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

Abstract

QCD at a finite quark-number chemical potential $\ensuremath{\mu}$ has a complex fermion determinant, which precludes its study by standard lattice QCD simulations. We therefore simulate lattice QCD at finite $\ensuremath{\mu}$ in the phase-quenched approximation, replacing the fermion determinant with its magnitude. (The phase-quenched approximation can be considered as simulating at finite isospin chemical potential $2\ensuremath{\mu}$ for ${N}_{f}/2$ $u$-type and ${N}_{f}/2$ $d$-type quark flavors.) These simulations are used to study the finite-temperature transition for small $\ensuremath{\mu}$, where there is some evidence that the position (and possibly the nature) of this transition is unchanged by this approximation. We look for the expected critical endpoint for 3-flavor QCD. Here, it has been argued that the critical point at zero $\ensuremath{\mu}$ would become the critical endpoint at small $\ensuremath{\mu}$, 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 $\ensuremath{\mu}$. We discuss how we might adapt techniques used for imaginary $\ensuremath{\mu}$ to improve the signal/noise ratio and strengthen our conclusions, using results from relatively low statistics studies.