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

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. (The phase-quenched approximation can be considered as simulating at finite isospin chemical potential 2μ for Nf/2 u-type and NF/2 d-type quark flavors.) These simulations are used to study the finite-temperature transition for small μ, 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 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