Chiral Properties of Pseudoscalar Mesons on a Quenched 204 Lattice with Overlap Fermions

The chiral properties of the pseudoscalar mesons are studied numerically on a quenched 204 lattice with the overlap fermion. We elucidate the role of the zero modes in the meson propagators, particularly that of the pseudoscalar meson. The non-perturbative renormalization constant ZA is determined from the axial Ward identity and the pion decay constants fπ is calculated from which we determine the lattice spacing to be 0.157 fm.. We look for quenched chiral log in the pseudoscalar decay constants and the pseudoscalar masses for both equal and unequal quark masses. We find that, given limited statistics, it is difficult to see quenched logs in pseudoscalar masses with equal or unequal quark masses. Whereas, it is relatively clear to see them in the pseudoscalar matrix element and the ratio of the pseudoscalar matrix element to fπ. The chiral log parameter delta turns out to be consistent with that predicted from quenched chiral perturbative theory