  We propose a new lattice framework to extract the relevant gluonic energy
scale of QCD phenomena which is based on a "cut" on link variables in momentum
space. This framework is expected to be broadly applicable to all lattice QCD
calculations. Using this framework, we quantitatively determine the relevant
energy scale of color confinement, through the analyses of the quark-antiquark
potential and meson masses. The relevant energy scale of color confinement is
found to be below 1.5 GeV in the Landau gauge. In fact, the string tension is
almost unchanged even after cutting off the high-momentum gluon component above
1.5 GeV. When the relevant low-energy region is cut, the quark-antiquark
potential is approximately reduced to a Coulomb-like potential, and each meson
becomes a quasi-free quark pair. As an analytical model calculation, we also
investigate the dependence of the Richardson potential on the cut, and find the
consistent behavior with the lattice result.
