Expansion schemes for finite density QCD equation of state: which one is the best?

Abstract

The finite density equation of state of QCD is a fundamental quantity for understanding the phase structure of the theory, and also for the realistic modeling of the QCD medium in simulations. While direct lattice simulations at finite density are extremely challenging, several expansion schemes have been devised to extrapolate into the QCD phase diagram. All of these schemes are based on susceptibilities of conserved charges, i.e. derivatives of the pressure with respect to the chemical potential(s). In this work we set out to determine which of these schemes possesses the best convergence properties. To this end, we employ extreme-statistics lattice simulations on a $16^3\times8$ lattice, which allow us to obtain susceptibilities up to order eight with remarkably small errors. We compare in particular two methods, based on contours of constant (normalized) baryon density and of constant entropy density. We find that the latter converges more quickly, effectively requiring susceptibilities only up to order four to cover the chemical potential range up to at least $μ_B \approx 500$ MeV. We also extend the comparison to the three dimensional space of chemical potentials, and find that the entropy-based method consistently shows superior convergence.