Low-lying mode contribution to the quenching meson correlators in the ε-regime

We present a quenched calculation of meson correlators using the overlap fermion with very small masses, 2.6-13 MeV. In this region, the pion Compton wavelength is larger than our lattice size (L≅1.23 fm), and the system is in the so-called ε-regime of chiral perturbation theory. We find that the scalar and pseudo-scalar correlators are accurately approximated by a few hundred low-lying fermion eigenmodes in this regime, whereas the axial-vector correlator contains significant contributions from higher eigenmodes. We also compute the disconnected pseudo-scalar correlator, which is well saturated with low-lying modes. Matching these lattice data with the one-loop expressions for the correlators in quenched chiral perturbation theory, we evaluate the decay constant Fπ and the chiral condensate Σ, as well as the parameters m02 and α, which describe the artifacts of the quenched approximation. (author)