We provide the most accurate results for the QCD transition line so far. We optimize the definition of the crossover temperature $T_c$, allowing for its very precise determination, and extrapolate from imaginary chemical potential up to real $mu_B ap
prox 300$ MeV. The definition of $T_c$ adopted in this work is based on the observation that the chiral susceptibility as a function of the condensate is an almost universal curve at zero and imaganiary $mu_B$. We obtain the parameters $kappa_2=0.0153(18)$ and $kappa_4=0.00032(67)$ as a continuum extrapolation based on $N_t=10,12$ and $16$ lattices with physical quark masses. We also extrapolate the peak value of the chiral susceptibility and the width of the chiral transition along the crossover line. In fact, both of these are consistent with a constant function of $mu_B$. We see no sign of criticality in the explored range.
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 $48^3times12$. Higher order fluctuations at $mu_B=0$ are obtained as derivatives of the l
ower 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.
I review a selection of recent finite temperature lattice results of the past years. First I discuss the extension of the equation of state towards high temperatures and fi- nite densities, then I show recent results on the QCD topological susceptibi
lity at high temperatures and highlight its relevance for dark matter search.
We determine the equation of state of QCD at finite chemical potential, to order $(mu_B/T)^6$, 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 res
ults are continuum extrapolated using lattices of up to $N_t=16$ temporal resolution. The QCD pressure and interaction measure are calculated along the isentropic trajectories in the $(T,~mu_B)$ 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 $mu_B=0$ from the simulations at imaginary chemical potentials. Strangeness neutrality and charge conservation are imposed, to match the experimental conditions.
We calculate the QCD cross-over temperature, the equation of state and fluctuations of conserved charges at finite density by analytical continuation from imaginary to real chemical potentials. Our calculations are based on new continuum extrapolated
lattice simulations using the 4stout staggered actions with a lattice resolution up to $N_t=16$. The simulation parameters are tuned such that the strangeness neutrality is maintained, as it is in heavy ion collisions.
Fluctuations of conserved charges in a grand canonical ensemble can be calculated as derivatives of the free energy with respect to the respective chemical potential. They are directly related to experimentally available observables that describe the
hadronization in heavy ion collisions. The same derivatives can be used to extrapolate zero density results to finite chemical potential. We review the recent lattice calculations in the staggered formalism and discuss its implications to phenomenology and resummed perturbation theory.
We calculate second- and fourth-order cumulants of conserved charges in a temperature range stretching from the QCD transition region towards the realm of (resummed) perturbation theory. We perform lattice simulations with staggered quarks; the conti
nuum extrapolation is based on $N_t=10dots24$ in the crossover-region and $N_t=8dots16$ at higher temperatures. We find that the Hadron Resonance Gas model predictions describe the lattice data rather well in the confined phase. At high temperatures (above $sim$250 MeV) we find agreement with the three-loop Hard Thermal Loop results.
We present continuum extrapolated lattice results for the higher order fluctuations of conserved charges in high temperature Quantum Chromodynamics. Through the matching of the grand canonical ensemble on the lattice to the net charge and net baryon
distribution realized in heavy ion experiments the temperature and the chemical potential may be estimated at the time of chemical freeze-out
We present possible indications for flavor separation during the QCD crossover transition based on continuum extrapolated lattice QCD calculations of higher order susceptibilities. We base our findings on flavor specific quantities in the light and s
trange quark sector. We propose a possible experimental verification of our prediction, based on the measurement of higher order moments of identified particle multiplicities. Since all our calculations are performed at zero baryochemical potential, these results are of particular relevance for the heavy ion program at the LHC.
Scale setting is of central importance in lattice QCD. It is required to predict dimensional quantities in physical units. Moreover, it determines the relative lattice spacings of computations performed at different values of the bare coupling, and t
his is needed for extrapolating results into the continuum. Thus, we calculate a new quantity, $w_0$, for setting the scale in lattice QCD, which is based on the Wilson flow like the scale $t_0$ (M. Luscher, JHEP 1008 (2010) 071). It is cheap and straightforward to implement and compute. In particular, it does not involve the delicate fitting of correlation functions at asymptotic times. It typically can be determined on the few per-mil level. We compute its continuum extrapolated value in 2+1-flavor QCD for physical and non-physical pion and kaon masses, to allow for mass-independent scale setting even away from the physical mass point. We demonstrate its robustness by computing it with two very different actions (one of them with staggered, the other with Wilson fermions) and by showing that the results agree for physical quark masses in the continuum limit.
