Effective Field Theory for Two-Body Systems with Shallow S-Wave Resonances

Abstract

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 $S$-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 $S$ 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.

23 pages, 12 figures

References in corpus (5)

• alpha-alpha Scattering in Halo Effective Field Theory
• ${}^6$He nucleus in halo effective field theory
• Naturalness in Nuclear Effective Field Theories
• Narrow resonances and short-range interactions
• Short-range interactions and narrow resonances in effective field theory

Cited by in corpus (8)

• Weinberg's Compositeness
• Nonrelativistic Effective Field Theory with a Resonance Field
• Effective field theory for shallow P-wave states
• Ladder resummation of spin 1/2 fermion many-body systems with arbitrary partial-wave content
• Causality and dimensionality in geometric scattering
• Effective field theory with resonant P-wave interaction
• Symmetries of the nucleon-nucleon $S$-matrix and effective field theory expansions
• UV/IR symmetries of the $S$-matrix and RG flow