Preweighting method in Monte-Carlo sampling with complex action --- Strong-Coupling Lattice QCD with 1/g² corrections, as an example ---

We investigate the QCD phase diagram in the strong-coupling lattice QCD with fluctuation and $1/g^2$ effects by using the auxiliary field Monte-Carlo simulations. The complex phase of the Fermion determinant at finite chemical potential is found to be suppressed by introducing a complex shift of integral path for one of the auxiliary fields, which corresponds to introducing a repulsive vector mean field for quarks. The obtained phase diagram in the chiral limit shows suppressed $T_c$ in the second order phase transition region compared with the strong-coupling limit results. We also argue that we can approximately guess the statistical weight cancellation from the complex phase in advance in the case where the complex phase distribution is Gaussian. We demonstrate that correct expectation values are obtained by using this guess in the importance sampling (preweighting).