Short-range interactions and narrow resonances in effective field theory

Abstract

We consider the effective field theory (EFT) treatment of two-body systems with narrow resonances. Within this approach, an s-wave scattering amplitude can be expanded in powers of a typical momentum scale of a system QΛ, where Λ represents a hard scale of a scattering system, and an energy difference δϵ=|E-ϵ0|ϵ0, where ϵ0 is a resonance peak energy. It is shown that at leading order in the double expansion a universal form of a two-body scattering amplitude is a sum of a Breit-Wigner term of order Q-1, a smooth background term of order Q0, and an interference term of order Q0. The techniques developed in this paper can be used to investigate the properties of narrow resonances that are produced by short-distance dynamics.