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- Title
Spurious poles in a finite volume.
- Authors
Pang, Jin-Yi; Ebert, Martin; Hammer, Hans-Werner; Müller, Fabian; Rusetsky, Akaki; Wu, Jia-Jun
- Abstract
Using effective-range expansion for the two-body amplitudes may generate spurious sub-threshold poles outside of the convergence range of the expansion. In the infinite volume, the emergence of such poles leads to the inconsistencies in the three-body equations, e.g., to the breakdown of unitarity. We investigate the effect of the spurious poles on the three-body quantization condition in a finite volume and show that it leads to a peculiar dependence of the energy levels on the box size L. Furthermore, within a simple model, it is demonstrated that the procedure for the removal of these poles, which was recently proposed in ref. [1] in the infinite volume, can be adapted to the finite-volume calculations. The structure of the exact energy levels is reproduced with an accuracy that systematically improves order by order in the EFT expansion.
- Subjects
FINITE, The; QUANTUM chromodynamics
- Publication
Journal of High Energy Physics, 2022, Vol 2022, Issue 7, p1
- ISSN
1126-6708
- Publication type
Article
- DOI
10.1007/JHEP07(2022)019