Short-range interactions and narrow resonances in effective field theory

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 << Lambda, where. represents a hard scale of a scattering system, and an energy difference delta epsilon = |E - epsilon(0)| << epsilon(0), where epsilon(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.