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 $Q\ll \Lambda$, where $\Lambda$ represents a hard scale of a scattering system and an energy difference $\delta \epsilon =|E-{\epsilon }_0|\ll {\epsilon }_0$, 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.

arXiv comment7 pages, LATEX2e, 3 figures

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Cited by in corpus (5)

• Nuclear effective field theory: status and perspectives
• Weinberg's Compositeness
• Nonrelativistic Effective Field Theory with a Resonance Field
• Effective Field Theory for Two-Body Systems with Shallow S-Wave Resonances
• Effective field theory for shallow P-wave states