Chiral logarithms in quenched QCD

The quenched chiral logarithms are examined on a [Formula Presented] lattice with Iwasaki gauge action and overlap fermions. The pion decay constant [Formula Presented] is used to set the lattice spacing, [Formula Presented] With pion mass as low as [Formula Presented] we see the quenched chiral logarithms clearly in [Formula Presented] and [Formula Presented] the pseudoscalar decay constant. We analyze the data to determine how low the pion mass needs to be in order for the quenched one-loop chiral perturbation theory [Formula Presented] to apply. With the constrained curve-fitting method, we are able to extract the quenched chiral logarithmic parameter [Formula Presented] together with other low-energy parameters. Only for [Formula Presented] do we obtain a consistent and stable fit with a constant [Formula Presented] which we determine to be 0.24(3)(4) (at the chiral scale [Formula Presented] By comparing to the [Formula Presented] lattice, we estimate the finite volume effect to be about 2.7% for the smallest pion mass. We also fitted the pion mass to the form for the re-summed cactus diagrams and found that its applicable region is extended farther than the range for the one-loop formula, perhaps up to [Formula Presented] The scale independent [Formula Presented] is determined to be 0.20(3) in this case. We study the quenched non-analytic terms in the nucleon mass and find that the coefficient [Formula Presented] in the nucleon mass is consistent with the prediction of one-loop [Formula Presented] We also obtain the low energy constant [Formula Presented] from [Formula Presented] We conclude from this study that it is imperative to cover only the range of data with the pion mass less than [Formula Presented] in order to examine the chiral behavior of the hadron masses and decay constants in quenched QCD and match them with quenched one-loop [Formula Presented].