Partially quenched chiral perturbation theory without Phi(0) - art. no. 114510

This paper completes the argument that lattice simulations of partially que nched QCD can provide quantitative information about QCD itself, with the a id of partially quenched chiral perturbation theory. A barrier to doing thi s has been the inclusion of Phi (0), the partially quenched generalization of the eta', in previous calculations in the partially quenched effective t heory. This invalidates the low energy perturbative expansion, gives rise t o many new unknown parameters, and makes it impossible to reliably calculat e the relation between the partially quenched theory and low energy QCD. We show that it is straightforward and natural to formulate partially quenche d chiral perturbation theory without Phi (0), and that the resulting theory contains the effective theory for QCD without the eta'. We also show that previous results, obtained including Phi (0), can be reinterpreted as apply ing to the theory without Phi (0). We contrast the situation with that in t he quenched effective theory, where we explain why it is necessary to inclu de Phi (0). We also compare the derivation of chiral perturbation theory in partially quenched QCD with the standard derivation in unquenched QCD. We find that the former cannot be justified as rigorously as the latter, becau se of the absence of a physical Hilbert space. Finally, we present an encou raging result: unphysical double poles in certain correlation functions in partially quenched chiral perturbation theory can be shown to be a property of the underlying theory, given only the symmetries and some plausible ass umptions.