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arXiv · 1706.05622

Short-range interactions and narrow resonances in effective field theory

Mohammad H. Alhakami
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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.

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Mohammad H. Alhakami. 2017-06-18. Short-range interactions and narrow resonances in effective field theory. https://doi.org/10.1103/physrevd.96.056019

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