Quenched chiral logarithms in lattice QCD with exact chiral symmetry

We examine quenched chiral logarithms in lattice QCD with the overlap Dirac quark. For 100 gauge configurations generated with the Wilson gauge action at $\beta =5.8\mathrm{}$ on the $8^3\times 24$ lattice, we compute quenched quark propagators for 12 bare quark masses. The pion decay constant is extracted from the pion propagator, and from this the lattice spacing is determined to be 0.147 fm. The presence of a quenched chiral logarithm in the pion mass is confirmed, and its coefficient is determined to be $\delta =0.203\mathrm{}\pm 0.014,$ in agreement with the theoretical estimate in quenched chiral perturbation theory. Further, we obtain the topological susceptibility of these 100 gauge configurations by measuring the index of the overlap Dirac operator. Using a formula due to exact chiral symmetry, we obtain the ${\eta }^{\prime }$ mass in quenched chiral perturbation theory, $m_{{\eta }^{\prime }}=901\mathrm{}\pm 64\hspace{0.5em}\mathrm{MeV},$ and an estimate of $\delta =0.197\mathrm{}\pm 0.027,$ which is in good agreement with that determined from the pion mass.