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

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 i...

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Detalles Bibliográficos
Autores principales: Grabowska, Dorota M., Hansen, Maxwell T.
Lenguaje:eng
Publicado: 2021
Materias:
Acceso en línea:https://dx.doi.org/10.1007/JHEP09(2022)232
http://cds.cern.ch/record/2789133
Descripción
Sumario: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 perturbative interactions on the energy spectrum, while also providing a useful basis for the analogous results concerning three-particle excited states, to appear. We have also developed a Mathematica notebook that automates the expansions described in this work.