The chiral critical line of N_f=2+1 QCD at zero and non-zero baryon density

TL;DR

The paper investigates the chiral critical line in $N_f=2+1$ QCD on $N_t=4$ lattices, exploring zero and imaginary baryon density. By replacing the inexact $R$-algorithm with the exact RHMC algorithm, the authors show substantial step-size artifacts in the critical mass, and map the chiral critical surface across degenerate and non-degenerate quark masses, locating a possible tricritical point. Simulations at imaginary chemical potential reveal a small or negative curvature of the critical surface, suggesting the first-order region may shrink with real $\mu$, and in some scenarios no QCD critical endpoint exists up to $\mu_B \lesssim 500$ MeV. They emphasize large cut-off effects on the coarse lattices used and advocate finer lattices to determine the true continuum behavior and the existence or location of a critical point. Overall, the results highlight the sensitivity of the phase structure to lattice discretization and mass parameters, and motivate continued, higher-precision studies using exact algorithms on finer lattices.

Abstract

We present numerical results for the location of the chiral critical line at finite temperature and zero and non-zero baryon density for QCD with N_f=2+1 flavours of staggered fermions on lattices with temporal extent N_t=4. For degenerate quark masses, we compare our results obtained with the exact RHMC algorithm with earlier, inexact R-algorithm results and find a reduction of 25% in the critical quark mass, for which the first order phase transition changes to a smooth crossover. Extending our analysis to non-degenerate quark masses, we map out the chiral critical line up to the neighbourhood of the physical point, which we confirm to be in the crossover region. Our data are consistent with a tricritical point at a strange quark mass of ~500 MeV. Finally, we investigate the shift of the critical line with finite baryon density, by simulating with an imaginary chemical potential for which there is no sign problem. We observe this shift to be very small or, conversely, the critical endpoint μ^c(m_{u,d},m_s) to be extremely quark mass sensitive. Moreover, the sign of this shift is opposite to standard expectations. If confirmed on a finer lattice, it implies the absence of a critical endpoint or phase transition for chemical potentials μ_B < 500 MeV. We thus argue that finer lattices are required to settle even the qualitative features of the QCD phase diagram.

Figures (12)

• Figure 1: Schematic phase transition behaviour of three flavour QCD for different choices of quark masses (from lp), at zero density.
• Figure 2: The chiral critical surface in the case of positive and negative curvature. If the physical point is in the crossover region for $\mu=0$, a finite $\mu$ phase transition will only arise in the scenario with positive curvature.
• Figure 3: Schematic phase diagram for QCD at imaginary chemical potential. The diagram is periodically repeated for larger values of $\mu_i$. The heavy lines indicate first order transitions, the thin lines crossovers. The nature of the temperature-driven transition depends on the parameters or the theory ($N_f$, quark masses).
• Figure 4: Left: Comparison of the Binder cumulant computed with the RHMC algorithm (leftmost data) and the zero stepsize extrapolation of the R-algorithm. The solid lines represent a common fit to all data, the vertical line marks the commonly used R-algorithm step size when no extrapolation is performed. Right: Determination of $m^c(\mu=0)=m^c_0$ with the RHMC algorithm. The arrow marks the result from the R-algorithm fp2.
• Figure 5: Finite size scaling of the Binder cumulant for $N_f=3$. The lines represent a common fit to the data, according to Eq. (\ref{['fssfit']}).