The chiral critical point of Nf=3 QCD at finite density to the order (mu/T)^4

TL;DR

This study investigates how the critical quark mass in three-flavor QCD changes with chemical potential, finding evidence that the critical endpoint may not exist at small chemical potentials on coarse lattices, impacting the understanding of the QCD phase diagram.

Contribution

The paper provides the first lattice-based Taylor expansion coefficients of the critical quark mass as a function of chemical potential, using novel finite difference methods and imaginary chemical potential data.

Findings

mu^2 and mu^4 coefficients are negative

mu^6 coefficient is likely negative

No chiral critical endpoint for mu/T  1 on coarse lattices

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 m^c_0, i.e. the chiral critical point. It is generally believed that as an (even) function of quark chemical potential, m_c(mu), the critical point moves to larger quark masses, constituting the critical endpoint of a first order phase transition in theories with m\geq m^c_0. To test this, we consider a Taylor expansion of m_c(mu) around mu=0 and determine the first two coefficients from lattice simulations with staggered fermions on N_t=4 lattices. We employ two different techniques: a) calculating the coefficients directly from a mu=0 ensemble using a novel finite difference method, and b) fitting them to simulation data obtained for imaginary chemical potentials. The mu^2 and mu^4 coefficients are found to be negative by both methods, with consistent absolute values. Combining both methods gives evidence that also the mu^6 coefficient is negative. Hence, on coarse N_t=4 lattices a three-flavour theory with m > m^c_0 does not possess a chiral critical endpoint for quark chemical potentials mu\lsim T. Simulations on finer lattices are required for reliable continuum physics. Possible implications for the QCD phase diagram are discussed.