Partially Quenched Gauge Theories and a Application to Staggered Fermions

TL;DR

This paper extends chiral perturbation theory to partially quenched gauge theories, analyzes infrared divergences related to the $ abla'$ in quenched approximations, and applies findings to staggered fermion QCD with square root determinants.

Contribution

It develops a lagrangian approach for partially quenched theories and explores divergence conditions, applying results to staggered fermion QCD with fractional determinants.

Findings

Identifies conditions for infrared divergences in partially quenched theories.

Provides a framework for analyzing staggered fermion QCD with square root determinants.

Extends chiral perturbation theory to include partially quenched scenarios.

Abstract

We extend our lagrangian technique for chiral perturbation theory for quenched QCD to include theories in which only some of the quarks are quenched. We discuss the relationship between the partially quenched theory and a theory in which only the unquenched quarks are present. We also investigate the peculiar infrared divergences associated with the $\eta'$ in the quenched approximation, and find the conditions under which such divergences can appear in a partially quenched theory. We then apply our results to staggered fermion QCD in which the square root of the fermion determinant is taken, using the observation that this should correspond to a theory with four quarks, two of which are quenched. [Uses harvmac macro package. No postscipt for the figures is available (sorry), but the figures are simple and we include do-it-yourself instructions for drawing them.]