  The fermion sign problem appearing in the mean-field approximation is
considered, and the systematic computational scheme of the free energy is
devised by using the Lefschetz-thimble method. We show that the
Lefschetz-thimble method respects the reflection symmetry, which makes physical
quantities manifestly real at any order of approximations using complex saddle
points. The formula is demonstrated through the Airy integral as an example,
and its application to the Polyakov-loop effective model of dense QCD is
discussed in detail.
