Unphysical operators in partially quenched QCD

We point out that the chiral Lagrangian describing pseudo Goldstone bosons in partially quenched QCD has one more four-derivative operator than that for unquenched QCD with three flavors. The new operator can be chosen to vanish in the unquenched sector of the partially quenched theory. Its contributions begin at next-to-leading order in the chiral expansion. At this order it contributes only to unphysical scattering processes, and we work out some examples. Its contributions to pseudo Goldstone properties begin at next-to-next-to-leading order, and we determine their form. We also determine all the zero and two derivative operators in the ${O(p}^6)$ partially quenched chiral Lagrangian, finding three more than in unquenched QCD, and use these to give the general form of the analytic next-to-next-to-leading order contributions to the pseudo Goldstone mass and decay constant. We discuss the general implications of such additional operators for the utility of partially quenched simulations.