Lattice QCD at finite temperature and density in the phase-quenched approximation

Abstract

QCD at a finite quark-number chemical potential $μ$ has a complex fermion determinant, which precludes its study by standard lattice QCD simulations. We therefore simulate lattice QCD at finite $μ$ in the phase-quenched approximation, replacing the fermion determinant with its magnitude. These simulations are used to study the finite temperature transition for small $μ$,where the position and nature of this transition are expected to be unchanged by this approximation. We look for the expected critical endpoint for 3-flavour QCD. Here, it had been argued that the critical point at zero $μ$ would become the critical endpoint at small $μ$, for quark masses just above the critical mass. Our simulations indicate that this does not happen, and there is no such critical endpoint for small $μ$. We discuss how we might adapt techniques used for imaginary $μ$ to improve the signal/noise ratio and strengthen our conclusions, using results from relatively low statistics studies.

20 pages, Latex source, 6 postscript figures. Version modified for publication. Most changes made in the introduction and conclusions. One reference removed and a number of references added