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

QCD at a finite quark-number chemical potential $\mu$ has a complex fermion determinant, which precludes its study by standard lattice QCD simulations. We therefore simulate lattice QCD at finite $\mu$ 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 $2\mu$ 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 $\mu$, 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 $\mu$ would become the critical endpoint at small $\mu$, 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 $\mu$. We discuss how we might adapt techniques used for imaginary $\mu$ to improve the signal/noise ratio and strengthen our conclusions, using results from relatively low statistics studies.