Why (staggered fermions)^{1/4} fail at finite density

Because the staggered fermion determinant is complex at nonzero mu, taking its fourth root leads to phase ambiguities. These unphysical effects cause the measure to become discontinuous; the problem becomes acute when Re mu exceeds approximately half the pion mass (when T>0 this rough bound probably moves towards larger mu). We show how to overcome the problem, but only very close to the continuum limit. This regime may be beyond reach with current resources.