Narrow resonances and short-range interactions

Abstract

Narrow resonances in systems with short-range interactions are discussed in an effective field theory (EFT) framework. An effective Lagrangian is formulated in the form of a combined expansion in powers of a momentum Q << Lambda--a short-distance scale--and an energy difference delta epsilon = |E-epsilon_0| << epsilon_0--a resonance peak energy. At leading order in the combined expansion, a two-body scattering amplitude is the sum of a smooth background term of order Q^0 and a Breit-Wigner term of order Q^2 (delta epsilon)^{-1} which becomes dominant for delta epsilon <~ Q^3. Such an EFT is applicable to systems in which short-distance dynamics generates a low-lying quasistationary state. The EFT is generalized to describe a narrow low-lying resonance in a system of charged particles. It is shown that in the case of Coulomb repulsion, a two-body scattering amplitude at leading order in a combined expansion is the sum of a Coulomb-modified background term and a Breit-Wigner amplitude with parameters renormalized by Coulomb interactions.