On the foundations of partially quenched chiral perturbation theory

TL;DR

This paper provides theoretical support for the validity of partially quenched chiral perturbation theory as the low-energy effective theory for partially quenched QCD, using transfer matrix construction and cluster property arguments.

Contribution

It extends the theoretical foundation by constructing a transfer matrix for partially quenched QCD and demonstrating its properties, supporting the use of chiral perturbation theory in this context.

Findings

Transfer matrix for partially quenched QCD can be constructed and is bounded.

Partially quenched QCD satisfies the cluster property.

Chiral perturbation theory is validated as the effective low-energy theory for partially quenched QCD.

Abstract

It has been widely assumed that partially quenched chiral perturbation theory is the correct low-energy effective theory for partially quenched QCD. Here we present arguments supporting this assumption. First, we show that, for partially quenched QCD with staggered quarks, a transfer matrix can be constructed. This transfer matrix is not Hermitian, but it is bounded, and it can be used to construct correlation functions in the usual way. Combining these observations with an extension of the Vafa--Witten theorem to the partially quenched theory allows us to argue that the partially quenched theory satisfies the cluster property. By extending Leutwyler's analysis of the unquenched case to the partially quenched theory, we then conclude that the existence and properties of the transfer matrix as well as clustering are sufficient for partially quenched chiral perturbation theory to be the correct low-energy theory for partially quenched QCD.