[Submitted on 14 Jul 2020]
Effective Field Theory for Two-Body Systems with Shallow S-Wave Resonances
J. Balal Habashi🇺🇸 · S. Sen🇺🇸 · S. Fleming🇺🇸 · U. van Kolck🇫🇷
Resonances are of particular importance to the scattering of composite particles in quantum mechanics. We build an effective field theory for two-body scattering which includes a low-energy -wave resonance. Our starting point is the most general Lagrangian with short-range interactions. We demonstrate that these interactions can be organized into various orders so as to generate a systematic expansion for an matrix with two low-energy poles. The pole positions are restricted by renormalization at leading order, where the common feature is a non-positive effective range. We carry out the expansion explicitly to next-to-leading order and illustrate how it systematically accounts for the results of a toy model -- a spherical well with a delta shell at its border.
- Comments:
- 23 pages, 12 figures
- Subjects:
- Nuclear Theory (nucl-th)
- arXiv:
- 2007.07360 [pdf]