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 imp...

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Bibliographic Details
Published in:Physical review. D 2021-08, Vol.104 (3), p.1, Article 034510
Main Authors: Draper, Zachary T., Sharpe, Stephen R.
Format: Article
Language:English
Subjects:
Amplitudes
Chiral dynamics
Correlation
Measurement
Perturbation theory
Pions
Quenching
Scattering
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Summary: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.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.104.034510