Towards a controlled study of the QCD critical point

TL;DR

This study investigates the QCD critical point using a sign-problem-free approach with imaginary chemical potential and Taylor expansion, revealing that the critical point shifts to smaller chemical potential with increasing quark mass, suggesting no chiral critical point below 500 MeV.

Contribution

The paper introduces a novel method combining imaginary chemical potential and Taylor expansion to study the QCD critical point without the sign problem, and analyzes its dependence on quark mass.

Findings

Critical point moves to smaller chemical potential as quark mass increases.

Deconfinement crossover remains a crossover at relevant chemical potentials.

No chiral critical point expected below approximately 500 MeV unless additional transitions exist.

Abstract

The phase diagram of QCD, as a function of temperature T and quark chemical potential mu, may contain a critical point (mu_E,T_E) whose non-perturbative nature makes it a natural object of lattice studies. However, the sign problem prevents the application of standard Monte Carlo techniques at non-zero baryon density. We have been pursuing an approach free of the sign problem, where the chemical potential is taken as imaginary and the results are Taylor-expanded in mu/T about mu=0, then analytically continued to real mu. Within this approach we have determined the sensitivity of the critical chemical potential mu_E to the quark mass, d(\mu_E)^2/dm_q|_{\mu_E=0}. Our study indicates that the critical point moves to {\em smaller} chemical potential as the quark mass {\em increases}. This finding, contrary to common wisdom, implies that the deconfinement crossover, which takes place in QCD at mu=0 when the temperature is raised, will remain a crossover in the mu-region where our Taylor expansion can be trusted. If this result, obtained on a coarse lattice, is confirmed by simulations on finer lattices now in progress, then we predict that no {\em chiral} critical point will be found for mu_B \lesssim 500 MeV, unless the phase diagram contains additional transitions.