Critical point of QCD at finite T and μ, lattice results for physical quark masses

TL;DR

This study locates the QCD critical endpoint on the $\mu$-$T$ plane using lattice QCD with $n_f=2+1$ staggered quarks on $L_t=4$ lattices and an exact overlap-improving multi-parameter reweighting method to finite $\mu$. By analyzing Lee–Yang zeros across volumes, it distinguishes crossover from first-order transitions and extrapolates to infinite volume, while reducing light-quark masses toward physical values and enlarging volumes relative to prior work. The authors find $T_c=164\pm2$ MeV at $\mu=0$ and an endpoint at $T_E=162\pm2$ MeV, $\mu_E=360\pm40$ MeV, with $\mu_E$ decreasing as quark masses approach their physical values; however, a continuum extrapolation remains for a definitive result. The work demonstrates improved control over finite-volume and quark-mass effects in the finite-$\mu$ regime, highlighting the computational challenges of approaching the continuum limit in this setting.

Abstract

A critical point (E) is expected in QCD on the temperature (T) versus baryonic chemical potential (μ) plane. Using a recently proposed lattice method for μ\neq 0 we study dynamical QCD with n_f=2+1 staggered quarks of physical masses on L_t=4 lattices. Our result for the critical point is T_E=162 \pm 2 MeV and μ_E= 360 \pm 40 MeV. For the critical temperature at μ=0 we obtained T_c=164 \pm 2 MeV. This work extends our previous study [Z. Fodor and S.D.Katz, JHEP 0203 (2002) 014] by two means. It decreases the light quark masses (m_{u,d}) by a factor of three down to their physical values. Furthermore, in order to approach the thermodynamical limit we increase our largest volume by a factor of three. As expected, decreasing m_{u,d} decreased μ_E. Note, that the continuum extrapolation is still missing