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 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.
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Grabowska, D.M., Hansen, M.T. Analytic expansions of multi-hadron finite-volume energies. I. Two-particle states. J. High Energ. Phys. 2022, 232 (2022). https://doi.org/10.1007/JHEP09(2022)232
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DOI: https://doi.org/10.1007/JHEP09(2022)232