Breakdown of staggered fermions at nonzero chemical potential

The staggered-fermion determinant is complex when the quark chemical potential μ is nonzero. Its fourth root, used in simulations with dynamical fermions, will have phase ambiguities that become acute when Reμ is sufficiently large. We show how to resolve these ambiguities, but our prescription only works very close to the continuum limit. We argue that this regime is far from current capabilities. Other procedures require being even closer to the continuum limit, or fail altogether, because of unphysical discontinuities in the measure. At zero temperature the breakdown is expected when Reμmπ/2, where mπ is the pion mass. Estimates of the location of the breakdown at nonzero temperature are less certain.