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arXiv · 2107.09742

Applicability of the two-particle quantization condition to partially-quenched theories

Zachary T. Draper·Stephen R. Sharpe
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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 L\"uscher 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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Zachary T. Draper, Stephen R. Sharpe. 2021-07-20. Applicability of the two-particle quantization condition to partially-quenched theories. https://doi.org/10.1103/physrevd.104.034510

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