Universal O(N) scaling and the chiral critical line in (2+1)-flavor QCD with small chemical potentials

TL;DR

This paper analyzes the phase transition line in (2+1)-flavor QCD at small chemical potentials, establishing a universal N scaling and determining the curvature of the transition line with minimal cutoff effects.

Contribution

It introduces a method to extract the curvature of the QCD phase transition line using universal scaling properties and mixed susceptibilities at small chemical potentials.

Findings

The curvature parameter shows small cutoff effects.

The transition line in the chiral limit is determined to leading order.

The critical temperature ratio is given by T_c(μ_B)/T_c(0) = 1 - 0.00656(66) (μ_B/T)^2.

Abstract

We show that for small values of the chemical potential the curvature of the phase transition line can be deduced from an analysis of scaling properties of the chiral condensate and its susceptibilities. We make use of a recent analysis of the magnetic equation of state in (2+1)-flavor QCD where a connection between the QCD parameters and the universal scaling fields could be established. The remaining dependence of the reduced temperature on the chemical potential can be fixed by an analysis of a mixed susceptibility, obtained from a derivative with respect to quark mass and chemical potential. We extract this dependence which describes the curvature of the phase transition line, at two values of the cut-off, $aT=1/4$ and $1/8$. We find that cut-off effects are small for the curvature parameter and determine the transition line in the chiral limit to leading order in the light quark chemical potential. We obtain $T_c(\mu_B)/T_c(0) = 1 - 0.00656(66) (\mu_B/T)^2 +{\cal O}(\mu_B^4)$.