  Both direct and HAL QCD methods are currently used to study the hadron
interactions in lattice QCD. In the direct method, the eigen-energy of
two-particle is measured from the temporal correlation. Due to the
contamination of excited states, however, the direct method suffers from the
fake eigen-energy problem, which we call the "mirage problem," while the HAL
QCD method can extract information from all elastic states by using the spatial
correlation. In this work, we further investigate systematic uncertainties of
the HAL QCD method such as the quark source operator dependence, the
convergence of the derivative expansion of the non-local interaction kernel,
and the single baryon saturation, which are found to be well controlled. We
also confirm the consistency between the HAL QCD method and the L\"uscher's
finite volume formula. Based on the HAL QCD potential, we quantitatively
confirm that the mirage plateau in the direct method is indeed caused by the
contamination of excited states.
