Chiral logarithms in quenched QCD

Abstract

The quenched chiral logarithms are examined on a 16³×28 lattice with Iwasaki gauge action and overlap fermions. The pion decay constant fπ is used to set the lattice spacing, a=0.200(3)fm. With pion mass as low as ∼180MeV, we see the quenched chiral logarithms clearly in mπ2/m and fP, 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 (χPT) to apply. With the constrained curve-fitting method, we are able to extract the quenched chiral logarithmic parameter δ together with other low-energy parameters. Only for mπ<~300MeV do we obtain a consistent and stable fit with a constant δ which we determine to be 0.24(3)(4) (at the chiral scale Λχ=0.8GeV). By comparing to the 12³×28 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 mπ∼500–600MeV. The scale independent δ 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 C1/2 in the nucleon mass is consistent with the prediction of one-loop χPT. We also obtain the low energy constant L5 from fπ. We conclude from this study that it is imperative to cover only the range of data with the pion mass less than ∼300MeV in order to examine the chiral behavior of the hadron masses and decay constants in quenched QCD and match them with quenched one-loop χPT.