  Recently, the complex Langevin method has been applied successfully to finite
density QCD either in the deconfinement phase or in the heavy dense limit with
the aid of a new technique called the gauge cooling. In the confinement phase
with light quarks, however, convergence to wrong limits occurs due to the
singularity in the drift term caused by small eigenvalues of the Dirac operator
including the mass term. We propose that this singular-drift problem should
also be overcome by the gauge cooling with different criteria for choosing the
complexified gauge transformation. The idea is tested in chiral Random Matrix
Theory for finite density QCD, where exact results are reproduced at zero
temperature with light quarks. It is shown that the gauge cooling indeed
changes drastically the eigenvalue distribution of the Dirac operator measured
during the Langevin process. Despite its non-holomorphic nature, this
eigenvalue distribution has a universal diverging behavior at the origin in the
chiral limit due to a generalized Banks-Casher relation as we confirm
explicitly.
