Chiral Logs in Quenched QCD

Y. Chen; S. J. Dong; T. Draper; I. Horváth; F. X. Lee; K. F. Liu; N. Mathur; J. B. Zhang

doi:10.1103/PhysRevD.70.034502

paper

Chiral Logs in Quenched QCD

arXiv:hep-lat/0304005 · doi:10.1103/PhysRevD.70.034502

Abstract

The quenched chiral logs are examined on a $1 6^{3} \times 28$ lattice with Iwasaki gauge action and overlap fermions. The pion decay constant $f_{π}$ is used to set the lattice spacing, $a = 0.200 (3) fm$ . With pion mass as low as $\sim 180 MeV$ , we see the quenched chiral logs clearly in $m_{π}^{2} / m$ and $f_{P}$ , 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 ( $χ$ PT) 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 $m_{π} \leq 300 MeV$ 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 $Λ_{χ} = 0.8 GeV$ ). By comparing to the $1 2^{3} \times 28$ 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 $m_{π} \sim 500 - 600$ 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 $C_{1/2}$ in the nucleon mass is consistent with the prediction of one-loop $χ$ PT\@. We also obtain the low energy constant $L_{5}$ from $f_{π}$ . We conclude from this study that it is imperative to cover only the range of data with the pion mass less than $\sim 300 MeV$ in order to examine the chiral behavior of the hadron masses and decay constants in quenched QCD and match them with quenched one-loop $χ$ PT\@.

37 pages and 24 figures, pion masses are fitted to the form for the re-summed cactus diagrams, figures added, to appear in PRD

Chiral Logs in Quenched QCD

Abstract

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