The chiral critical point ofNf= 3 QCD at finite density to the order (μ/T)4

Abstract

QCD with three degenerate quark flavours at zero baryon density exhibits a first order thermal phase transition for small quark masses, which changes to a smooth crossover for some critical quark mass mc0, i.e. the chiral critical point. It is generally believed that as an (even) function of quark chemical potential, the critical point mc(μ) moves to larger quark masses, constituting the critical endpoint of a first order phase transition in theories with m ≥ mc0. To test this, we consider a Taylor expansion of mc(μ) around μ = 0 and determine the first two coefficients from lattice simulations with staggered fermions on Nt = 4 lattices. We employ two different techniques: a) calculating the coefficients directly from a μ = 0 ensemble using a novel finite difference method, and b) fitting them to simulation data obtained for imaginary chemical potentials. The μ2 and μ4 coefficients are found to be negative by both methods, with consistent absolute values. Combining both methods gives evidence that also the μ6 coefficient is negative. Hence, on coarse Nt = 4 lattices a three-flavour theory with m > mc0 does not possess a chiral critical endpoint for quark chemical potentials μ T. Simulations on finer lattices are required for reliable continuum physics. Possible implications for the QCD phase diagram are discussed.