The QCD Phase Diagram for Three Degenerate Flavors and Small Baryon Density

TL;DR

The paper investigates the QCD phase diagram for three degenerate flavors at small baryon density by using simulations at imaginary chemical potential to enable positive weights, followed by analytic continuation to real μ. The authors extract the critical line $T_c(μ)$ up to terms of order $(μ/(π T))^4$ and study the μ-dependence of the critical quark mass $m_c(μ)$ via Binder cumulants, finding a weak μ-dependence and a conservative bound on the leading μ^2 coefficient. They determine the zero-density critical mass $m_c(0)$ with high precision and estimate the μ^2 and μ^4 contributions to the endpoint location, noting a significant discrepancy with some prior reweighting results. The work demonstrates the feasibility and limitations of this approach, emphasizing the need for larger-scale simulations to reach physical 2+1 flavor masses and to resolve the endpoint structure with controlled systematic errors.

Abstract

We present results for the phase diagram of three flavor QCD for μ_B ~ 500 MeV. Our simulations are performed with imaginary chemical potential μ_I for which the fermion determinant is positive. Physical observables are then fitted by truncated Taylor series and continued to real chemical potential. We map out the location of the critical line T_c(μ_B) with an accuracy up to terms of order (μ_B/T)^6. We also give first results on a determination of the critical endpoint of the transition and its quark mass dependence. Our results for the endpoint differ significantly from those obtained by other methods, and we discuss possible reasons for this.

Figures (10)

• Figure 1: Schematic phase diagram in the $(\mu_I,T)$ plane. Solid lines mark first order phase transitions, dotted ones crossover. The vertical line corresponds to a $Z(3)$ transition and the curves to the deconfinement/chiral transition at imaginary $\mu$. Both terminate in critical points, each belonging to the 3d Ising universality class.
• Figure 2: Left: critical lines in the $(T,\mu^2)$-plane for different quark masses $m$. The bold curve $T^*(\mu)$ characterizes second-order transitions, separating the crossover and the first order regimes. Right: critical lines in the $(T,m)$-plane for different chemical potentials $\mu^2$. The bold curve represents $T^*(m)$.
• Figure 3: Schematic line of critical quark mass separating the first order and crossover region. The line is constrained by the $\mu=0$ data point (diamond, kls) and the fact that for $m=0$ the phase transition has to be first order for all imaginary $\mu^2<0$, implying that intersection with the $Z(3)$-line happens at some quark mass $\hat{m}\geq 0$.
• Figure 4: Combined data for $L=8-12$ and various quark masses. Data for different $am$ are shifted to $a m_c(0)$ according to the best fit of Table 1, which is also shown. A weak $\mu^4$-dependence is visible.
• Figure 5: Left: One sigma error bands on $T_c(\mu_B)$ for different $N_f$ ($N_f=4$ from el). Only the $N_f=3$ calculation is accurate enough to include a quartic term. Right: Comparison of $N_f=3$ with $N_f=2+1$ from fk2.