Quenched QCD at finite density

Simulations of quenched QCD at a relatively small but nonzero chemical potential μ on 32×${16}^3$ lattices indicate that the nucleon screening mass decreases linearly as μ increases predicting a critical chemical potential of one-third the nucleon mass, ${\mathit{m}}_{\mathit{N}}$/3, by extrapolation. The meson spectrum does not change as μ increases over the same range, from zero to ${\mathit{m}}_{\mathrm{\pi }}$/2. Past studies of quenched lattice QCD have suggested that there is phase transition at μ=${\mathit{m}}_{\mathrm{\pi }}$/2. We discuss a number of technical reasons why standard lattice simulation techniques suffer from greatly enhanced fluctuations and finite size effects for μ ranging from ${\mathit{m}}_{\mathrm{\pi }}$/2 to ${\mathit{m}}_{\mathit{N}}$/3. We find evidence for such problems in our simulations, and suggest that they can be surmounted by improved measurement techniques, which should enable us to extend our calculations to the interesting domain ${\mathit{m}}_{\mathrm{\pi }}$/2${\mathit{m}}_{\mathit{N}}$/3.