The quenched chiral logs 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 logs 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 log 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∼500−600 MeV. 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\@.Comment: 37 pages and 24 figures, pion masses are fitted to the form for the
re-summed cactus diagrams, figures added, to appear in PR