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

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.

11 pages, 4 figures (v2: typos corrected, matches published version)

References in corpus (3)

• Quark disconnected diagrams in chiral perturbation theory
• Discretization errors in the spectrum of the Hermitian Wilson-Dirac operator
• Constraints on Disconnected Contributions in $\pi \pi$ Scattering