Chiral Perturbation Theory for the Quenched Approximation of QCD

TL;DR

This paper develops an effective chiral theory for quenched QCD, enabling calculations of meson properties and finite-volume effects with a novel graded symmetry approach that simplifies virtual quark loop contributions.

Contribution

It introduces a new technique for constructing the effective chiral Lagrangian for quenched QCD using graded symmetries, simplifying calculations of meson observables.

Findings

Calculated chiral logarithms for $f_K/f_$, $m_$, $m_K$, and quark condensate ratios.

Derived leading finite-volume corrections for these quantities.

Provided a framework for future studies of quenched QCD effects.

Abstract

[This version is a minor revision of a previously submitted preprint. Only references have been changed.] We describe a technique for constructing the effective chiral theory for quenched QCD. The effective theory which results is a lagrangian one, with a graded symmetry group which mixes Goldstone bosons and fermions, and with a definite (though slightly peculiar) set of Feynman rules. The straightforward application of these rules gives automatic cancellation of diagrams which would arise from virtual quark loops. The techniques are used to calculate chiral logarithms in $f_K/f_\pi$, $m_\pi$, $m_K$, and the ratio of $\langle{\bar s}s\rangle$ to $\langle{\bar u}u\rangle$. The leading finite-volume corrections to these quantities are also computed. Problems for future study are described.