Quenched Finite Volume Logarithms

TL;DR

This paper uses quenched chiral perturbation theory to calculate the leading finite volume correction to the chiral condensate, highlighting divergence issues and proposing methods to extract key QCD parameters from Dirac eigenvalues.

Contribution

It provides the first calculation of finite volume corrections to the chiral condensate in the quenched approximation and discusses extracting physical constants from eigenvalue distributions.

Findings

Finite volume correction diverges logarithmically with volume.

Both the chiral condensate and pion decay constant can be obtained from Dirac eigenvalues.

Finite volume effects are significant and must be carefully considered in lattice QCD simulations.

Abstract

Quenched chiral perturbation theory is used to compute the first finite volume correction to the chiral condensate. The correction diverges logarithmically with the four-volume $V$. We point out that with dynamical quarks one can obtain both the chiral condensate and the pion decay constant from the distributions of the lowest Dirac operator eigenvalues.