We calculate several diagonal and non-diagonal fluctuations of conserved charges in a system of 2+1+1 quark flavors with physical masses, on a lattice with size 48 3 × 12.Higher order fluctuations at µ B = 0 are obtained as derivatives of the lower order ones, simulated at imaginary chemical potential. From these correlations and fluctuations we construct ratios of net-baryon number cumulants as functions of temperature and chemical potential, which satisfy the experimental conditions of strangeness neutrality and proton/baryon ratio. Our results qualitatively explain the behavior of the measured cumulant ratios by the STAR collaboration.
Fluctuations and imaginary chemical potentialsThe chemical potentials are implemented on a flavor-by-flavor basis, their relation to the phenomenological baryon (B), electric charge (Q) and strangeness (S) chemical potentials
We determine the equation of state of QCD at finite chemical potential, to order (µB/T ) 6 , for a system of 2+1 quark flavors. The simulations are performed at the physical mass for the light and strange quarks on several lattice spacings; the results are continuum extrapolated using lattices of up to Nt = 16 temporal resolution. The QCD pressure and interaction measure are calculated along the isentropic trajectories in the (T, µB) plane corresponding to the RHIC Beam Energy Scan collision energies. Their behavior is determined through analytic continuation from imaginary chemical potentials of the baryonic density. We also determine the Taylor expansion coefficients around µB = 0 from the simulations at imaginary chemical potentials. Strangeness neutrality and charge conservation are imposed, to match the experimental conditions.
Like fluctuations, non-diagonal correlators of conserved charges provide a tool for the study of chemical freeze-out in heavy ion collisions. They can be calculated in thermal equilibrium using lattice simulations, and be connected to moments of event-by-event net-particle multiplicity distributions. We calculate them from continuum extrapolated lattice simulations at µB = 0, and present a finite-µB extrapolation, comparing two different methods. In order to relate the grand canonical observables to the experimentally available net-particle fluctuations and correlations, we perform a Hadron Resonance Gas (HRG) model analysis, which allows us to completely break down the contributions from different hadrons. We then construct suitable hadronic proxies for fluctuations ratios, and study their behavior at finite chemical potentials. We also study the effect of introducing acceptance cuts, and argue that the small dependence of certain ratios on the latter allows for a direct comparison with lattice QCD results, provided that the same cuts are applied to all hadronic species. Finally, we perform a comparison for the constructed quantities for experimentally available measurements from the STAR Collaboration. Thus, we estimate the chemical freeze-out temperature to 165 MeV using a strangeness-related proxy. This is a rather high temperature for the use of the Hadron Resonance Gas, thus, further lattice studies are necessary to provide first principle results at intermediate µB.Hadron Collider (LHC) have been able to create the Quark Gluon Plasma (QGP) in the laboratory, and explore the low-to-moderate baryon density region of the QCD phase diagram.At low baryon density, the transition from a hadron gas to a deconfined QGP was shown by lattice QCD calculations to be a broad crossover [1] at T 155 MeV [1][2][3][4]. At large baryon densities, the nature of the phase transition is expected to change into first order, thus implying the presence of a critical end point. A strong experimental effort is currently in place through the second Beam
In recent years there has been much progress on the investigation of the QCD phase diagram with lattice QCD simulations. In this review we focus on the developments in the last two years. Especially the addition of external influences or new parameter ranges yields an increasing number of interesting results. We discuss the progress for small, finite densities from both extrapolation-based methods (Taylor expansion and analytic continuation for imaginary chemical potential) and complex Langevin simulations, for heavy quark bound states (quarkonium), the dependence on the quark masses (Columbia plot) and the influence of a magnetic field. Many of these conditions are relevant for the understanding of both the QCD transition in the early universe and heavy ion collision experiments, which are conducted for example at the LHC and RHIC.
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