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.
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