Short-range interactions and narrow resonances in effective field theory

摘要

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 Q «: Λ, where Λ represents a hard scale of a scattering system, and an energy difference Se = |E - ∈_0| «∈_0, where ∈_0 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 Q~0, and an interference term of order Q~0. The techniques developed in this paper can be used to investigate the properties of narrow resonances that are produced by short-distance dynamics.