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… Click to show full abstract
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 Lüscher 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.
               
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