Overview of the QCD phase diagram: Recent progress from the lattice.

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.

QCD Crossover at Finite Chemical Potential from Lattice Simulations.

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 µ_{B}≈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 imaginary µ_{B}. We obtain the parameters κ_{2}=0.0153(18) and κ_{4}=0.00032(67) as a continuum extrapolation based on N_{t}=10, 12, 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 µ_{B}. We see no sign of criticality in the explored range.