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arXiv · 2110.06878

Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states

Dorota M. Grabowska·Maxwell T. Hansen
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Abstract

We derive analytic expansions for the finite-volume energies of weakly-interacting two-particle systems, using the general relations between scattering amplitudes and energies derived by Lüscher and others. The relations hold for ground and excited states with both zero and non-zero total momentum in the finite-volume frame. A number of instructive aspects arise in the derivation, including the role of accidental degeneracies and the importance of defining a power-counting scheme in the expansions. The results give intuition concerning the imprint of weakly-interacting systems on the energy spectrum, while also providing a useful basis for the analogous results concerning three-particle excited states, to appear.

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Dorota M. Grabowska, Maxwell T. Hansen. 2021-10-13. Analytic expansions of multi-hadron finite-volume energies: I. Two-particle states. https://doi.org/10.1007/jhep09(2022)232

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