing the resources required for this step. We computed the number of operations required to calculate the correlators up to 8 Be, and observed a significant speedup compared to other techniques. For the calculation of 4 He and 8 Be correlation functions in the fully relativistic case O(10 8 ) operations are required, whereas for nonrelativistic operators this number can be reduced to e.g. O(10 4 ) in the case of 4 He.