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

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.U.S. Department of Energy24 month embargo; available online 20 August 2020This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu