Applicability Of The Two-Particle Quantization Condition To Partially-Quenched Theories

Partial quenching allows one to consider correlation functions and amplitudes that do not arise in the corresponding unquenched theory. For example, physical s-wave pion scattering can be decomposed into I = 0 and 2 amplitudes, while, in a partially-quenched extension, the larger symmetry group implies that there are more than two independent scattering amplitudes. It has been proposed that the finite-volume quantization condition of Luscher holds for the correlation functions associated with each of the two-particle amplitudes that arise in partially-quenched theories. Using partially-quenched chiral perturbation theory, we show that this proposal fails for those correlation functions for which the corresponding one-loop amplitudes do not satisfy s-wave unitarity. For partially-quenched amplitudes that, while being unphysical, do satisfy one-loop s-wave unitarity, we argue that the proposal is plausible. Implications for previous work are discussed.