Partially quenched gauge theories and an application to staggered fermions

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 7' 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.

On the foundations of partially quenched chiral perturbation theory

“…These arise in particular when valence and ghost masses vanish with sea masses held fixed and nonzero ("partially quenched chiral logarithms") and are caused by double poles in flavor-neutral propagators [1,21]. The double poles are properties of PQQCD itself, not just of the chiral effective theory, as shown (with some assumptions) in Ref.…”

“…14 Until further notice, we use for simplicity the language of the "fake symmetries" introduced in Ref. [1], which do not take into account all the subtleties coming from the ghost sector, rather than the correct symmetries introduced in Refs. [17,19,23].…”

“…QCD as the special case in which valence and sea quark masses are set equal to each other (for each flavor) [1]. PQChPT is, correspondingly, the generalization of chiral perturbation theory to the partially quenched setting.…”

“…PQChPT is, correspondingly, the generalization of chiral perturbation theory to the partially quenched setting. 1 The ability to vary valence and sea quark masses independently is useful for a variety of reasons. First, the computation of quark propagators needed for the contractions making up a correlation function is significantly less expensive in most applications than the generation of gauge field configurations, which depend on the sea quark mass.…”

“…Fourth, lattice theories with staggered fermions that use the fourth-root procedure [5] to eliminate unwanted "taste" degrees of freedom are closely related to PQQCD because 1 For a review, see Ref. [2].…”