Phase of the Fermion Determinant at Nonzero Chemical Potential

We show that in the microscopic domain of QCD (also known as the $ϵ$ domain) at nonzero chemical potential the average phase factor of the fermion determinant is nonzero for $\mu <m_{\pi }/2$ and is exponentially suppressed for larger values of the chemical potential. This follows from the chiral Lagrangian that describes the low-energy limit of the expectation value of the phase factor. Explicit expressions for the average phase factor are derived using a random matrix formulation of the zero momentum limit of this chiral Lagrangian.