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This project aims to give indications to find monopole and instanton effectsin QCD on the observables by experiments. First, we add the monopole andanti-monopole to the QCD vacuum of the quenched SU(3) and calculate thephysical observables using the eigenvalues and eigenvectors of the overlapDirac operator that preserves the exact chiral symmetry. We have found that theadditional monopole and anti-monopole make the long monopole loops are closelyrelated to the quark confinement without changing the vacuum structure.Furthermore, we have confirmed that the additional monopole and anti-monopolecreate instantons and anti-instantons are closely associated with the chiralsymmetry breaking. We have shown that the chiral condensate (minus value)decreases in direct proportion to the square root of the number density of theinstantons and anti-instantons. The decay constants and masses of pion and kaonincrease in direct proportion to the one-fourth root of the number density ofthe instantons and anti-instantons. This report estimates the eta meson massusing these outcomes as the input values, and the eta-prime meson mass iscalculated in two ways: (i) Substituting the numerical results of thetopological charge and pion decay constant to the Witten and Veneziano massformula. (ii) Calculating the correlations of the disconnected (hairpin)graphs. The preliminary results of the eta-prime meson mass estimated in thequenched SU(3) are as follows. (i) m$_{\eta'}$ = 1.055(15)$\times10^{3}$ [MeV](at the continuum limit). (ii) m$_{\eta'}$ = 1.04(2)$\times10^{3}$ [MeV] (atthe chiral and continuum limits). Finally, we demonstrate that the eta-primemeson mass becomes heavy with increasing the number density of the instantonsand anti-instantons.

Instanton effects on chiral symmetry breaking and hadron spectroscopy