Effective field theory for two-body systems with shallow S-wave resonances

Abstract

Resonances are of particular importance in the scattering of composite particles in quantum mechanics. We build an effective field theory for two-body scattering which includes a low-energy S-wave resonance. Our starting point is the most general La-grangian with short-range interactions. We demonstrate that these interactions can be organized into various orders so as to generate a systematic expansion for an S 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. (C) 2020 Elsevier Inc. All rights reserved.